cfa with no experience

Study Session 7 - Financial Reporting and Analysis

2010-03-27T09:34:00.000-07:00

Reading 29: Financial Statement Analysis: An Introduction

a. discuss the roles of financial reporting and financial statement analysis;

The role of financial reporting is to provide a variety of users with userful information about a company's performance and financial position.

The role of financial statement analysis si to use the data from financial statements to support economic decisions.

b. discuss the role of key financial statements (income statement, balance sheet, statement of cash flows, and statement of changes in owners’ equity) in evaluating a company’s performance and financial position;

The income statement shows the results of a firm's business activities over the period. Revenues, the cost of generating those revenues, and the resulting profit or loss are presented on the income statement.

The balance sheet shows assets, liabilities, and owner's equity at a point in time

The cash flow statements shows the sources and uses of cash over the period

The statement of changes in owners' equity reports the amount and sources of changes in the equity owners' investment in the firm

c. discuss the importance of financial statement notes and supplementary information, including disclosures of accounting methods, estimates, and assumptions, and management’s discussion and analysis;

Important information about accounting methods, estimate, and assumptions is disclosed in the footnotes to the financial statements and supplementary schedules.
These disclosures also contain info about segment results, commitments and contingencies, legal proceedings, acquisitions or divestitures, issuance or stock options, and details of employee benefit plans
Management's Discussion and Analysis contains an overview of the company and important info about business trends, future capital needs, liquidity, significant events, and significant choices of accounting methods requiring mgmt judgment

d. discuss the objective of audits of financial statements, the types of audit reports, and the importance of effective internal controls;

audit is to provide an opinion on the statements' fairness and reliability - unqualified, qualified, adverse
opinion gives evidence of an independent review that verifies that
appropriate accounting principles were used,
that standard auditing procedures were used to establish reasonable assurance that the statements contain no material errors,
and that management's report on the company's internal controls has been reviewed.
company's management is responsible for maintaining effective internal control system to ensure the accuracy of financial statements
for US Public Companies, Sox requires management report on firm's internal controls, description of the method used to evaluated their effectiveness, and a statement as to their effectiveness over the accounting period

e. identify and explain information sources other than annual financial statements and supplementary information that analysts use in financial statement analysis;

Along with financial statements, important info sources are:
company's quarterly and semi-annual reports,
proxy statements (info about board members, stock options, compensation),
press releases as well as information on industry and peer companies from external sources

f. describe the steps in the financial statement analysis framework.

state the objective of the analysis
gather data
process the data
analyse and interpret the data
report the conclusions or recommendations
update the analysis

Reading 30: Financial Reporting Mechanics

a. explain the relationship of financial statement elements and accounts, and classify accounts into the financial statement elements;

Transactions are recorded in accounts that form the financial statement elements:

Assets - the firm's economics resources
Liabilities - creditor's claims on the fimr's resources
Owner's equity - paid in capital (common and preferred sotck), retained earnings, and cumulative other comprehensive income
Revenues - sales, investment income, and gains
Expenses - COGS, selling and admin expenses, depreciation, interest, taxes, and losses

b. explain the accounting equation in its basic and expanded forms;

basic accounting equation:
assets = liabilities + shareholders' equity

expanded accounting equation:
assets = liabilities + contributed capital + ending retained earnings

also:
assets = liabilities + contributed capitals + beginning retained earnings + revenue - expenses - dividends

c. explain the process of recording business transactions using an accounting system based on the accounting equations;

Keeping the accounting equation in balance (A-L=E) in balance requires double entry accounting i.e. every transaction is recorded in at least two accounts that offset one another;

e.g. an increasse in an asset account must be balanced by a decrease in another asset account or by an increase in a liability or owner's equity account

d. explain the need for accruals and other adjustments in preparing financial statements;

firm must recognise revenues when they are earned and expenses when they are incurred;

accruals are required when the timing of cash flows in and out do not match timing of the revenue or expense recognition on the financial statements e.g. wages or unearned revenue

e. explain the relationships among the income statement, balance sheet, statement of cash flows, and statement of owners’ equity;

balance sheet shows a company's financial position at a point in time

changes in balance sheet accounts during an accounting period are reflected in the income statement, the cash flow statement, and the statement of owners's equity

f. describe the flow of information in an accounting system;

info enters accounting system as journal entries

sorted by account into general ledger GL

trial balances are formed at the end of an accounting period

accounts are then adjusted and presented in financial statements

g. explain the use of the results of the accounting process in security analysis.

financial reporting requires choices of method, judgment and estimates

analyst must understand the accounting process used to produce the financial statements in order to understand the business and the results for the period

analysts should be alert to the use of accruals, changes in valuations, and other notable changes that may indicate management judgment is incorrect or that the financial statements have been deliberately manipulated

Issues from Problem Sets

I find expenses versus liabilities confusing in certain cases. I also find contra-assets confusing

accumulated depreciation and allowance for bad debts are both assets (since they are contra assets to offset the corresponding asset)

depreciation is an expense

deferred tax items - deferred tax assets are assets and deferred tax liabilities are liabilities

Reading 31: Financial Reporting Standards

a. explain the objective of financial statements and the importance of reporting standards in security analysis and valuation;

objective of financial statements = to provide economic decision makers with useful information about a firm's financial performance and changes in a financial position
reporting standards ensure comparability and narrow reasonable estimates on which statements are based
users of financial statemetn rely on them for info about the company's activities, profitability, and creditworthiness

key SEC filings:

S-1 prior to sale of new securities
10-K annual filing similar to annual report; 40-F for Canadians; 20-F for other foreign issuers
10-Q quarterly unaudited statements
DEF-14A company prepares a proxy statement
144 issue of unregistered securities to certain qualified buyers
3,4 and 5 beneficial ownership of securities by company's officers and directors; learn about purchases by insiders

b. explain the role of standard-setting bodies, such as the International Accounting Standards Board and the U.S. Financial Accounting Standards Board, and regulatory authorities such as the International Organization of Securities Commissions, the U.K. Financial Services Authority, and the U.S. Securities and Exchange Commission in establishing and enforcing financial reporting
standards;

standard setting bodies are private sector organisations that establish financial reporting standards e.g. IASB (international i.e. IFRS) and FASB (US i.e. GAAP)
regulatory authorities are gov agencies that enforce compliance with financial reporting standards e.g. SEC in USA and FSA in UK. Many belong to Interntational Organisation of Securities Commissions (IOSCO)

c. discuss the ongoing barriers to developing one universally accepted set of financial reporting standards;

barriers to convergence = differences of opinion among standard-setting bodies and regulatory agencies from difference countries and political pressure within countries from groups affected by changes in reporting standards

d. describe the International Financial Reporting Standards (IFRS) framework, including the qualitative characteristics of financial statements, the required reporting elements, and the constraints and assumptions in preparing financial statements;

IFRS "Framework for the Preparation and Presentation of Financial Statements" defines the qualitative characteristics of financial statements, specifies the required reporting elements, and notes the constraints and assumptions involved in preparing financial statements
Qualitative characteristics of financial statements include understandability, relevance, reliability, and comparability
Elements of financial statements are assets, liabilities, and owners' equity (for measuring financial position) and income and expenses (for measuring performance)
Constraints on financial statement preparation include cost, the need to balance reliability with timeliness, and the difficulty of capturing non-quantifiable information in financial statements
the two primary assumptions: (1) accrual basis and (2) going concern assumption

e. explain the general requirements for financial statements;

required financial statements are (as expected):

balance sheet
income statement
cash flow statement
statement of changes in owners' equity
explanatory notes

Principles for preparing financial statements stated in IAS No. 1 are:

Fair presentation
going concern basis
accrual basis
consistency between periods
materiality
aggregation (like with like, no mixing of dissimilar items)
no offsetting (unless required or permitted specifically to do so)
classified balance sheet showing current and non-current assets and liabilities
minimum required information e.g. bs must show specific items such as cash and cash equivalents, plant property and equipment, and inventories; income statement must show revenue, profit or loss, tax expense, and finance costs, etc.
comparative information

f. compare and contrast key concepts of financial reporting standards under IFRS and alternative reporting systems, and discuss the implications for financial analysis of differing financial reporting systems;

IFRS and GAAP usually agree in overall framework and purpose and are working toward convergence, however:

IFRS requires users to consider framework in the absence of specific standard;
US GAAP distinguishes between objectives for business and non-business entities;
the IASB framework gives more emphasis to the importance of the accrual and going concern assumptions than FASB
GAAP framework establishes a hierarchy of qualitative financial statement characteristics;
some differences in how each defines, recognises, and measures individual elements of financial statements
companies reporting under standards other than GAAP that trade in USA must reconcile their statements with GAAP but the analyst must reconcile differences in other cases.

g. identify the characteristics of a coherent financial reporting framework and barriers to creating a coherent financial reporting network;

A coherent financial reporting framework should exhibit transparency, comprehensiveness and consistency
barriers to coherent framework include issues of valuation, standard setting and measurement

h. discuss the importance of monitoring developments in financial reporting standards and of evaluating company disclosures of significant accounting policies.

an analyst should be aware that sh*t changes and new stuff doesn't always fit neatly into the categories i.e. these are living documents in many ways
under IFRS and GAAP, companies must disclose accounting policies and estimates in the footnotes and MD&A
public companies are also required to disclose the likely impact of recently issued accounting standards on their financial statements

Study Session 14 - Industry and Company Analysis

2010-03-16T16:26:00.000-07:00

An Introduction to Security Valuation and Industry Analysis

Two basic valuation techniques:

valuation based on PV of expected future cash flows
relative valuation based on expected multiple of firm's expected performance e.g. earnings per share or sales per share (more appropriate when market itself is neither severely under or over valued)

if firm pays dividends and is mature (growth is stable), use PV of expected future dividends discounted at the cost of equity
if firm does not pay dividends, use PV of operating free cash flow or free cash flow to equity discounted at WACC

LOS 56a - Explain the top-down approach, and its underlying logic to the security valuation process

go from general to specific in your evaluation:

economic analysis -> industry analysis -> stock analysis

1. Forecast Macroeconomic Influences

aggregate demand may be affected by:

fiscal policy
tax cuts (increases demand)
tax increases
government spending (increases demand)
Monetary policy can have many effects:
decrease in money supply = interest rate rise = costs rise = demand shrinks
increase in money supply = interest rate fall = costs fall = demand grows
increase money supply too quickly can cause inflation
rising interest rates reduce demand for investment funds

2. Determine Industry Effects

Identify industries that should prosper or suffer from the economic outlook
are the industries sensitive to economic change?
are they cyclical industries?

3. Perform firm analysis

Compare firms within each attractive industry from #2 using financial ratios and cash flow analysis
or, if shorting, identify those that should suffer
not only past performance, but prospects

LOS 56b - State the various forms of investment returns

many forms:

cash flows from projects
interest income on bonds
dividend income on stocks
capital gains (increase in the price of an asset)
earnings per share
operating cash flow

LOS 56c: Calculate and interpret the value of both a preferred stock and a common stock using the dividend discount model

Valuing perferred stock is like valuing a perpetuity:

pref. stock value = Dp/kp

where kp is the discount rate i.e. the yield on the preferred shares

NB do not confuse the dividend rate with the discount rate or the par with the price

default risk involved means that firm's required rate on perferred (kp) should be above the firms bond rate but the fact that 80% of dividends are tax exempt means that they preferred yields are below the yields on the firm's highest grade bonds

We are calculating what the price "should" be i.e. its instrinsic value

One year holding period so this is just the holding period return i.e. the future expected sum of the dividend and the stock price discounted at the required rate of return ke (which can be found using CAPM)

value = (dividend to be rec'd/(1 + ke)) + (year end price/(1 + ke))

so predict the year end dividend to be received (D1) by multiplying prior dividend by 1 + g

Two year holding period so this is just like valuing a bond in some ways. It is the NPV of all the cash flows where the final cash flow is the sum of the final dividend plus the stock price (all discounted at ke)

Infinite Period DDM is just like valuing a perpetuity because that is exactly what it is for firms with a constant growth rate so...

PVo = D1/(ke - g)
where D1 is D0 multiplied by 1 + g
rearranging the terms we get ke = (D1/PVo) + g which we have seen in WACC analysis
also note that this is the same as valuing preferred stock but where g = 0

relationship between ke and g:

As difference between ke and g widens, the value of the stock falls and vice versa
Small changes in ke and g cause large changes in stock's value

assumptions of the infinite period DDM

stock pays dividends and they grow at a constant rate
constant growth rate g is never expected to change
ke must be greater than g if not the math will not work

if any of these assumptions is not met, the model breaks down

NB look for words like "indefinitely", "forever", "infinitely" to determine infinite DDM. Also look for words like "just paid" or "recently paid" for ref to last dividend and "will pay" or "is expected to pay" for D1.

value of a Common Stock for a Company Experiencing Temporary Supernormal Growth

value = (D1/(1+ke)) + (D2/(1+ke)²) + ... + (Dn/(1+ke)ⁿ) + (Pn/(1+ke)ⁿ)
where:
Dn = last dividend of supernormal growth period
Dn+1 = first dividend that will grow at constant rate g forever
Pn = Dn+1/(ke - g)

this is actually intuitive: find the NPV of the supernormal growth period and add it to the infinite DDM value (discounted for the number of periods away from t = 0) of the post supernormal (stable) period to obtain the value.

watch out i often mess up by how many periods i should discount the perpetuity part of this equation because it is misleading. Discount back the number of periods that there is supernormal growth e.g. if you have two dividends during the supernormal period and then a dividend at the constant growth rate, find the value of the perpetuity and discount back two periods.

if dividends are not paid during the supernormal growth period, you need only find the PV of the infinite DDM for the stock and dividend when the stable period begins

LOS 56d: Show how to use the DDM to develop an earnings multiplier model and explain the factors in the DDM that affect a stock's price-to-earnings (P/E) ratio

DDM related to P/E like this: take the infinite DDM model where P0 = D1/(ke - g) and divide both sides by next year's projected earnings E1 and you get:

P0/E1 = ((D1/E1)/(ke - g))

So P/E is a function of:

D1/E1 = the expected dividend payout ratio
k = the reuqired rate of return on the stock
g = the expected constant growth rate of dividends

So ceteris paribus the P/E ratio will increase with:

a higher dividend payout rate
a higher growth rate
a lower required rate of return

key facts about earnings multiplier approach to valuation is that:

the main determinant of size of the P/E ratio is the difference between k and g since it has a significant impact on sotkc price
the relevant P/E ratio is the expected or leading P/E ratio i.e. P0/E1 not the historical P/E ratio
the P/E ratio is just a restatement of the DDM, so anything that influences stock prices in the DDM will have the same effect on the P/E ratio

problems with using P/E analysis

Earnings are historical cost accounting numbers and may be of differing quality
Business cycles may affect P/E ratios
like infinite DDM, when k <>

LOS 56e: Explain the components of an investor's required rate of return (i.e. the real RFR, the expected rate of inflation, and a risk premium) and discuss the risk factors to be assessed in determining an equity risk premium for use in estimating the required return for the investment in each country

RFRreal is determined the supply and demand for capital in the country i.e. the RFR is the rate investors would require if there were absolutely no risk or inflation
inflation premium (IP) is the premium required to compensate investors for expected loss of purchasing power
a risk premium (RP) to compensate for the uncertainty of returns expected from an investment.
RFRnominal is approximated as RFR + IP
so required return = (1+RFRreal)(1+IP)(1+RP)-1
or approx. RFRreal + IP + RP
so CAPM (required return) is just RFRnominal + beta adjusted risk premium
a real rate is without inflation, nominal rates include inflation. if it doesn't specify, it is probably nominal

Estimating required return for foreign securities

variables and models are the same world over but the equity risk premium for foreign securities must take into account:

Business risk - variability of country's economic activity and degree of operating leverage of firms within the country
Financial risk will be different in different countries
Liquidity risk is often found in countries with small or inactive capital markets
Exchange rate risk
Country risk from unexpected economic and political events

LOS 56f: estimate the dividend growth rate given the components of the required rate of return incorporating the earnings retention rate and current stock price

g = (RR)(ROE)

which makes sense since growth will be determined by how much money is retained (RR) by the company and plowed back in to fuel growth

Since Retention Rate (RR) is the money kept back, it follows that (1-RR) is the dividend payout

ROE = net profit margin * asset turnover * financial leverage

key facts about dividend growth:

if a firm's net profit margin increases, ROE will increase
if ROE increases, g will increase because g is (RR)(ROE)
if g increases, the difference between k and g will decrease
if k-g decreases, price of stock will increase

LOS 56g: Describe a process for developing estimated inputs to be used in the DDM, including the required rate of return and expected growth rate of dividends

Dm holds that the value of a share of stock is the PV of its cash flows (including cash flow from sale of stock itself) so it requires three inputs:

estimate of stock's future cash flows i.e. dividends and future price
dividend growth rate
discount rate, which is the appropriate required return on equity

Once PV of the asset has been estimated, compare it to the current market price

Full Example of Application

For XYZ company:

stock price = $18
earnings per share = $2
ROE = 10% (and stable for the future)
dividend payout is 40% (and stable for the future)
nomrinal RFR i= 7%
expected market return = $12
Beta for XYZ = 1.2

So...

calculate required return using CAPM: k = 7% + 1.2(12%-7%) = 13%
calculate growth rate: (RR)(ROE)
so calc RR = (1 - 0.4) = 0.6
calc (RR)(ROE) = (0.6)(0.10) = 0.06 i.e. 6%
determine last year's dividend: Do = E0(dividend payout) = $2(0.4) = $0.80
determine next year's dividend: D1 = Do (1 + g) = $0.80 * 1.06 = $0.85
Estimate the value using infinite DDM = D1/(k-g) = $0.85/(0.13-0.06) = $12.14
Compare to stock price of $18, you would not buy (and possibly short)

LOS 57: Describe how structural economic changes (e.g. demographics, technology, politics, and regulation) may affect industries

Not sure how far to go into this one because they seem a little obvious e.g younger people in their 20's would consume houses, furniture whereas if older people dominate population, expect uptick in retirement community sales etc. Technology helps and hurts differently based on the technology. Regulation can cause extra costs and decrease in sales or protectionist tariffs can temporarily boost domestic domand.

Trends and lifestyles and cause temporary boons for the item in vogue.

Issues from problem sets

Some of the supernormal growth questions were confusing in their words e.g.

"Assume that a stock is expected to pay dividends at the end of year 1 and year 2 of $1.25 and $1.56 respectively. Dividends are expected to grow at 5% rate thereafter. Assuming that ke is 11%, the value of the stock is closest to:"

NB This means that the second dividend is where the stable growth begins i.e. $1.56 is the dividend rate for the normal constant infinite growth period and so you would calculate it using D1/ke-g or $1.56/0.11-0.05 and add it to the $1.25 then discount the sum by 11% over one period (not sure why it is one period rather than one period for the 1.25 and two periods for the stock price).

Price/Earnings Ratio or Earnings Mutiplier

This is not very well explained in Schweser and I'll probably look it up elsewhere to fully understand what its purpose is.

The P/E is sometimes referred to as the "multiple", because it shows how much investors are willing to pay per dollar of earnings. If a company were currently trading at a multiple (P/E) of 20, the interpretation is that an investor is willing to pay $20 for $1 of current earnings

So P/E = ((stock price using infinite DDM)/E) -> I am weak on this use

if you don't have dollar amount for a dividend, use the payout rate e.g. 0.6 for the dividend and divide by ke - g
P/E ration based on the DDM is:
(1-RR)/[k - RR(ROE)]
this is just substituting dividend payout rate (1-RR) for D1 and (RR)(ROE) for g to demonstrate the relationship between the features.

COMPANY ANALYSIS AND STOCK VALUATION

Company vs. Stock Analysis

LOS 58a: Differentiate between 1) a growth company and a growth stock 2) a defensive company and a defensive stock 3) a cyclical company and a cyclical stock, 4) a speculative company and a speculative stock, and 5) a value stock and a growth stock

Growth company = managers consistently make investments with positive NPV
Growth stock = stock consistently outperforms other stocks of equivalent risk
NB all of this good stuff may be already priced into the stock price and bandwagon effect can make it an unwise investment; if a stock's intrinsic value is lower than its current price, it can be a growth stock
Defensive company = company's earnings are not sensitive to downturns in economy e.g. utility and retail grocery chains.
Defensive Stock will not decline as much as the market when the overall market declines (low betas)
Cyclical Company earnings tend to follow business cycle e.g. steel, automobile, heavy equipment producers - high levels of fixed costs (business risk) or leverage (financial risk)
Cyclical Stock = beta greater than 1, change more than market either up or down
Speculative company = risky assets but potential for assets to generate very large earnings e.g. diamond mining, oil exploration, some real estate etc.
Speculative Stock = highly likely to have low or negative returns compared to market because almost always overpriced but slight chance of enormous return
Growth stock = earnings growth rate of stock;
Value stock = stocks that are priced low in relation to their current earnings (rather than expected growth in their earnings) or in relation to the value of their fixed assets, real estate or cash.
Value stocks are characterised by low price-book ratios, low price-earnngs ratios, and often high dividends.

LOS 58b: Describe and estimate the expected earnings per share (EPS) and earnings multiplier for a company and use the multiple to make an investment decision regarding the company

EPS can be estimated by ((est. forecast sales * est. net profit margin)/shares outstanding)

A company's earnings multiplier (P/E ratio) can be estimated by macroanalysis of the market and the industry or by microanalysis to estimate the company's dividend payout ratio, sustainable growth rate, and required rate of return.
if you know the current share price is $32 and dividend will be $0.96 and earnings will be $3 and the year end P/E will be 12 then year end price will be Earnings * P/E = year end expected price or 3 * 12 = $36
and HPY is P1-P0+D/P0 so (($36-$32+$0.96)/$32) = 15.5% which is the expected return.
NB this is the opposite process to the CAPM problems. Here we are finding the expected return and comparing it to the known required return.
To make an investment decision, est. stock's value by multiplying its estimated EPS and expected P/E ratio and compare this value to the current stock price to determine whether under or over-valued

LOS 59a: Discuss the rationals for, and the possible drawbacks to, the use of price-to-earnings ratio (P/E), price-to-book value (P/BV), price-to-sales ratio (P/S), and price-to-cash flow (P/CF) in equity valuation.

All methods are significantly related to long-run average stock returns

Advantages of P/E ratios in valuation:

widely used in investment community
earnings power is the primary determinant of investment value

Disadvantages of P/E

earnings can be negative = useless P/E
the volatile, transitory portion of earnings makes the interpretation of P/E ratios difficult for analysts
management disretion in accounting practices can distort reported earnings and thus P/E

Advantages of using P/BV

usually positive
BV more stable than EPS, so more useful than P/E when EPS is very high/low/volatile
BV = appropriate measure for firms with primarily liquid assets e.g. banks, insurance, finance, etc.
P/BV good for valuing companies that are expected to go out of business

Disadvantages of P/BV

does not recognise value of assets not on balance sheet such as human capital
can be misleading when there are significant differences in the net balance sheet values of the assets used by the firms being compared
diff. accounting conventions can obscure the true investment in the firm made by shareholders
inflation and tech change can cause the book and market value of assets to differ significantly

Advantages of using P/S ratios are:

the ratio is meaningful, even for distressed firms
sales figures are not as easy to manipulate or distort as EPS and BV
not as volatile as P/E
particularly appropriate for valuing stocks in mature or cyclical industries as well as start up fims with no record of earnings

Disadvantages of using P/S ratios

high sales do not necessarily indicate operating profits as measured by earnings and cash flow
P/S ratios do not capture differences in cost structures across companies
affected by revenue recognition methods (although less prone to distortion than earnings)

Advantages of using P/CF

cash flow harder to manipulate than earnings
more stable than P/E
addresses problem of differences in quality of earnings that arises when using P/E

Disadvantages of using P/CF

some items affecting actual cash flow from operations are ignored when the EPS plus noncash charges estimation method is used. e.g. noncash revenue and net changes in working capital are ignored
some measure of free cash flow is theoretically perferred to operating cash flow; free cash flow to equity can be used, but can be negative and is generally more volatile than operating cash flow

LOS 59b: Calculate and interpret P/E, P/BV, P/S, and P/CF

all are mkt price per share/some income measure per share
trailing P/E = mkt price per share/EPS over prev. 12 months
leading P/E = mkt price per share/expected EPS over next 12 months
P/BV = mkt price per share/book value per share
book value of equity = (total assets - total liabilities) - preferred stock
P/S = mkt price per share/sales per share
P/CF = mkt price per share/cash flow per share
cash flow can be CF, FCFE, adjusted CFO or EBITDA

Problem set issues

Sometimes you will not be given the share price and will have to work it out first using DDM; clues would be when they give you ke etc.
If they give you a date for a dividend and do not give you any other dates, it seems to imply that this is Do so D0 * (1 + g) = D1
Sales per share = revenue per share
accounting standard differences cause problems for most ratios to varying degrees including P/BV, P/E and P/S (although P/S is less prone to distortion)
BV = shareholder's equity
calculate margin call price

Calculation Formulas

2010-03-15T17:37:00.000-07:00

As I start to freak out a little about this exam and feel that the universe of formulas we are given is just too overwhelming, I thought it would be useful to differentiate between the formulas we are expected to explain/understand versus the formulas we are expected to use to make calculations (which is another way of saying I am procrastination in a way that makes me feel like I am actually doing something).

Below are all the LOS's for CFA Level 1 which refer to computation, estimation, or calculation:

Reading 5: The Time Value of Money
c. calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding;
d. solve time value of money problems when compounding periods are other than annual;
e. calculate and interpret the future value (FV) and present value (PV) of a single
sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows;
f. draw a time line and solve time value of money applications (for example, mortgages and savings for college tuition or retirement).

Reading 6: Discounted Cash Flow Applications
a. calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment, contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule;
b. define, calculate, and interpret a holding period return (total return);
c. calculate, interpret, and distinguish between the money-weighted and timeweighted rates of return of a portfolio and appraise the performance of portfolios based on these measures;
d. calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill;
e. convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.

Reading 7: Statistical Concepts and Market Returns
c. calculate and interpret relative frequencies and cumulative relative frequencies, given a frequency distribution;
e. define, calculate, and interpret measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean (including a portfolio return viewed as a weighted mean), geometric mean, harmonic mean, median, and mode;
f. describe, calculate, and interpret quartiles, quintiles, deciles, and percentiles;
g. define, calculate, and interpret 1) a range and a mean absolute deviation and
2) the variance and standard deviation of a population and of a sample;
h. calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev’s inequality;
i. define, calculate, and interpret the coefficient of variation and the Sharpe ratio;

Reading 8: Probability Concepts
k. calculate and interpret covariance and correlation;
l. calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio;
m. calculate and interpret covariance given a joint probability function;
n. calculate and interpret an updated probability using Bayes’ formula;
o. identify the most appropriate method to solve a particular counting problem and solve counting problems using the factorial, combination, and permutation notations.

Reading 9: Common Probability Distributions
d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;
f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;
h. describe the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform probability distribution;
j. determine the probability that a normally distributed random variable lies inside a given confidence interval;
k. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;
l. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion;
n. distinguish between discretely and continuously compounded rates of return and calculate and interpret a continuously compounded rate of return, given a specific holding period return;

Reading 10: Sampling and Estimation
e. calculate and interpret the standard error of the sample mean;
h. explain the construction of confidence intervals;
i. describe the properties of Student’s t-distribution and calculate and interpret its degrees of freedom;
j. calculate and interpret a confidence interval for a population mean, given a normal distribution with 1) a known population variance, 2) an unknown population variance, or 3) an unknown variance and a large sample size;

Reading 13: Elasticity
a. calculate and interpret the elasticities of demand (price elasticity, cross elasticity, and income elasticity) and the elasticity of supply and discuss the factors that influence each measure;
b. calculate elasticities on a straight-line demand curve, differentiate among elastic, inelastic, and unit elastic demand, and describe the relation between price elasticity of demand and total revenue.

Reading 16: Organizing Production
f. calculate and interpret the four-firm concentration ratio and the Herfindahl-Hirschman Index and discuss the limitations of concentration measures;

Reading 22: Monitoring Jobs and the Price Level
d. explain and calculate the consumer price index (CPI) and the inflation rate, describe the relation between the CPI and the inflation rate, and explain the main sources of CPI bias.

Reading 34: Understanding the Cash Flow Statement
h. explain and calculate free cash flow to the firm, free cash flow to equity, and other cash flow ratios.

Reading 35: Financial Analysis Techniques
d. calculate, classify, and interpret activity, liquidity, solvency, profitability, and valuation ratios;
g. calculate and interpret the ratios used in equity analysis, credit analysis, and segment analysis;

Reading 36: Inventories
c. compute ending inventory balances and cost of goods sold using the FIFO, weighted average cost, and LIFO methods to account for product inventory and explain the relationship among and the usefulness of inventory and cost of goods sold data provided by the FIFO, weighted average cost, and LIFO methods when prices are 1) stable, 2) decreasing, or 3) increasing;
f. compute and describe the effects of the choice of inventory method on profitability, liquidity, activity, and solvency ratios;
g. calculate adjustments to reported financial statements related to inventory assumptions to aid in comparing and evaluating companies;

Reading 37: Long-Lived Assets
b. compute and describe the effects of capitalizing versus expensing on net income, shareholders’ equity, cash flow from operations, and financial ratios, including the effect on the interest coverage ratio of capitalizing interest costs;
e. discuss the use of fixed asset disclosures to compare companies’ average age of depreciable assets and calculate, using such disclosures, the average age and average depreciable life of fixed assets;
j. calculate and describe both the initial and long-lived effects of asset revaluations on financial ratios.

Reading 38: Income Taxes
d. calculate income tax expense, income taxes payable, deferred tax assets, and deferred tax liabilities, and calculate and interpret the adjustment to the financial statements related to a change in the income tax rate;

Reading 39: Long-Term Liabilities and Leases
a. compute the effects of debt issuance and amortization of bond discounts and premiums on financial statements and ratios;

Reading 44: Capital Budgeting
d. calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, and profitability index (PI);

Reading 45: Cost of Capital
a. calculate and interpret the weighted average cost of capital (WACC) of a company;
f. calculate and interpret the cost of fixed rate debt capital using the yield-to-maturity approach and the debt-rating approach;
g. calculate and interpret the cost of noncallable, nonconvertible preferred stock;
h. calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach;
i. calculate and interpret the beta and cost of capital for a project;

Reading 46: Working Capital Management
e. compute and interpret comparable yields on various securities, compare portfolio returns against a standard benchmark, and evaluate a company’s short-term investment policy guidelines;

Reading 50: An Introduction to Portfolio Management
c. compute and interpret the expected return, variance, and standard deviation for an individual investment and the expected return and standard deviation for a portfolio;
d. compute and interpret the covariance of rates of return and show how it is related to the correlation coefficient;

Reading 51: An Introduction to Asset Pricing Models
e. calculate, using the SML, the expected return on a security and evaluate whether the security is overvalued, undervalued, or properly valued.

Reading 56: An Introduction to Security Valuation
c. calculate and interpret the value of both a preferred stock and a common stock using the dividend discount model (DDM);
f. estimate the dividend growth rate, given the components of the required rate of return incorporating the earnings retention rate and current stock price;

Reading 58: Company Analysis and Stock Valuation
b. describe and estimate the expected earnings per share (EPS) and earnings multiplier for a company and use the multiple to make an investment decision regarding the company.

Reading 59: Introduction to Price Multiples
b. calculate and interpret price-toearnings ratio (P/E), price-to-book value (P/BV), price-to-sales ratio (P/S), and price-to-cash flow (P/CF).

Reading 61: Risks Associated with Investing in Bonds
f. compute and interpret the duration and dollar duration of a bond;

Reading 63: Understanding Yield Spreads
e. compute, compare, and contrast the various yield spread measures;
i. compute the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security;

Reading 64: Introduction to the Valuation of Debt Securities
c. compute the value of a bond and the change in value that is attributable to a change in the discount rate;
d. explain how the price of a bond changes as the bond approaches its maturity date and compute the change in value that is attributable to the passage of time;
e. compute the value of a zero-coupon bond;

Reading 65: Yield Measures, Spot Rates, and Forward Rates
b. compute and interpret the traditional yield measures for fixed-rate bonds and explain their limitations and assumptions;
c. explain the importance of reinvestment income in generating the yield computed at the time of purchase, calculate the amount of income required to generate that yield, and discuss the factors that affect reinvestment risk;
d. compute and interpret the bond equivalent yield of an annual-pay bond and the annual-pay yield of a semiannual-pay bond;
e. describe the methodology for computing the theoretical Treasury spot rate curve and compute the value of a bond using spot rates;
h. explain a forward rate and compute spot rates from forward rates, forward rates from spot rates, and the value of a bond using forward rates.

Reading 66: Introduction to the Measurement of Interest Rate Risk
d. compute and interpret the effective duration of a bond, given information about how the bond’s price will increase and decrease for given changes in interest rates, and compute the approximate percentage price change for a bond, given the bond’s effective duration and a specified change in yield;
f. compute the duration of a portfolio, given the duration of the bonds comprising the portfolio, and explain the limitations of portfolio duration;
g. describe the convexity measure of a bond and estimate a bond’s percentage price change, given the bond’s duration and convexity and a specified change in interest rates;
i. compute the price value of a basis point (PVBP), and explain its relationship to duration.

Reading 68: Forward Markets and Contracts
g. calculate and interpret the payoff of an FRA, and explain each of the component terms;

Reading 69: Futures Markets and Contracts
d. describe price limits and the process of marking to market and compute and interpret the margin balance, given the previous day’s balance and the change in the futures price;

Reading 70: Option Markets and Contracts
f. compute and interpret option payoffs, and explain how interest rate option payoffs differ from the payoffs of other types of options;
h. determine the minimum and maximum values of European options and American options;
i. calculate and interpret the lowest prices of European and American calls and puts based on the rules for minimum values and lower bounds;

Reading 71: Swap Markets and Contracts
b. define, calculate, and interpret the payment of currency swaps, plain vanilla interest rate swaps, and equity swaps.

Reading 72: Risk Management Applications of Option Strategies
a. determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of the strategies of buying and selling calls and puts, and indicate the market outlook of investors using these strategies;
b. determine the value at expiration, profit, maximum profit, maximum loss, breakeven underlying price at expiration, and general shape of the graph of a covered call strategy and a protective put strategy, and explain the risk management application of each strategy.

Reading 73: Alternative Investments
f. calculate the net operating income (NOI) from a real estate investment, the value of a property using the sales comparison and income approaches, and the aftertax cash flows, net present value, and yield of a real estate investment;
h. calculate the net present value (NPV) of a venture capital project, given the project’s possible payoff and conditional failure probabilities;

Review Checklist

2010-03-03T18:16:00.001-08:00

learn as much about my calculator and ways it can help me calculate %change, depreciation, annualising, breakeven point
go through all the LOS's for the word calculate or compute and make notecards of those formulas and know them well
QBank LOS's in which i am weak and create sample tests to constantly review

Study Session 12 - Equity

2010-03-02T17:14:00.000-08:00

Reading 52: Organization and Functioning of Securities Markets

a. describe the characteristics of a well-functioning securities market;

Timely and accurate information
Liquidity
Internal efficiency (low transaction costs)
External (informational) efficiency i.e. rapid and unbiased price adjustments to new info

b. distinguish between primary and secondary capital markets and explain how secondary markets support primary markets;

primary market = newly issued securities (U.S. Treasuries, new issues of common stock)
secondary market = market for existing securities (NYSE, Nasdaq etc.)
well functioning secondary markets make it easier for firms to raise capital in the primary market as they provide both value information and liquidity

c. distinguish between call and continuous markets;

call markets = security trades executed at specific times at a single price and after buy and sell orders have accumulated
continuous markets = trading takes place at various prices and times as buy and sell orders arrive

d. compare and contrast the structural differences among national stock exchanges, regional stock exchanges, and the over-the-counter (OTC) markets;

stock exchanges are physical places where traders and dealers gather to trade
national stock exchanges list the shares of large and well-known firms and have more stringent listing requirements than regional or over-the-counter markets
regional stock exchanges trade the shares of local firms (smaller firms) and of some firms also listed on national exchanges
OTC market is network of dealers (market makers) in various locations who stand ready to purchase or sell securities at posted prices udring the hours the market is open

e. compare and contrast major characteristics of various exchange markets, including exchange membership, types of orders, and market makers;

types of stock exchange members include specialists who act as market makers, traders who provide liquidity by trading for their own accounts and commission brokers and floor brokers who execute public orders
import types of orders are market orders (buy/sell at best price available), limit orders (buy/sell at a specific max/min price i.e. buy at price x or less), stop orders (triggers to get you out of or into a position - defensive move usually), and short sales
specialists are the exchange market makers that handle the limit order book and maintain an orderly market by buying and selling shares for their own accounts

f. describe the process of selling a stock short and discuss an investor’s likely motivation for selling short;

Selling short = borrowing securities and selling them at market price, expecting the price to go back down so you can rebuy them at the lower price and return them to the owner
Short seller must pay any dividends to the lender of the securities as they are due and must deposit a margin as a guarantee of payment in the case stock price increases lead to losses on their part

g. describe the process of buying a stock on margin, compute the rate of return on a margin transaction, define maintenance margin, and determine the stock price at which the investor would receive a margin call.

in a margin transaction, investors borrow against securities to purchase them, leaving securities at the brokerage house as collateral for the loan
the rate of return on margin transactions is calculated as the profit or loss on the security position divided by the cash equity (margin) deposited to make the trade
the stock price at which an investor who purchases stock on margin will receive a margin call can be calculated as:
trigger price = P0[(1-initial margin)/(1-maintenance margin)]

Reading 53: Security-Market Indexes

a. compare and contrast the characteristics of, and discuss the source and direction of bias exhibited by, each of the three predominant weighting schemes used in constructing stock market indices and compute a price-weighted, a valueweighted, and an unweighted index series for three stocks;

b. compare and contrast major structural features of domestic and global stock indices, bond indices, and composite stock-bond indices;
c. state how low correlations between global markets support global investment.

Reading 54: Efficient Capital Markets
a. define an efficient capital market and describe and contrast the three forms of the efficient market hypothesis (EMH);
b. describe the tests used to examine each of the three forms of the EMH, identify various market anomalies and explain their implications for the EMH, and explain the overall conclusions about each form of the EMH;
c. explain the implications of stock market efficiency for technical analysis, fundamental analysis, the portfolio management process, the role of the portfolio manager, and the rationale for investing in index funds;
d. define behavioral finance and describe prospect theory, over-confidence bias, confirmation bias, and escalation bias.

Reading 55: Market Efficiency and Anomalies
a. explain the three limitations to achieving fully efficient markets;

Study Session 12 - Portfolio Management

2010-03-02T16:08:00.000-08:00

PORTFOLIO MANAGEMENT

The Asset Allocation Decision

LOS 49a: describe the steps in the portfolio management process and explain the reasons for a policy statement

write policy statement = goals, constraints, itemised risks taken to meet goals
develop investment strategy to satisfy policy goals
implement plan = construct portfolio and allocation of assets
monitor and update

policy statement is articulation of agreement that both parties have understood one another; imposes investment discipline on portfolio manager; portfolio should be measured against benchmark rather than raw returns

LOS 49b: Explain why investment objectives should be expressed in terms of risk and return and list the factors that may affect an investor's risk tolerance

Investment objectives should be expressed in tersm of risk and return so investor is aware of both and can make sound decisions.
return objectives may be stated in absolute terms, or as pre-tax or after-tax percentage returns
return considerations also cover capital preservation, capital appreciation, current income needs, and total returns
risk tolerance is a function of investor's psychological make up and personal factors such as age, family situation, existing wealth, insurance coverage, current cash reserves and income

LOS 49c: Describe the return objectives of capital preservation, capital appreciation, current income, and total returns

capital preservation = equal to inflation, little/no risk, no decrease in purchasign power
capital appreciation = e.g. saving for retirement, nominal return should exceed rate of inflation
current income = primary purpose is to generate income as opposed to capital appreciation e.g. supplement other income such as living expenses or in retirement
total return = have portfolio grow in value to meet a future need through capital gains and reinvestment of current income

risk hierarchy = capital appreciation > total return > current income > capital preservation

LOS 49d: describe the investment constraints of liquidity, time horizon, tax concerns, legal and regulatory factors, and unique needs and preferences

liquidity = ability to convert investments into cash
time horizon (investment horizon) refers to the time between making an investment and needing funds; lower-risk investments are better if you have short time horizons
tax concerns = after-tax returns are what investors should be concerned with. interest and dividends and capital gains all taxed at the same rate. Taxes on unrealised gains can be deferred indefinitely.
trade-off between changing positions to diversify and the tax "cost" of doing so
some investments (e.g. munis) are tax exempt
tax-deferred investments e.g. IRA, 401(k) and 403(b) - these are good for young investors - and various life insurance contracts
retirees may not want tax-deferred options, may want current income max so taxed investments (w/ higher return) may be better than tax-exempt
Legal and regulatory factors = more of a concern to institutional investors; penalty for early withdrawal from tax-deferred retirement fund

LOS 49e: Describe the importance of asset allocation, in terms of the percentage of a portfolio's return that can be explained by the target asset allocation, and explain how political and economic factors result in differing asset allocations by investors in various countries

90% of variation in a single portfolio's returns over time can be explained by target asset allocation and 40% of variation in returns acrosss funds can be explained by this
differences in returns among asset classes are much more important than differences in security selection in determining overall portfolio returns
countries with younger populations have greater avg allocation to equities
some countries have legal restrictions on the percentage of equities that various institutions can hold
German society has historical aversion to risk and equity ownership is not typical for its citizens
countries with higher historical inflation rates tend to have greater investor allocations to equities

Introduction to Portfolio Management

LOS 50a: Define risk aversion and discuss evidence that suggests that individuals are generally risk averse

Risk aversion = individuals prefer less risk to more risk; risk averse investors will prefer lower to higher risk for given return and will only accept a riskier investment if they are compensated in the form of greater expected return
Indifference curves = for every point of risk (variance) and return (mean) along each curve, the investor is indifferent. Preferred indifference curves will be the curves more to the northwest of the Return and Risk diagrams below since they represent more return and less risk (the preference of the risk averse investor).
insurance proves that people are generally risk averse but risk aversion varies based on the topic per person

LOS 50b: List the assumptions about investor behaviour underlying the Markowitz model

returns distributions = investors see each investment opportunity as a probability distribution of expected returns over a given investment horizon
utility maximisation = investors maximise expected utilitu over given timeline; indifference curves exhibit diminishing utility of wealth (they are convex)
risk is variability = variance (standard deviation) of returns
risk/return = investors make all investment decisions based on only the risk and return i.e. utility indifference curves are only a function of expected return (mean) and risk (variance)
risk aversion = given two investments with equal exp. returns, investors prefer the one with lower risk and if risk is equal, they prefer the one with higher returns

LOS 50c: Compute and interpret the expected return, variance, and standard deviation for an individual investment and the expected return and standard deviation for a portfolio

expected return for an individual security = for a risky asset and given probabilities for the return based on (say) different states of the economy, the Expected Return is the sum of exp. return multiplied by the probability of that return occuring.
variance (standard deviation) of returns for an individual security = for a risky asset and given probabilities for returns based on (say) different states of the economy, the variance is the sum of (the squared deviations from the mean multiplied by the probability of the return taking place). Standard deviation is just the square root of the variance.
expected return for a portfolio of risky assets is the weighted average of the returns on the individual assets, using their portfolio weights (i.e. the percentage of the total portfolio value invested in each asset).

LOS 50d: Compute and interpret the covariance of rates of return and show how it is related to the correlation coefficient

Covariance zero means no linear relationship; positive = they move together;

Covariance = sum of the probability times the product of the deviations from mean for each asset in each probability so COVa,b = Σ{ Pi [Ri,a - E(Ra)][Ri,b - E(Rb)] }

Covariance using historical data will be the n-1 average of the product of the deviations from the mean for the assets i.e. it will be the same as normal covariance except probability is equal to 1 (because it has actually taken place) and so average the returns using simple sample averaging and don't multiply by probability.

COV1,2 = P1,2(σ1 σ2) where P1,2 = correlation of Asset 1 and 2
Correlation (P1,2) of Asset 1 and 2 = Cov 1,2/(σ1 σ2)
The term P1,2 is the correlation coeffecient and is bounded by -1 and +1 with zero being no correlation.
zero correlation means that knowing something about how one of the assets moves tells you nothing about how the other will move

LOS 50e: list the components of the portfolio standard deviation formula

Var(Rp) = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_BCorr(A,B)
Standard Deviation (Rp) = square root of Var(Rp)
Note: σ_Aσ_BCorr(A,B) is the covariance(A,B) so if you are not given the Corr, you can find it for the first half of the formula and then substitute the Cov(A,B) after the weights in the second half. Also, this is for a portfolio of only two stocks.
for more than two stocks, there will be the same numer of weighted risks in the first half and then the second half would consist of all the different permutations of how all the assets can be paired off and their covariance compared
if assets are negatively correlated then last term will be negative and this (naturally) reduces the portfolio standard deviation; if correlation is zero then st. dev. for portfolio is greater than when correlation is negative (which makes sense)
NB! The risk of a portfolio of risky assets depends on the asset weights, the standard deviation of the assets' returns, and crucially on the correlation (covariance) of the assets' returns

PORTFOLIO RISK AND RETURN FOR A TWO-ASSET PORTFOLIO

Suppose you have two stocks, A and B. If they are not perfectly positively correlated (i.e. their correlation is less than one or even negative) then mixing the two of them together can create either (a) a portfolio with a lower risk and higher reward than a portfolio with just one of the stocks or (b) a portfolio with the same risk as say stock A but a much higher reward.

This is the principle of diversification: as the correlation between assets decreases, their tendency to move together decreases and, hence, the volatility of the portfolio decreases. The lower the correlation between the returns of the stocks in the portfolio, ceteris paribus, the greater the diversification benefits

LOS 50f: Describe the efficient frontier and explain the implications for incremental returns as an investor assumes more risk

We make the assumption of normality because it greatly simplifies the portfolio selection problem.
The entire distribution of an individual stock's return can be described by two parameters: the mean and the variance.
We can figure out a portfolio's mean and variance by examining the means, variances and covariances of the component securities.
Most importantly, we can compare different portfolios on the basis of mean and variance.

Our discussion of utility functions and risk aversion provided two conclusions.

First, consumers like more to less. In terms of a security or portfolio, consumers prefer more return to less return.
Second, consumers like less variance to more variance - the consumer will prefer a portfolio with less variance to another higher variance portfolio with an equal expected return.

We will now consider the effects of diversification. Previously, we combined securities and looked at the effect on the portfolio variance for different correlation coefficients between the securities. We found that using equal weights in the two portfolios, a lower the correlation coefficient led to lower portfolio variance.

To build a Markowitz portfolio, we need:

the expected return for each asset
the standard deviation for each asset
the correlations between every pair of assets

a portfolio is considered efficient if no other portfolio offers a higher expected return for the same (or lower) risk or if no other portfolio offers a lower risk for the same (or higher) return

the efficient frontier (above) represents the set of portfolios that will give you the highest return at each level of risk (or, alternatively, the lowest risk for each level of return).
anything below this line is an inefficient portfolio and is inferior in either risk or return or both to those which lie on the efficient frontier.

LOS 50g: Explain the concept of an optimal portfolio and show how each investor may have a different optimal portfolio

The optimal portfolio for each investor is at the point wher ethe investor's highest indifference curve is tangent to the efficient frontier.
the optimal portfolio is the portfolio that is the most preferred of the possible portfolios (i.e. the one that lies on the highest indifference curve)

NB the steeper the slope at the point of tangency, the greater the level of risk aversion because it takes more additional return to compensate for each additional unit of risk i.e. their indifferent curve will curl up on the right hand side more steeply the more risk averse they are

LOS 51b: Explain the capital market theory, including its underlying assumptions, and explain the effect on expected returns, the standard deviation of returns, and possible risk-return combinations when a risk free asset is combined with a portfolio of risky assets

The assumptions of capital market theory are:

Markowitz investors - all investors want to choose portfolios that lie along the efficient frontier, based on their utility functions
unlimited risk-free lending and borrowing
homogeneous expectations - everyone sees same risk-return functions
one-period horizon - all investors have same one-period time horizon
divisible assets - all investments are infinitely divisible
frictionless markets - no transaction costs or taxes
no inflation and constant interest rates
equilibrium - the capital markets are in equilibrium

Markowitz efficient frontier uses only risky assets. Adding the RF asset transforms it into a straight line because the big long formula for standard deviation of a two asset portfolio is transform into σp = Wm σm because there is no correlation between the RF asset and any of the others.

This straight line is called the capital market line (CML) and is essentially the efficient frontier plus various combinations of RF and Risky assets.

So the best possible mean and standard deviation combinations are from the riskless and tangency portfolio.

If 100% of your wealth is invested in the riskless asset, then you return is R_f and the standard deviation is zero.
If 50% of your wealth is invested in the riskless asset and 50% of your wealth is in the tangency portfolio, then your portfolio lies in between R_f and M on the straight line.
If 100% of your money is in the tangency portfolio, the your expected return is the expected return on the tangency portfolio and your standard deviation is the standard deviation on the tangency portfolio.
Finally, if you borrow money at the riskless rate and combine your borrowing with your initial wealth to buy the tangency portfolio, then your portfolio is to the right of M on the straight line. This is a levered position.

This straight line is called the Capital Market Line.

Since total lending equals total borrowing in the economy, the tangency portfolio is the market portfolio.
The market portfolio represents total invested wealth in risky assets. It is a portfolio with weights defined to be the total value of the asset divided by the total value of all risky assets. These weights are referred to as value weights.

LOS 51b: Identify the market portfolio and describe the role of the market portfolio in the formation of the capital market line (CML)

all investors have to do to get the risk/return combination that suits them is the vary the proportion of their investment in the risky Portfolio M and the RF asset
since all investors see risk-return using the same method, they all see the optimal risky portfolio as being the market portfolio that lies tangent between the efficient frontier and the CML
all investors want to hold some combination of the RF asset and the market portfolio
the market portfolio includes all risky assets and is therefore completely diversified.

LOS 51c: Define systematic and unsystematic risk and explain why an investor should not expect to receive additional return for assuming unsystematic risk

unsystematic risk is the firm-specific risk that can be diversified away
systematic risk is the risk that is inherent in the system and cannot be diversified away. If your stock is very responsive to market changes (e.g. luxury goods) you have a high systematic risk
total risk = systematic risk + unsystematic risk

Studies have shown that it takes around 18-30 stocks to achieve 90% of total possible diversification

One conclusion from capital market theory is that equilibrium security returns depend on a stock's or a portfolio's systematic risk, not its total risk as measured by standard deviation.
The riskiest stock does not necessarily have the highest return; you are rewarded only for systematic risk not unsystematic risk since unsystematic risk can be diversified away for free

LOS 51d: Explain the CAPM, including the security market line (SML) and beta and describe the effects of relaxing its underlying assumptions

SML is a described by a stock or portfolio's Beta and its expected return and is a graphical representation of CAPM.
Beta is systematic risk i.e. how responsive is a stock or portfolio to market movements
All properly price securities will plot on the SML because the SML is really just a graphical representation of the CAPM i.e. the required return based on a securities Beta

LOS 51e: Calculate, uing SML, the expected return on a security and evaluate whether the security is overvalued, undervalued or properly valued

if they are underpriced, they will plot above the SML because the expected return is higher than the required return. if they are overpriced, they will plot below the SML because the expected return is lower than the required return based on the security's beta.
CAPM determines required return so if stock is forecast to be $10 and CAPM has it at $8 then buy the stock.

! ! ! Differences between the CML and the SML

CML measures the efficiency of a portfolio i.e. the tradeoff between Expected Return and Total Risk (unsystemic risk + systemic risk)
Efficient portfolios will plot along the CML meaning that there is not a better combination that will produce a better tradeoff for the amount of risk or expected return
Below the market portfolio, you have some of your investment in RF assets (lending).
At the market portfolio, you have everything in risky assets but it is as diversified as risky assets can get i.e. the systematic risk should be nil
Above the market portfolio, you are borrowing money to purchase portions of your portfolio of risky assets so you are in a levered position which means that both your risk and expected return will be higher
Inefficient portfolios will plot beneath the CML because there is a better combination; nothing will plot above the CML because it would mean that there were a better combination at a higher point and the CML itself would move up
SML measures systemic risk only i.e. how a security's Beta (systemic risk) affects its expected return. It does not measure unsystemic (or firm-specific) risk which can be diversified away for free.
SML is a measure of required return based on the Beta of a security and therefore all properly priced securities will lie on the SML (if forecast plots it above then underpriced because exp. return is higher than required return and vice versa)
The CAPM (SML) is an equilibrium model that predicts the expected return on a stock given the expected return on the market, the stock's Beta and the risk free rate
A low beta stock is not necessarily a low risk stock e.g. pharmaceutical researcher
Any asset on the SML is expected to earn the market return

Relaxing the CAPM assumptions changes the model's implications:

the CAPM cannot be derived without equal borrowing and lending rates, unless investor's can create a zero beta portfolio (e.g. RF assets)
positive transaction costs, heterogeneous expectations, and multi-period investment horizon will each produce a Security Market band rather than a SML
Introducing taxes with different tax rates for different investors produces heterogeneous after-tax returns expectations and results in different SML's for different investors

Corporate Finance - Study Session 11

2010-03-01T16:18:00.000-08:00

Review Notes:

Know the relationship between BDY, BEY, HPY and EAY well i.e. what the drawbacks are of each and which gives higher or lower results relative to the others.
Know how to calculate BDY, BEY, HPY and EAY very well
The money market yield (MMY) is the holding period yield (HPY) times 360/t and is always greater than the discount yield (BDY) which is the actual discount from face value times 360/t, since the holding period yield is always greater than the percentage discount from face value. A security’s BDY and MMY always <>, and its EAY always > BEY.
So EAY > BEY > MMY > BDY
For pricing debt or equity, use market price rather than face value or book value
weak on finding the Beta for a project calculation - probably just a brute for memorization

LOS 44b - Discuss the basic principles of capital budgeting, including the choice of the proper cash flows

Capital budgeting includes 5 key principles:

Decisions are based on cash flows, not accounting income; so take into account incremental cash flows; do not consider sunk costs such as market research into a potential new product; consider negative externalities such as cannibalisation and positive ones which may boost another product.

conventional cash flow pattern = negative first cash flow, positive cash flows from then on
unconventional cash flow pattern = sign on the cash flow changes more than once
Cash flows are based on opportunity costs e.g. account for the cost of the company-owned land that a proposed new building would occupy
Timing of cash flows - earlier cash flows are more valuable than later ones
cash flows are analysed on an after-tax basis - we want to know what we keep from the project
financing costs are already reflected in the required rate of return i.e. the discount rate used in the capital budgeting analysis takes account of the firms cost of capital; only projects expected to return more than the cost of capital needed to fund them will increase the value of the firm

LOS 44c - Explain how the following project interactions affect the evaluation of a capital project:

Independent versus Mutually Exclusive Projects Independent projects are unrelated to one another and can be evaluated based on their own profitability. Mutually exclusive projects = only one project in a set of projects can be accepted.
Project Sequencing Just as it sounds. the order of projects is important. choosing a certain project now may provide opportunities for other projects if profitable. If unprofitable, it precludes the other project.
Unlimited Funds versus Fund Rationing If you have unlimited money, choose the projects which will make more than the cost of capital. With constraints on money, you will have to prioritise projects and ration money to those projects that make the most monetary sense.

LOS 44d - Calculate and interpret the results using each of the following to evaluate a single capital project: NPV, IRR, payback period, discounted payback period, and profitability index (PI)

NPV is the sum of all the present values (including any initial negative outlay) of the expected incremental after-tax cash flows if a project is undertaken, discounted at the firm's cost of capital (adjusted for risk). A positive NPV is expected to increase shareholder wealth and vice versa. For independent projects, the NPV decision rule is to accept any project with a positive NPV

IRR is the discount rate that makes the after tax PV of all the cash flows (discounted at the firm's cost of capital) equal to the initial cost of the project i.e. makes PV(inflows)=PV(outflows) and therefore is the discount rate that makes the NPV = 0. IRR Decision Rule (1) determine required rate of return for a project (usually firm's cost of capital adjusted for risk) and (2) if IRR > cost of capital then accept.

Payback Period (PBP) is the number of years it takes to recover the initial cost. You may be given a Cumulative Net Cash Flows (NCF) table which is a running total of how much you have paid down on the initial cost or how much profit you have made. If the breakeven point is between two years, divide the NCF at the start of the year by the next cash inflow (the next year) e.g. -400/1200 will give you 0.333 of a year.

PBP Decision rule Payback period is about liquidity i.e. when will i have the money back so i can do something else with it. It is not for accept/reject because it does not take into account time value of money or cash flows beyond the payback period (so terminal/salvage value wouldn't be included).

Discounted Payback Period = # of years it takes to pay back intial outlay in PV terms and therefore is always greater than non-discounted PBP. Addresses TMV drawback of PBP but does not address the other concerns.

Profitability Index (PI) = the PV of a project's future cash flows divided by the initial cash outlay. i.e. PI = PV of future cash flows including intial cash flow/initial cash flow = CF0 + NPV/CFo

If NPV is positive then PI will be greater than one. Therefore, if PI > 1.0 accept the project.

So if NPV is positive, IRR will be greater than cost of capital and PI will be > 1.0

LOS 44e: Explain the NPV profile, compare and contrast the NPV and the IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods

NPV profile depicts the NPV of (multiple) projects at varying costs of capital. The cost of capital is along the x axis so the IRR will be where the NPV profile intersects the x axis i.e. where NPV = 0
NPV profiles intersect where their NPV's are equal (the crossover rate); in the below profile, project 1 has a higher NPV at discount rates lower than 7.2% and project 2 has higher NPV at discount rates higher than 7.2% (so the discount rate determines which project has a higher NPV)
The NPV profiles intersect because of the timing of their cash flows; the NPV of a project (e.g. project 1) will fall faster if it has later cash flows than another project (project 2)

key advantage of NPV = direct measure of the expected increase in shareholder value (therefore, preferred method). disadvantage = does not tell you the size of the project e.g. a project that cost a $1,000,000 but has a positive NPV of $10 is probably not a wise investment

key advantage of IRR is that it solves the latter problem; measures profitability as a percentage i.e. return on each dollar invested. We can tell how far the project has to fall before it becomes uneconomical/ distadvantage: (1) can produce different rankings than NPV approach for same projects (2) possibility that there are multiple IRR's or no IRR for a project (due to unconventional cash flows for projects with positive NPV)

when in doubt (for mutually exclusive projects) use NPV IRR can be huge for a very small project e.g. investing $10 and making $100 might give you an IRR of 85% but only increases shareholder value by $90 whereas a large investment of a smaller IRR (say 20% IRR on a million bucks) is obviously a better investment.

NPV implicitly assumes that the money made could be reinvested at the discount rate used which is realistic whereas IRR implies it could be reinvested at the IRR rate which is not realistic.

LOS 44f: Describe and account for the relative popularity of the various capital budgeting methods and explain the relation between NPV and company value and stock price

Capital budgeting method varies according to:

Location European countries tend to use PBP method as much as IRR/NPV

Sophistication - the more sophisticated the company (size/education/private) the more likely the IRR/NPV method is used

Relationship between NPV and Stock Price

in theory, a positive NPV should cause a proportionate increate in a company's stock price. e.g.

if share price is $10 with 1000 shares outstanding then value = $10,000
if NPV of new project is $2000 then new value of company = $12,000
new share price = 12,000/1000 = $12

in reality, share price is more function of expectations about earnings so announcement of NPV positive project may cause share price to drop if NPV is less than expect or it might rise disportionately if the project signals other projects or expectations

LOS 45a: Calculate and interpret the weighted average cost of capital (WACC) of a company

Calculate WACC = (wd)[kd(1 - t)] + (wps)(kps) + (wce)(kce)

where:

wd = weight of debt
kd = cost of debt
t = marginal tax rate
wps = weight preferred stock
kps = cost of preferred stock
wce = weight common equity
kce = cost of common equity

WACC gives you the opportunity cost of capital or the discount rate for discounting future cash flows when capital budgeting

For any given project, your IRR should be higher than your WACC in order to approve the project
If your project is riskier than the risk of the projects that make up the firm, the WACC may need to be revised upward or vice versa

LOS 45b: describe how taxes affect the cost of capital from different capital sources

Interest paid on debt is often tax deductible hence the debt is often discounted by 1-t (which decreases the cost of debt by the marginal tax rate). Other sources of capital (ps and ce) are not typically tax deductible so they are not discounted.

LOS 45c: Describe alternative methods of calculating the weights used in the WACC, including the use of the company's target capital structure

WACC should be based on firm's target capital structure - the weights (based on market values) of debt, ps, and ce the firm expects to achieve over time
if no info is available, use firms current structure
if there is a trend (e.g. firm has been increasing debt) then follow that trend in your weighting system
otherwise use industry average capital structure as target structure for firm

LOS 45d: Explain how the marginal cost of capital and the investment opportunity schedule are used to determine the optimal capital budget

Company creates wealth for shareholders by earning more on its investment in its assets than is required by those who provide capital to the firm (the WACC)
Marginal Cost of Capital (cost of raising capital) generally increases as larger amounts are invested - hence the upward sloping marginal cost of capital curve
Expected returns (IRR's) of potential projects can be ordered from highest IRR to lowest IRR to create a downward sloping investment opportunity schedule
where the MCC curve intersects the investment opp schedules is the optimal capital budget which makes sense because the firm should take on all projects with an IRR greater than the cost of capital

LOS 45e: Explain the marginal cost of capital's role in determining the NPV of a project

WACC is the appropriate discount rate for projects with the same level of risk as the firm's existing projects; WACC's should be adjusted up/down for higher/lower risk projects
implicit assumption that capital structure of a firm will remain the same over the span of the project
NPV should be calculated using the WACC/Marginal Cost of Capital and those projects with a positive after tax NPV should be accepted

LOS 45f: Calculate and interpret the cost of fixed rate debt capital using the YTM approach and the debt rating approach

After-tax cost of debt is the rate, kd(1 - t) is the interest rate at which firms can issue new debt net of the tax savings
Cost of debt is the market interest rate (YTM) of new (marginal) debt, not coupon rate on firm's existing debt
if YTM is not available (e.g. debt is not publicly traded), analyst may use the rating and maturity of the firm's existing debt e.g. if firm's debt is rated AA with maturity of 15 yrs, you can use yield curve for AA rates debt with maturity of 15 yrs
if anything (e.g. covenants, seniority) affect the yeidl, adjust appropriately
for firms with floating rate debt, estimate the longer-term cost of the firm's debt using the current yield curve (term structure for the appropriate rating category)

LOS 45g: Calculate and interpret the cost of non-callable, non-convertible preferred stock

cost of preferred stock (kps) = Dps/P
where Dps is preferred dividends and P is market price

LOS 45h: Calculate and interpret the cost of equity capital using the capital asset pricing model approach, the divident discount model approach, and the bond-yield-plus risk-premium approach

All of these approaches measure the required rate of return on the firm's common stock - the opportunity cost of capital i.e. the firm can lower some of this part of the WACC by using retained earnings to buy back shares (lowering cost of common stock outstanding)

Hence all of these approaches are ways of valuing the cost of common stock

1) CAPM = RFR + B[E(Rm) - RFR]

RFR = Risk free rate
E(Rm) = expected return on the market
Beta is the stock's risk measure
this is another formula that makes sense when you break it down. it is the risk free rate plus the risk premium multiplied by the market risk

2) Dividend discount model approach

Po = D1/(kce - g)

where:

D1 = next year's dividend
kce = the required rate of return on common equity
g = the firm's expected constant growth rate

Rearranging the terms you can solve for kce = (D1/P0) + g

Use the growth rate projected by security analysts or estimate growth using:

g = (retention rate)(return on equity) = (1 - payout rate)(ROE)

this is also intuitive; the growth rate is the amout of ROE the firm will keep

3) Bond yield plus risk premium approach

ballpark figure constructed by adding a risk premium (3-5%) to the market yield on the firm's long term debt

kce = bond yield + risk premium of 3-5%

LOS 45i: Calculate and interpret the beta and cost of capital for a project

Project's beta = systematic or market risk; use project's beta to adjust for differences between a specific project's risk adn the average risk fo a firm's projects

Pure-play method = find a publicly traded firm purely engaged in the same biz as the project and begin with that firm's beta and then unlever it (to adjust for the company's dependence on debt financing) and then relever it based on the financial structure of the company evaluating the project. Then use this equity beta to calculate the cost of equity to be used in evaluating the project.

To get asset beta for publicly traded firm, discount the equity beta for the form by the after tax debt-to-equity ratio

ΒASSET = ΒEQUITY[1/1+(1(1-t)D/E)]

to get equity beta for the project, use the subject firm's tax rate and debt-to-equity ratio and re-lever the beta so...

BPROJECT = BASSET[1+((1-t)D/E)]

issues for this method:

beta is estimated using historical returns which may be sensitive to the length of time used
estimate is affected by the index chosen to represent market return
betas are believe the revert to 1 over time - need to account for this
estimates of betas for small cap firms may include a risk premium for risk of smaller firm not captured by usual estimation methods

LOS 45j: Explain the country equity risk premium in the estimation of the cost of equity for a company located in a developing market

CAPM is problematic in developing countries because Beta does not capture country risk premium

general risk of developing country is reflected in its sovereign yield spread (the difference between yields of sovereign debt and similar maturity Treasuries)

we must also adjust the sovereign yield spread by the ratio of the volatility of equities in dev country/volatility of sovereign bonds for that country (for bonds denominated in developed market's currency)

so revised CAPM: kce = B[E(Rmkt)-RFR+CRP]

where CRP is:
country risk premium = sovereign yield spread * (volatility dev. equities/ volatility dev. bonds in US$)

LOS 45k: Describe the marginal cost of capital schedule, explain why it may be upward sloping with respect to additional capital, and calculate and interpret its break points

marginal cost of capital schedule tends to be upward sloping because as a firm raises more and more capital , the costs of different sources of financing will increase
e.g. cost of debt may rise due to increased risk, convenant protecting seniority of earlier debt issues, flotation costs of issuing new stock
marginal cost of capital schedule shows the WACC for different amounts of financing
break points occur any tiem the cost of one of the components of the company's WACC changes and is calculated thusly:

break point =
amt of capital at which a component's cost of capital changes
weight of the component in the capital structure

LOS 45l: Explain and demonstrate the correct treatment of flotation costs

Flotation costs are a fixed one-off costs and should rightly be accounted for as part of the initial cost of the project and NOT as part of WACC in any way

Problem set issues:

calculate Marginal Cost of Capital
calculate ke using dividend discount approach

Reading 46: Working Capital Management

LOS 46a. describe primary and secondary sources of liquidity and factors that influence a company’s liquidity position;

primary sources of liquidity are the sources of cash the company usese in its day-to-day operations e.g. cash balances from sales of goods and services, collecting receivables and investment income. Short term funding includes trade credit from vendors and lines of credit from banks
secondary sources of liquidity indicates trouble e.g. liquidating short-term or long-lived assts, renegotiating debt agreements, filing for bankruptcy and restructured
drags and pulls drags on liquidity are things that delay/reduce cash inflows (bad debts, incollected receivables, obsolete inventory, etc.) pulls are things that accelerate cash outflows e.g. paying vendors sooner than is optimal

LOS 46b. compare a company’s liquidity measures with those of peer companies;

most of the comparisons are performed comparing the following ratios to industry norms

current ratio = current assets/current liabilities high ratio means better ability to pay short term bills; less than one means trouble
quick ratio = (cash + marketable securities + receivables)/current liabilities i.e. same as current ratio but only using the most liquid assets

Measures of how well a company is managing its working capital include:

receivables turnover = credit sales/average receivables
number of days of receivables = 365/receivables turnover
inventory turnover = COGS/average inventory
number of days of inventory = 365/inventory turnover
payables turnover = purchases/average trade payables
number of days of payables = 365/payables turnover
NB all of these are measures of turnover i.e. the item/average of the opposite measure e.g. COGS/avg inventory and the number of days is just 365/turnover
NB you want these to mostly be close to industry norms

LOS 46c. evaluate overall working capital effectiveness of a company, using the operating and cash conversion cycles, and compare its effectiveness with other peer companies;

operating cycle = number of days it takes to turn raw materials into cash proceeds from sales
operating cycle = days of inventory + days of receivables
cash conversion cycle or net operating cycle is the length of time it takes to turn the firm's cash investment in inventory back into cash, in teh form of collections from the sales of that inventory
cash conversion cycle = (avg days of receivables) + (avg days of inventory) + (avg days of payables)
NB high cash conversion cycles are undesirable - implies too much investment in working capital
NB understand what the ratios are saying about the business

LOS 46d. identify and evaluate the necessary tools to use in managing a company’s net daily cash position;

Need to ensure there is sufficient cash without letting it sit idle; answer is to keep much of it highly liquid, low risk securities etc. such as:

Treasuries
Bank COD's
Banker's Acceptances
Repurchase Agreements
Commercial Paper
Money Market Mutual Funds
Adjustable-rate preferred stock = stock which resets quarterly to current market yields and has tax advantage

LOS 46e. compute and interpret comparable yields on various securities, compare portfolio returns against a standard benchmark, and evaluate a company’s short-term investment policy guidelines;

% discount from face value = (face value - price)/face value
discount basis yield (or BDY) = % discount * (360/t)
money market yield = ((face value - price)/price)* (360/t) = HPY * (360/t)
bond equivalent yield = HPY * (365/t)

returns on firm's short term securities investments should be stated as BEY's. Return on portfolio should be expressed as weighted average of those yields

LOS 46f. assess the performance of a company’s accounts receivable, inventory management, and accounts payable functions against historical figures and comparable peer company values;

A firm's inventory, receivables, and payables management can be evaluated by comparing days of inventory, days of receivables, and days of payables for the firm over time, and by comparing them to industry averages or averages for a group of peer companies.
A receivables aging schedule and a schedule of weighted average days of receivables can each provide additional detail for evaluating receivables management.

LOS 46g. evaluate the choices of short-term funding available to a company and recommend a financing method.

Choices for short term borrowing depends on firm's size and credit-worthiness; options (in order of decreasing firm creditworthiness and increasing cost):

commercial paper
bank lines of credit
collateralised borrowing
nonbank financing
factoring (of receivables)

FINANCIAL STATEMENT ANALYSIS

LOS 47: Demonstrate the use of pro forma income and balance sheet statements

Pro forma income and balance sheet statements are forward-looking financial statements constructed based on specific assumptions about future business conditions and firm performance.
process begins with making an assumption about which variable is the overall driver (e.g. sales) of income and balance sheet items
e.g. if sales are forecast to increase by 10% then we could forecast that COGS, fixed assts, total assets, debt and interest expense etc. could increase by 10%
i.e. that the percentage of each relative to sales will be maintained

Constructing a sales-driven pro forma financial statement:

Estimate the relation between change in sales and the changes in sales-driven income statement and balance sheet items
Estimate the future tax rate, interest rate on debt, lease payements, etc.
Forecast sales for the period of interest
Estimate fixed operating costs and fixed financial costs
Integrate these estimates into pro forma financial statements for the period of interest

To calculate future sales, you can:

calculate average compound growth rate of sales over 5 or 10 year period and use that rate to forecast future sales
regression analysis to estimate relationship between GDP growth and growth in sales and use economists' estimates of future GDP growth to forecast (assumes correlation)
economic cycles, seasonality of sales, specific events, changes in regulation/tax rate etc. can also be incorporated into model

We can move the financial statements through iterations based on "what if" scenarios such as what if the company decided not to pay dividends and yielded a surplus. Then what if this surplus was used to pay down debt? Interest payments would come down and more money would come in from the savings there... etc. etc.

The Corporate Governance of Listed Companies: A Manual For Investors

LOS 48a: Define and describe corporate governance

Corporate governance is the set of internal controls, processes, and procedures by which firms are managed. It defines the appropriate rights, roles, and responsibilities of the management, the board of directors, and shareholders within an organisation. It is the firm's checks and balances.

Good corporate governance seeks to ensure that:

the board of directors protects shareholders interests
the firm acts lawfully and ethically in dealings with shareholders
the rights of shareholders are protected and shareholders have a voice in governance
the board acts independently from management
proper procedures and controls cover management's day-to-day operations
the firm's financial, operating, and governance activities are reported to shareholders in a fair, accurate, and timely manner

LOS 48b: Discuss and critique characteristics and practices related to board and committee independence, experience, compensation, external consultants, and frequency of elections, and determine whether they are supportive of shareowner protection

Corporate governance is the set of internal controls, processes, and procedures by which firms are managed. Good corporate governance practices ensure that the board of directors is independent of management and that firm and its managers act lawfully.

LOS 48c: Describe board independence and explain the importance of independent board members in corporate governance

Majority of board should be independent but experienced enough to advise management and review its activities.

LOS 48d: Identify factors that indicate a board and its members possess the experience required to govern the company for the benefit of its shareholders

experience with:

the products or services the firm produces
financial operations, accounting, and auditing
legal issues
strategies and planning
firm's business and financial risks

LOS 48e: Explain the provisions that should be included in a strong corproate code of ethics and the implications of a weak code of ethics with regard to related-party transactions and personal use of company assets

code of ethics - practice what you preach;
comply with corp gov standards in home country and stock exchange;
no advantages to outsiders that are not available to shareholders;
have someone responsible for corp governance

LOS 48f: State the key areas of responsibility for which board committees are typically created and explain the criteria for assessing whether each committee is able to adequately repesent shareholder interests

Audit committee - proper account procedures, external independent auditor, free commuincations
Compensation committee - ensure fair and appropriate (not excessive) compensation which is linked to long term profitability; shareholder approval for share based compensation (dilution issues); be transparent about compensation
Nominations committee - recruitment of new, qualified board members; review existing board members; succession planning

LOS 48g: Evaluate, from a shareholder's perspective, company policies related to voting rules, sharehodler sponsored proposals, commons stock classes, and takeover defenses

don't make it difficult to vote proxies
confidence voting and remote proxy voting are good
takeover defenses are generally not in the shareholders' best interest

rules of thumb:

independence is good; promoting rights and interests of shareholders is good
any conflict of interest e.g.tie to management, consulting fees, personal loans from company, long-serving board members, family ties, cross-directorships, unreasonable compensation packages, chairman is also CEO = bad

The Out-of-whack order

2010-03-01T16:13:00.000-08:00

OK. In case, anyone is actually reading this, let me explain the messy postings: I've decided to move FRA to last so that I can spend the required time on it (and i'm going to do the "real" reading for that i.e. CFAI books). I started it as you can see but quickly realised i need time to internalise it and become more fluent in the fundamentals and learn more depth so it is now last where it can expand a little without the pressure of getting to other books.

Because i want ~one month to revise and take practice tests, it means i am about three behind schedule (fun!). So my plan is to try and study corporate finance/portfolio management/equity investments (book 4) in the evening and study the rest of the derivates/alternative investments during my lunch hour at work to try and make up the time. We'll see how well that works out considering today was day one of the new schedule and i studied zero hours during the day.

General Thoughts on Formulas and Mistakes

2010-02-22T17:55:00.000-08:00

1. many mistakes I make are on the small things e.g. not reading the question correctly, forgetting to do something simple like divide the interest rate or coupon by the number of periods etc.
2. to reinforce the above: underline key data in a question including putting a big circle around words like least likely or most appropriate etc. - getting these right could easily improve my scores by 5-10% and are a stupid-ass reason to lose points.

Understanding Formulas
Several formula seem to crop up again and again in various guises so I'm going to try and explain generally what they are useful for and how they work:

1. weighted average - whenever you are trying to find an average (e.g. expected return) on a set of outcomes that are not equally represented in the set
2. powers - raising returns/yields to a power of n represents compounding that yield over n periods
3. geometric mean - when the return/yield is different for each of n periods and you need an average, multiply all the returns/yields together and take the nth root
4. percentage change between two periods e.g. Holding period return, change in bond price after interest rate change etc. is the (final period value - original value)/original value NB this not the way you would do it when calculating change in price say for the elasticity calc - that would be P1-P0/(avg P1,P0)
5. discounting - discounting cash flows or even interest rates (unsurprisingly) happens a lot and is usually happening over several periods so you are undoing compounding of interest etc. so: value to be discounted/(1+I/Y)ⁿ
6. spot versus forward rates spot rates are the one interest rate for the period of the loan e.g. a 3 yr spot rate would be the discount rate for the entire three years whereas a forward rate would be used for each of the periods to discount the cash flows. So for two periods if you have 1 yr spot of 5% and fwd of 5% and 2yr spot of 6% and fwd of 6% then to calc PV of cash at the end of two years using spot rate, you would use 6% as your discount. To calc PV of cash at the end of two years using forward rate, you would discount year one at 5% and yr 2 cash flow at 6% then 5%
7. Increasing or decreasing an amount by a certain percentage (e.g. finding next/last dividend, profit on a stock portfolio based on growth rate, etc.): increase = amt*(1+x), decrease = amt*(1-x)

Valuing a security
most valuations involve a PV of the expected cash flows
expected return can be compared against required return to decide buy or sell

Conducting any analysis tends to consist of these kinds of steps:

set the objective or goal
collect the relevant data
process the data to get usable numbers
analyse and interpret the data
recommendation based on data
monitor and update the analysis

this appears to be true of individual company analysis, financial statement analysis, hypothesis testing, etc.

when conducting the analysis, work from general to specific e.g. economic analysis, industry analysis, firm analysis, firm security analysis.

Study Session 15 - Readings 60-65 Fixed Income

2010-02-13T08:59:00.000-08:00

Fixed Income

Notes:

The duration of a floating rate bond is equal to the time until the next coupon payment takes place. As the coupon rate changes semi-annually with the level of the interest rate, a floating rate bond has the same duration as a pure discount bond with time to maturity equal to the time to the next coupon payment of the floating rate bond.
duration for fixed rate bonds is Duration = Price Yield Down – Price Yield Up / 2 * (initial price) *change in yield in decimals

LOS 61a - Explain the risks associated with investing in bonds

Interest rate risk - approximated by measure call duration; when interest rates rise, bonds fall

Yield Curve Risk - change in shape of yield curve means that yields change by different amounts for bonds with different maturities
Call Risk - risk of issuer calling back the bond, investor must reinvest at a lower rate

Prepayment Risk - increase in interest rate volatility (like with call risk) causes prepayment; investor must reinvest at lower rate

Reinvestment Risk - when market rates fall, cash flows (principal and coupon) from bond must be reinvested at lower rate

NB Investor can be faced with choice between reinvestment risk and price risk e.g. non-callable zero coupon bond has no reinvestment risk (no cash flows to reinvest) but has more interest rate risk than a coupon bond of same maturity) and vice versa

Credit Risk - if creditworthiness of issuer declines, required return increases, decreasing security's value

Liquidity Risk - if bond is not very liquid, may have trouble selling it and sell for discount

Exchange-rate risk e.g. foreigner investing in T-bills will risk relative value of home currency to dollar
Inflation Risk - uncertainty about future purchasing power of cash flows

Volatility Risk - with embedded options (call/put/prepayment) interest rate volatility affect value of the options and therefore the value of the security

Event Risk - events outside of the financial market e.g. catastrophe, corporate takeover

Sovereign Risk - risk of changes in government attitudes and policies toward repayment and servicing of debt; also change in Sovereign's ability to pay, etc.

LOS 61b - Identify the relations among a bond's coupon rate, the yield required by the market, and the bond's price relative to par value (i.e., discount, premium or equal to par)

Bonds tend to be issued with the coupon rate of similar bonds so they initially trade at par

they trade at a discount to par when they become more risky (e.g. credit issues with issuer) or less desirable relative to other assets (interest rate rises)

if required yield falls, bondy trades at a premium

LOS 61c - Explain how features of a bond (e.g. maturity, coupon, and embedded options) and the level of a bond's yield affect the bond's interest rate risk
Interest rate risk = duration = sensitivity of a bond's price to a change in yield (inverse relationship) = similar to elasticity except inverse i.e. bond yield goes up, price goes down

ceteris paribus longer maturity = higher duration

ceteris paribus higher coupon rate = lower duration

both of these are intuitive: with longer maturity, you are locked in to a particular coupon until maturity, so the value of your bond will be sensitive to returns on other securities. with higher coupon rate, the percentage different between your coupon and the yields of other investments would be smaller

callable bond will have lower duration because the upside for the investor is capped at the call price; when interest rates decline, bond price will rise but (almost) never above the call price
putable bond will have lower duration as well because downside for the invest is capped at put price; when interest rates rise, bond price will fall but (alomst) never below put price
This is also intuitive; embedded options limit the price movement of a bond because the privileged part will either put or call the bond at the strike price

maturity up = interest rate up = higher interest rate sensitivity/duration
coupon up = interest rate down = lower interest rate sensitivity/duration
add a call = interest rate down = lower interest rate sensitivity/duration
add a put = interest rate down = lower interest rate sensitivity/duration

NB remember duration is basically sensitivity to changes in yield

LOS 61d - Indentify the relationship among the price of a callable bond, the price of an option-free bond, and the price of the embedded call option

call option favours issuer, put option favours bondholder
call option decreases value of bond compared to option-free bond

callable bond = value of option-free bond-value of embedded call option

difference between value of option-free bond and callable bond will be greater at lower yields because price will rise as yield declines but as price gets closer to call price...

LOS 61e - Explain the interest rate risk of a floating-rate security and why such a securities prcie may differ from par value

floating rate is an imperfect insurance against interest rate risk; it is imperfect because the coupon does not float fluidly with market yields but instead is reset at particular dates (and should return to par value).

The longer the reset period the greater the interest rate risk at any reset date; the closer you are to a reset date, the lower the interest rate risk

Coupon resets may not return the bond to par value due if one or both of the following factors are present:

caps - if interest rates rise above the bond's yield cap, the floating rate security will trade at a discount (cap risk)
fixed margin - e.g. LIBOR plus 2% - the 2% margin reflects liquidity and credit risk of issuer; if these improve, the security will trade at above part; even if firm's creditworthiness remains constant, a chance in the market's required yield premium for the firm's risk level will cause the value of the floater to differ from par

LOS 61f - Computer and interpret the duration and dollar duration of a bond

duration = approximation of the percentage change in security price for a 1% change in yield (so yield is denominator)

duration = -(% change in bond price/yield change in %)
minus sign because it is an inverse relationship; price goes up, yield goes down
duration of a zero coupon bond will be ~years to maturity;
duration of floater = fraction of a year until the next reset date

NB if you are given the duration, remember inverse relation between price and yield. If you are given a duration of 2 and a yield increase of 5 then you would expect the price to go down by 2*5 = 10% decrease

percentage price change = -duration * (yield change in %)

dollar duration = approx. price change in dollars in response to a 1% change in yield e.g.with a duration of 5.2 and bond value of $1.2 million, dollar duration is 5.2% * $1.2 million = $62,400 which make sense since duration tells you the movement in price per 1% change in yield

LOS 61g - Describe yield-curve risk and explain why duration does not account for yield-curve risk for a portfolio of bonds

OK. So a yield curve illustrates the relationship between bond maturity and yield;
the yield curve risk is the changes in the shape of the yield curve that are not captured by the duration
portfolio's duration is just the market-weighted average of the individual bond's durations and will capture parallel shifts in the yield curve i.e. the curve remains the same shape but moves up or down so yields on all maturity lengths are affected equally
non-parallel shifts change the shape of the curve e.g. short maturity bonds have different sensitivities to change in yield than longer ones
to estimate impact of these non-parallel shifts, use key rate durations i.e. measure sensitivity of portfolio's value to changes in yields for specific maturities (or portions of the yield curve)

LOS 61h - Explain the disadvantages of a callable or prepayable security to an investor

This is intuitive, the disadvantages are:

you cannot benefit from a decline in interest rates (and corresponding increase in value of your asset) beyond the strike price of call option and similarly your benefits are capped if the issuer prepays
there is less security to your cash flows because your issuer may pay back the principal thereby stopping coupon payments
All of this will likely happen when interest rates are low and your opportunities to reinvest will be in a low interest market

LOS 61i - Identify the factors that affect the reinvestment risk of a security and explain why prepayable amortising securities expose investors to greater reinvestment risk than nonamortising securities

NB lower coupon increases (duration) interest rate risk but decrease reinvestment risk (since your return was lower to begin with) ceteris paribus

A security has more reinvestment risk when:

coupon is higher so that interest cash flows are higher
call feature is present
it is amortising
it contains a prepayment option (this also adds risk/uncertainty)

because with each you may be stuck with your principal and no more cash flows at a time when interest rates are low and investment opportunities suck.

LOS 61j - Describe the various forms of credit risk and describe the meaning and role of credit risk

rating indicates probability of default so lower rated bonds have more default risk

difference between yield on Treasuries and lower rated bond of similar maturity is credit spread

yield on a risky bond = yield on a default free bond + credit spread

Credit Spread Risk = default risk premium required in market can increase even when there is no change in similar Treasuries; increase in credit spread risk decreases value of the bond

Downgrade Risk = risk of rating downgrade which would increase required return and decrease price

Bonds issued by the same company may have different ratings depending on capital and priority of bondholder's claims

S&P's ratings:

AAA = least risk
AAA through BBB- are investment grade
BB and below are speculative (junk bonds or high yield bonds)
D are currently in default

LOS 61k - Explain liquidity risk and why it might be important to investors even if the expect to hold a security to the maturity date

Investors prefer more liquidity to less; low liquidity decreases the number of buyers for my asset so I must sell at a lower (possibly discount) rate

bid-ask spread is an indication of liquidity - highly liquid assets have a very low bid-ask spread

low liquidity = high liquidity risk

even if you are holding to maturity, liquidity can still be an issue when you have to mark to market at lower price because of decrease in liquidity/widening of bid-ask spread
MTM is done for portfolio performance reporting
MTM also affect repurchase agreements to ensure that collateral value is adequate to support the funds being borrowed; lower valuation = higher cost of funds and decreasing portfolio returns

LOS 61l - Describe the exchange rate risk an investor faces when a bond makes payments in foreign currency

Exchange-rate risk e.g. foreigner investing in T-bills will risk relative value of home currency to dollar

LOS 61m - Explain Inflation Risk

Inflation Risk - uncertainty about future purchasing power of cash flows

LOS 61n - Explain how yield volatility affects the price of a bond with an embedded option and how changes in volatility affect the value of a callable bond and a putable bond

Without any volatility in interest rates, call provision and put provision have little value ceteris paribus.

value of a callable bond = value of option-free bond - value of embedded call option
value of a putable bond = value of option-free bond + value of embedded put option

the value of either option is increased by an increase in yield volatility but look at the formulas to determine effect on the bond price
since the call is subtracted from the value of the bond and the put is added (better for investor), yield volatility will decrease value of callable bond and increase value of putable bond

fluctation in interest rates affects these in opposite ways

volatility risk for callable bonds is risk that interest rate volatility will increas

volatility risk for putable bonds is risk that interest rate volatility will decrease

LOD 61o - Describe the various forms of event risk

Event risk = something significant happening to a company or market segment e.g

disasters impair the ability of corporation to meet debt obligations if disaster reduces cash flow
corporate restructurings [spin-offs, leveraged buy outs, mergers]may affect cash flows, value of collateral assets, etc.
regulatory issues e.g. clean air requirements may reduce cash available to bondholders and result in downgrade

Problem Set Issues

if you know the duration and the change in yield then multiple the change in yield by the duration (to get the new duration?) and multiple this by the price.
e.g. a bond with a 7.3% has a duration of 5.4 and is trading at $985. If yield decreases to 7.1%, the new bond price is -5.4*(-0.2) = 1.08%. New price is 1.0108 * 985 = $995.64
the value of an embedded put option is the difference between the price of the putable bond and the price of the straight bond (not the face value of the bond)
zero coupon bond will have the greatest duration and therefore subject to greatest interest rate risk
Treasury bond pays semi-annual coupon and therefore has reinvestment risk
AAA bonds can lose their AAA rating and therefore have downgrade risk
Bond with a call feature has volatility risk even when call cannot be exercised immediately

READING 62

Caution:

Remember for TIPS the coupon is fixed (divide by 2 for semi-annual) but the face value upon which the coupon is based fluctuates based on the inflation rate. For $100,000 worth of TIPS trading at par with a 4% coupon and annula inflation rate at 2.5% what is the inflation adjusted principal value of the bond after 6 months.
It pays the product of the par value, half the coupon, and half the inflation rate so:

coupon payment = ($100,000 * 1.0125) * (0.04/2) = $2025

Measuring Return With Yield
Coupon is not yield. Yield is essentially your return based as a ratio of the value of the bond. Yield is a figure that shows the return you get on a bond. The simplest version of yield is calculated using the following formula: yield = coupon amount/price. When you buy a bond at par, yield is equal to the interest rate. When the price changes, so does the yield.

Why is yield inversely related to price?
Let's demonstrate this with an example. If you buy a bond with a 10% coupon at its $1,000 par value, the yield is 10% ($100/$1,000). Pretty simple stuff. But if the price goes down to $800, then the yield goes up to 12.5%. This happens because you are getting the same guaranteed $100 on an asset that is worth $800 ($100/$800). Conversely, if the bond goes up in price to $1,200, the yield shrinks to 8.33% ($100/$1,200).

Yield to maturity (YTM)
YTM is a more advanced yield calculation that shows the total return you will receive if you hold the bond to maturity. It equals all the interest payments you will receive (and assumes that you will reinvest the interest payment at the same rate as the current yield on the bond) plus any gain (if you purchased at a discount) or loss (if you purchased at a premium). The key point here is that YTM is more accurate and enables you to compare bonds with different maturities and coupons.

If you are a bond buyer, you want high yields. A buyer wants to pay $800 for the $1,000 bond, which gives the bond a high yield of 12.5%. On the other hand, if you already own a bond, you've locked in your interest rate, so you hope the price of the bond goes up. This way you can cash out by selling your bond in the future.

When interest rates rise, the prices of bonds in the market fall, thereby raising the yield of the older bonds and bringing them into line with newer bonds being issued with higher coupons. When interest rates fall, the prices of bonds in the market rise, thereby lowering the yield of the older bonds and bringing them into line with newer bonds being issued with lower coupons.

Government Bonds
In general, fixed-income securities are classified according to the length of time before maturity. These are the three main categories:

Bills - debt securities maturing in less than one year.
Notes - debt securities maturing in one to 10 years.
Bonds - debt securities maturing in more than 10 years

READING 63

63e - Computer, compare, and contrast the various yield spread measures

Yield Spread = Yield on Bond A – Yield on Bond B (doesn't capture interest rate movements if they both move in unison)
Relative Yield Spread =Yield on bond A- Yield on Bond B/ Yield on Bond B
Yield Ratio = Yield on Bond A / Yield on Bond B

Even though the way most investors discuss spreads is based on a Treasury security with the same maturity as the one it is being compared to, an investor can also talk about spreads between any two bonds with the following measures:

1. Absolute Yield Spread
This is the way most spreads are measured in the market. This spread measures the difference in spread between two bonds in terms of basis points.

Yield Spread = Yield on Bond A – Yield on Bond B

2.Relative Yield Spread
This ratio measures the yield spread relative to the reference bond.

Relative Yield Spread =Yield on bond A- Yield on Bond B/ Yield on Bond B

3.Yield Ratio
This is just the ratio of the yields between the two bonds.

The equation is: Yield on Bond A / Yield on Bond B

Market convention is to use the on-the-run government security as the reference yield or bond. So in the above equations, one would replace Bond B with the comparable government security.

Example: Yield Ratios
We want to compare an IBM five-year bond with a yield of 4.5 % and the on- the-run government five-year with a yield of 3.75%

Answer:

Absolute Yield Spread = 4.5% - 3.75% = .75% or 75 basis points
Relative Yield Spread = 4.5%- 3.75% / 3.75% = .20 = 20%
Yield Ratio = 4.5% / 3.75% = 1.20

Why Relative Spreads Are Better
Investors may find relative spreads a better measure because they measure the magnitude of the yield spread and the way it is affected by interest-rate levels. While absolute spread may be maintained as rates change, relative spreads will move in or out depending on the level of rates.

LOS 63f - Describe a credit spread and discuss the suggested relation between credit spreads and the well-being of the economy

A credit spread is difference in yields between two issues that are similar in all respects except for credit rating
these spreads show effect of credit quality on yields and reveal risk-return tradeoff investor can expect
during expanding economy, more companies are flush and credit spreads tighten
during contracting economy, credit spreads widen and investors tend toward "flight to quality" such as Treasuries

LOS 63g - Identify how embedded options affect yield spreads

Yield spreads against a benchmark such as Treasuries will be greater for a callable bond than a similar non-callable bond to compensate the bondholder for reinvestment risk

Similarly, mortgage passthrough securities which have a prepayment option will have higher yield spreads to compensate boldholder for reinvestment risk
Putable options will have lower yield spreads than otherwise similar option free bonds to compensate issuer for risk of having the bonds sold back to them
important b/c this tells us that spreads for bonds with embedded options are not purely premiums for credit risk, liquidity differences, and maturity (duration) risk

LOS 63h - Explain how the liquidity or issue size of a bond affects its yield spread relative to risk free securities and relative to other securities

Bonds that have less liquidity have higher spreads
Larger issues tend to be more liquid
Issues with greater size tend to be more liquid and tend therefore to have lower yield spreads

LOS 63i - Computer the after-tax yield of a taxable security and the tax-equivalent yield of a tax-exempt security

After-tax yield = taxable yield * (1 - marginal tax rate)

Tax exempt securities can offer lower yields due to the tax savings. to compare between taxable and non-taxable yields, use the taxable equivalent yield i.e. the yield an investor must make on a taxable bond to have the same after tax return they would on a tax exempt issue (rearrange the after tax yield formula).

taxable-equivalent yield = tax-free yield/(1-marginal tax rate)

LOS 63j - define LIBOR and explain its importance to funded investors who borrow short term

London Interbank Offered Rate - the most important reference rate for floating-rate debt securities and short term lending
A funded investor is borrowing at LIBOR + x to fund investments; his profits depend on his ability to earn more than LIBOR + x

READING 64

If the discount rate is higher than the coupon rate the PV will be less than par. If the discount rate is lower than the coupon rate, the PV will be higher than par value.

How Does a Bond’s Price Change as it Approaches its Maturity Date?
As a bond moves closer to its maturity date, its price will move closer to par. The break down on the three scenarios is as follows:

1.If a bond is at a premium, the price will decline over time towards its par value.
2.If a bond is at a discount, the price will increase over time towards its par value
3.If a bond is at par, its price will remain the same

watch out for:
confusing yield price with coupon payment percentage
read carefully for semi-annual versus annual

LOS 65a - Explain the sources of return from investing in a bond

coupon interest payments

recovery of principal

income from reinvesting the periodic coupon payments

LOS 65b - Computer and interpret the traditional yield measures for fixed-rate bonds and explain their limitations and assumptions

1. current yield expresses only bond's annual interest income - ignores capital gains/losses or investment income:

current yield = annual cash coupon payment/bond price

2. yield to maturity = annualised IRR based on price and promised cash flows. For bond with semiannual coupon payments, YTM is stated as two times the semiannual IRR implied by the bond's price. The formula that relates the bond price (including accrued interest) to YTM for semi-annual coupon is:

[insert clearer version of bond price formula]
bond price = (CPN1/(1+YTM/2)) + (CPN2/(1+YTM/2)²)+...+(CPN_2N+PAR/(1+YTM/2)^2N)

where:
bond price = full price including accrued interest
CPNt = the semi-annual coupon payment rec'd after t periods
N = number of years to maturity
YTM = Yield to Maturity

YTM and price give the same information i.e. given YTM you can calc. price and given price you can calc. YTM (but not easily in the latter case)

To compute YTM compute as if you were calculating IRR remembering:

first cash flow is negative and is the bond price

payments are usually semi-annual so divide coupon payment by two and

double the number of periods (minus one payment)

final payment is PAR + semi-annual coupon payment

multiply the final figure by 2 to get the annual payment

or calculate as if it were an annuity:

PMT = semi-annual coupon

PV = neg. bond price

FV = PAR value

N = 2 * number of years

CPT I/Y = semi-annual YTM (so multiply by two)

YTM will be the discount rate you will use to find the price i.e. the YTM/2 will be the discount rate to discount the semi-annual cash flows and the recovered principal to get the bond's price.

if price = par then coupon rate = current yield = YTM

if price <>

if price > par then coupon rate > current yield > YTM

bond equivalent yield = semi-annual pay YTM's (mult. by two to get annual pay YTM). This is the discount rate using semi-annual interest, double the periods, etc. If you were to calculate it on annual interest and annual payments it would just be called the annual pay YTM

the bond equivalent yield is the non-compounded annual rate received from a security that pays semi-annually with only simple interest. So to get an annual pay rate from a BEY you would to:

get the semi-annual payment rate (so divide by two)
then compound the semi-annual payment rate over two periods

example: what is the annual-pay yield for a bond with a BEY of 5.6%?
answer: [(1+(0.056/2))²-1

BEY/semi-annual pay YTM example: for a semi-annual pay bond, you can calculate the YTM if you know price (PV), par value (FV), number of years (N*2) and then CPT the I/Y and multiply by two i.e. you are trying to find the semi-annual discount rate that would make $1000 become the current price of $768

to find the annual pay YTM you would use the same above except number of years would just be N and not N*2 (gives a slightly higher number obviously). This is the number that would make $1000 become the current price of $768 when discounted annually instead of semi-annually

Yield To Call simply substitutes the call price for the par value and the number of periods until the call date is substituted for the number of periods until maturity

Yield to First Call simple subsitutes the call price for the par value and the number of periods until the first call date is subbed for the number of periods until maturity

Yield to Worst is the worst outcome of all possible provisions of the bond, so find worst case scenario (e.g. Yield to First Call) and calculate; usually the first date on which the money is repaid in some form (e.g. call, refunding, repayment)

Yield to Refunding is same calc as YTM or YTC but here the YTRefunding would use the call price but the date is the date when refunding protection ends

Yield to Put is used for bonds with embedded puts which are selling at a discount. Yield would likely be higher than YTM (advantage investor). The YTP calc is just like YTM but number of semi-annual periods until put date is N and put price is FV

NB Don't forget to:

N = ensure this multiplied by 2 or kept whole as appropriate
PMT = ensure divided by 2 or kept whole as appropriate
I/Y = don't forget to multiple by two as appropriate
take it easy when you input the numbers, the time will pay off

NB Bonds trading at a discount to par value, YTC will be higher than YTM; bond yields quoted on a yield to call basis when the YTC is less than the YTM which can only be the case for bonds trading at a premium to the call price

Cash Flow Yield (CFY) is used for mortgage backed securities and other amortising asset-backed securities. Amount of principal repayment can be greater than the amount required to amortise the loan over its life. Once cash flows are projected, calculate CFY as a monthly IRR based on the market price of the security.

Primary LIMITATION of YTM is that it does not consider the rate of return we might receive on the reinvested coupon payments i.e. assumes that everything appreciates at the same rate (YTM) whereas in real life the investor might reinvest the coupon payments in a riskier, higher yielding security and may not hold the bond until maturity.

The realised yield is usually computed at the end of the investment horizon (when all the reinvestment rates are known) and captures the reinvestment rate of the coupon payments. If the coupons are invested at a rate equal to YTM then the YTM = realised yield

LOS 65c - Explain the importance of reinvestment income in generating the yield computed at the time of purchase, calculate the amount of income needed to generate that yield and discuss factors that affect reinvestment risk

The realised yield will always be between the YTM and the (assumed) reinvestment rate

Once we calculate the total amount needed for a particular level of compound return over a bond's life, we can subtract the principal and coupon payments to determine the amoutn of reinvestment income necessary to achieve the target yield.

So, to calculate the required reinvestment income needed to get a compound return of X:
1. calculate the FV of the par based on the required rate of return
2. subtract the principal payment (plus any discount/premium from par) plus the coupon payments e.g. 180.61 - 100 - 60 = $20.61

LOS 65d - Compute and interpret the BEY of an annual pay bond and the annual pay yield of a semi-annual pay bond

i.e. turn a semi-annual return into an annual return and vice versa

BEY = [ (1+ annual pay YTM)^1/2 -1] * 2

EAY = (1+ semi-annual pay YTM/2)² -1

NB must nail down relationship between BEY and YTM. BEY converts annual YTM to what it would be at semi-annual compounding and allows for the comparisons with semi-annual compounding securities. EAY does the opposite i.e. "converts" a semi-annual paying YTM to annualised so it can be compared to annual paying securities.

LOS 65e - Describe the methodology for computing the theoretical Treasury spot rate curve and compute the value of a bond using spot rates

begin with the 6 month spot rate

set the value of the 1 year bond equal to the present value of the cash flows with the 1 year spot rate divided by 2 as the only unknown

solve for the 1 year spot rate

use the 6 month and 1 year spot rates and equate the present value of the cash flows of the 1.5 year bond equal to its price, with teh 1.5 year spot rate as the only unknown

solve for the 1.5 year spot rate

Valuing a bond using spot rates

sum the discounted value for each of the cash flows at the appropriate rate/2 and number of periods e.g. for the second coupon payment, discount it at the 1 yr spot rate/2; the final payment (at 1.5 years) would be the discounted value of final payment plus the coupon rate using the spot rate for 1.5 years divided by 2 and the number of periods would be 3

LOS 65f - Differentiate between the nominal spread, the zero-volatility spread and the option-adjusted spread

nominal spread = YTM for bond minus YTM for Treasury of similar maturity
nominal spread suffers from same limitations as YTM and ignores the shape of the spot curve (assumes it is flat)

zero-volatility spread = in order to value a bond correctly, we have to increase each of the Treasury spot rates by some equal amount so that the PV of the risky bond's cash flows discounted at the (increased) spot rates equals the market value of the bond.

use trial and error to solve this.

Discount each of the cash flows by the spot rate plus some fixed estimated amount until you hit the amount that will discount the cash flows such that they equal the price of the bond

NB the nominal spread assumes the spot rate curve is flat, therefore, if the spot rate curve is upward sloping, the zero volatility spread (which is based on the spot rate curve) will be higher than the nominal spread and if it is downward sloping the zero volatility spread will be lower than the nominal spread

NB similarly, if the bond is amortising such as an MBS the diff. between the nominal and the zero volatility spread will be higher than regular bond; also, the earlier the principal is paid off, the greater the difference between the two spread measures

the option adjusted spread (OAS) This is a measurement tool for evaluating price differences between similar products with different embedded options.

A larger OAS implies a greater return for greater risks. This measure removes the effect of options or prepayment on the spread and allows for comparison between products.

The OAS is the spread for non-option characteristics such as credit risk, liquidity risk, and interest rate risk.

LOS 65g - Describe how the option-adjusted spread accounts for the option cost in a bond with an embedded option

option cost in percent = Z-spread - OAS

A callable bond: option cost > 0 (investor is compensated) and OAS > Z-spread

A puttable bond: option cost <>

LOS 65h - Explain a forward rate and compute spot rates from forward rates, forward rates from spot rates, and the value of a bond using forward rates

Borrowing for X years at the Xyear rate should cost the same as borrowing for 1 yr periods, X years in succession. So the spot rate for 3 years will be the same as the geometric mean of the three separate forward rates.

uses forward rate notation such that _xf_y is the forward rate for an x year loan to be made y years from now so...

(1+S₃)³ = (1 + ₁f₀)(1+₁f₁)(1+₁f₂) for finding a forward rate three periods from now

S₃ = [(1 + ₁f₀)(1 + ₁f₁)(1 + ₁f₂)]^1/3- 1 for finding a spot rate equivalent to forwards for three periods

The latter is familiar - it is the geometric mean b/c you are finding the single return that creates the same PV of the cash flows as the single rate in the X year loan.

A spot rate for a maturity of N periods is the geometric mean of forward rates over N periods. The same relation can be used to solve for a forward rate given spot rates for two different periods.

To find a forward rate from a spot rate use the first formula and isolate the unknown on one side of the equation e.g. say we know the spot rate for a two year bond is 8% and we know the current 1 period spot rate is 4% then we can calulate the missing 2nd year forward rate using (1+0.08)² = (1 + 0.04)(1+₁f₁) minus one
divide both sides by 1.04 to isolate the unknown:

(1.08)²/1.04 = (1+₁f₁) and we get 1.1664/1.04
or 1.12154 = 1+ 1f1 = 1.12154-1 = 12.154%

why do we want to do this? to know whether it is better to buy the one period bond or the two period bond. In this case, we know buying a one year bond for 4% and a forward rate one year bond for one year from now at 12.154% is better than buying one 2 year 8% bond

multiple years calculation

if you know the 1, 2 and 3 yr spot rates, you can back out to the 1 yr forward and the 2 yr forward. in the above example, we found the 2 yr foward rate. if we know the 3 yr spot rate is 12% we can do the same thing again except using cube of the three year equal to the product of the known one year forward rates (including the unknown):

(1.12)³ = (1.04)(1.12154)(1 + x)
1.4049/(1.04)(1.12154) = 1 + x
1.4049/1.1664 = 1+x
1.2045-1= x
20.45% = x

Quick and dirty way = is to use a simple average of the spot rates to solve for the forward rate; may come close enough to answer the question

Calculate price of T-note using spot rates use the appropriate spot rate for each cash flow to discount the cash flow over the appropriate number of periods e.g. a cash flow of $20 in the second period when the spot rate is 5% would be N=2, I/Y = 2.5, FV=$20, CPT PV

Calculate implied forward rates for loans for more than one period given spot rates of: 1 yr = 5%, 2 yr = 6%, 3 yr = 7% and 4 yr = 8% we can calculate the implied rate on a two year loan two years from now by:

[(1+S4)⁴/(1+S2)²]^1/2-1 = [1.08⁴/1.06²]^1/2-1 = 10.04%

i.e. raise the larger year spot rate to the power of the number of years in the future and divide by the smaller of the years raised to the power of the number of year in the future and then take the x root where x is the duration of the loan in years

Computing a bond value using forward rates

Discount each cash flow by the relevant periods and sum them together. e.g. if one of the cash flows takes place two years from now, discount it by the two year forward rate and then again by the one year current rate.

So if 1 yr rate is 4%, 2 yr forward is 5% and 3 yr forward is 6% and we want to find the value of a 3yr 5% coupon bond with face value of $1000 then we do the following:

(50/1.04) + (50/(1.04)(1.05)) + (1050/(1.04)(1.05)(1.06)) = $1000.98

READING 66

Please let me get to the end of these books... it's scary to think how relieved i will be when all i am doing is revising instead of learning. There is so much i feel i don't have a handle on right now.

full valuation or scenario analysis approach to measuring interest rate risk is based on applying the valuation techniques we have learned for a given change in the yield curve. for more complex bonds, a pricing model incorporating yield volatility as well as specific yield curve change scenarios is required to use full valuation approach. if valuation model is sufficiently good, this is the theoretically preferred approach

duration/convexity approach provides approximationof the actual interest rate sensitivity of a bond or bond portfolio -- for parallel shifts in the yield curve

bond characteristics on duration (price sensitivity)

higher coupon = lower duration (and vice versa)

longer maturity means higher duration (and vice versa)

higher market yield = lower duration (and vice versa)

all of these relations are intuitive if you stop to think about it instead of just memorizing them. If my bond is paying me a lot of money in coupons, I'm less concerned about my ability to invest elsewhere and there will be strong demand for my bond. The longer my bond has to maturity, the more sensitive it will be to interest rate changes because you will be locked into the bond for a longer period and if prices change for the worse, you are stuck with an asset that is no longer as attractive relatively. The shorter the maturity, the closer I am to collecting money and the less uncertainty I have about my assets value. if interest rates go down, I will shortly be able to take advantage of them. the higher my market yield, the lower my sensitivity to interest rate changes for similar arguments advanced above about high coupons.

positive convexity
wow. that term sounds like you're smart when it's actually a pretty simple concept:

yield and prices for bonds are negatively correlated so yield curve is downward sloping

this inverse relationship is not a simple straight line but a curve bending toward the origin

the shape shape of this curve determines the severity of a change in price/yield at each level

the positive convexity will mean that as yields increase, price decreases at a decreasing rate i.e. prices rise faster than they fall for a given change in yield down or up which is a good thing for a bondholder

for price-yield relationship to be convex, the slope (rate of decrease) of the curve must be decreasing (level out) as move from left to right

duration = slope of price-yield curve at any given point

Callable Bonds, Prepayable Securities, and Negative Convexity
All of these securities come with enhanced risk/uncertainty for the bondholder because at certain points, the security could be essentially redeemed/paid off and the bondholder has to find a place to reinvest the money (reinvestment risk).

upside price appreciation is limited (price compression) because as interest rates go down, debtors will be more likely to pay off principal and issuers will more likely call the bond in when it hits the call price (so they can refund for a better rate on their debt)

so for callable bonds the curve bulges out on the left hand side up to the call price, so as yields decrease the price increases at a decreasing rate (which makes sense - lower demand as we approach call price) or negative convexity... as move to the right along the curve, the curve returns to positive convexity

In the above diagram, the *P price is the call price and the yield that matches the call price is *Y

The curve for yields below *Y will exhibit negative convexity and will eventually flatten out as we approach the call price *P

Price volatility for lower yields will naturally be lower for a callable bond than an option free bond (more certainty with callable bond around that price-yield area)

The curve for yields above *Y will exhibit positive convexity

MBS or similar securities with prepayment risk will exhibit similar behaviour and therefore have greater reinvestment risk, especially as yields fall

Price volatility characteristics of putable bonds

Less price volatility at higher yields because as the yield rises, price falls and the put becomes more valuable

Put option is of no value when price is above the putable price and it behaves just like an option free bond

NB all of this information about convexity implies that i should be able to determine whether a bond has call (or prepayment) or a put depending on the % change in price up or down relative to a parallel shift up or down in yield... but it is difficult because an option free bond would still have a price which drops slower than it rises. I guess it would depend where i am on the curve.

Effective Duration

remember: duration is ratio of % change in price/% change in yield
given convexity, we know price increases faster when rates fall x than price decreases when they rise x

effective duration uses the average of the price changes in response to equal increases and decreases in yield to account for this fact

if we have a callable bond trading in the area of negative convexity, the price increase is smaller than the price decrease but using the average still makes sense
formula effective yield =

(bond price when yields fall - bond price when yields rise)
2*(initial price)*(change in yield in decimal form)

or average price change (difference between the bond prices divided by 2) divided by current price (so it is now average price as a percentage of current price) and then divided by the change in yield in decimal form (to get change in price as a percentage of current price expressed as a precentage of the change in yield)

Looking at the formula step by step helps me remember it. Much watch my fat fingered mistakes on the calculator.

NB if the question shows a parallel yield shift of 50 bps e.g. current rate is 10% and we want to know the price change at 9.5% and 10.5% then the change in yield will be 50 bps or 0.005% because this is the swing either side

Also helpful:

price increase in response to the 0.005 decrease above would be PYieldDown-InitialPrice/InitialPrice

price decrease in response to the 0.005 increase above would be PYieldUp-InitialPrice/InitialPrice

The average of the percentage price increase and the percentage price decrease.
If the change in yield was 50 bps, we can find the duration by multiplying the price change by two to get the percent change in price for a 1% change in yield.

Using effective duration
Once you have your effective duration (e.g. -2.5) for say a bond when yield increases by 50bps, you can calculate the new up or down price by:

percent change in bond price = - effective duration x change in yield in percent
or -2.5 * 0.005 = 0.0125 = 1.25%
so if the bond were priced at $100, it would now be worth $98.75

Other types of duration...

Macaulay duration = estimate of bond's interest rate sensitivity based on the time in years until the promised cash flows will arrive; because Macaulay duration is based on the expected cash flows for an option free bond, it is not an appropriate estimate of the price sensitivity of bonds with embedded options

Modified duration = derived from Macaulay duration and is slight improvement b/c it takes the current YTM into account; also based on expected cash flows for option free bond so not good for bonds with embedded options

Effective duration is the most appropriate measure of interest rate risk for bonds with embedded options because effective duration is calculated from expected price changes in response to changes in yield that explicitly take into account a bond's option provisions (i.e. they are the price-yield function used).

Interpreting Duration

duration is the slope of the price-yield curve at the bond's current YTM
(Macaulay) duration is a weighted average of the time (in years) until each cash flow will be received; the weights are in proportions of the total bond that each cash flow represents
duration is the approx. change in price for a 1% change in yield (price sensitivity to a change in yield)

Duration of a portfolio is just the weighted (by market value i.e. market price * par value e.g. 102 * 1,000,000 means 102% of 1,000,000 or 1,020,000) average of the individual bonds within the portfolio

duration is a good measure of the sensitivity of portfolio value to parallel shifts in the yield curve; changes to the shape of the yield curve may affect different securities differently and this will not be captured in the portfolio duration

convexity is a measure of the curvature of the price-yield curve; a straight line has a convexity of zero

duration assumes the price-yield curve is zero (ignores changes in shape) and will underestimate the price of the bond (except when curve is flat)

A bond's approximate percentage price change based on duration and convexity
Combining duration and convexity gives us more of a full picture and a more accurate estimate of the % change in price of a bond - esp. for large changes in yield

percentage change in price = duration effect + convexity effect

= {[-duration * change Y] + [convexity * (changeY)²]} * 100

with changeY entered as a decimal, the *100 is necessary to see it as a percentage

watch out: the duration will be negative when yield rises and positive when yield falls so percentage change in price will be different for a rise than for a fall i.e. will not both rise and fall by x. Say duration is -2% (yield has risen) and convexity is 8% then total change will be 6% but if yield falls and duration is +2% then total change will be 10% (2+8)

when convexity is negative (e.g. low yields cause negative convexity for callable bonds) the convexity adjustment to the duration-only based estimate of the percentage change will be negative for both yield increases and decreases

Effective Convexity takes into account changes in cash flows due to embedded options while modified convexity does not and therefore effective convexity is the appropriate measure for bonds with embedded options just as effective duration is appropriate for measuring bonds with embedded options instead of modified duration

Price value of a basis point (PVBP) is the dollar change in the price/value of a bond or portfolio when the yield changes by one basis point or 0.01%

PVBP = duration * 0.0001 * bond value

This is actually a little more complicated than it looks. Don't forget that semi-annual effective durations will need to be multiplied by 2 to get annualised version. if you want to know the difference in price. It is actually:

PVBP = initial price - price if yield changes by 1bp

calculate the duration (e.g. 5%) and add one basis point (5.01) and redo the calculation using this new rate and then find the difference between the two prices.

Study Session 7 - Financial Reporting and Analysis

2010-02-09T16:19:00.000-08:00

Classification of Business Activities

Operating Activities = day-to-day business activities
Investing Acvitivies = investment in long term assets (inc. securities/physical plant)
Financing Activities = borrowing or repaying capital

Within each of these any activity can be classified as (OREAL):

Owner's Equity = residual claim on the resources of the company, partner's capital
Revenue* = inflows of economic resources to the company
Expenses* = outflows of economic resources or increase in liabilities
Assets = economic resources of a company
Liabilities = creditors' claims on resources of a company

* Gains and Losses are like Revenue and Expenses but arise from secondary activities outside of operating activities e.g. selling excess equipment for more than its value would be a gain, decline in the value of inventory would be a loss

Accounts are subcategories under each of the OREAL headings e.g. under assets might be the accounts of cash, accounts receivable, inventory etc. These may then be grouped under each of the OREAL headings to further summarise the books.

Actual accounts are set forth in a chart of accounts

contra accounts = accounts that are used to offset other accounts e.g.

allowance for bad debts offsets trade receivables,
accumulated depreciation offsets property, plant and equipment,
sales and allowances offsets revenue and reflects discounts etc. for unsatisfactory goods etc.

COMMON ACCOUNTS

Assets (tend to be listed in the order of liquidity)

Cash and cash equivalents
Accounts receivable, trade receivables
pre-paid expenses
inventory
property, plant and equipment - noncurrent
investment property - noncurrent
intangible assets (patents, trademarks, licenses, copyright, goodwill) - noncurrent
financial assets, trading securities, investment securities
investments accounted for by the equity method
current and deferred tax assets
[for banks, loans receivable - b/c that is their business
noncurrent assets benefit company over extended period of time (over one year)
current assets expected to be consumed within a year or converted into cash

Liabilities

Accounts payable, trade payables
provisions or accrued liabilities
financial liabilities
current and deferred tax liabilities
reserves
minority interest [equity owned in subsidiaries?]
unearned revenue
debt payable
bonds (payable0
[for banks, deposits - b/c these are the amounts the bank is 'borrowing']

Owner's Equity

Capital such as common stock par value
additional paid-in capital
retained earnings
other comprehensive income

Revenue

Revenue, sales
Gains
Investment income (e.g. interest and dividends)

Expenses

Cost of goods sold
Selling, general, and administrative expenses (SG&A) e.g. rent, utilities, salaries, advertising
depreciation
interest expense
tax expense
losses

Accounting Equations

balance sheet

Assets = Liabilities + Owner's Equity
Assets - Liabilities = Owner's Equity
Owner's Equity = Contributed Capital + Retained Earnings
Expanded: Assets = Liabilities + Contributed Capital + Beginning retained earnings + Revenue - Expenses - Dividends
A = L + CC + RE(beg) + R - Ex - Div

income statement

Revenue - Expenses = Net income

ending retained earnings

ending retained earnings = beg. RE + Net Income - Dividends
ending retained earnings = beg. RE + (Revenues - Expenses) - Dividends

Retained earnings = the net income retained by the company and not distributed as dividends; usually kept for investment. RE is a component of owner's equity and links the "as of" balance sheet equation with the "activity" equation of the income statement, so

Assets = Liabilities + Contributed Capital + Beginning Retained Earnings + Revenue - Expenses - Dividends
if asked to calculate this remember Assets = everything else - (expenses + liabilities)

Retained Earnings is the net earnings not distributed as dividends and as such shows up on the Balance Sheet (under shareholder's equity). The income statement will tell you how much net income has increased during a period and the net income will be added to existing retained earnings.

Income Statement and Statement of Retained Earnings show movement over a period (in and out, plus and minus) whereas balance sheet just shows snapshot

Rules of Thumb:

selling something for x that cost y has two parts:
- the cash received increases cash (asset) by x and revenue (income) by x and
- decreases inventory (asset) by y : offset by increase in COGS (expense) by y
- so in balance sheet cash asset is increased, inventory asset is decreased, difference between the two is profit (retained earnings)
- in income statement revenue is increased under income and COGs is increased under expenses and difference is reflected in net income
when you purchase something that will last over multiple periods, you are just converting one asset (cash) into another - so you reduce cash asset and increase the bought asset total
when you purchase a something that you will consume in the current period, it is an expense
when you purchase something on credit, the asset is offset in liabilities (accounts payable)
unearned fees are identical to unearned premiums therefore liabilities which are earned incrementally e.g. each month you might earn one more month's worth of the unearned premiums so liabilities would decrease by one month value and fee revenue would increase by one month value
contributed capital is both an asset (cash) and owners' equity (since the owners have a claim on this economic resource); liabilities reduce the owners' equity since liabilites represent creditors claims on the resources (which supercede the shareholders)
Receiving cash for services not yet rendered adds cash to the assets but adds the same amount in liabilities (unearned fees)
Receiving cash for services rendered counts as revenue (if it is from operations)
Assets and Liabilities = balance sheet
Revenues and Expenses = income statement
Borrowing increases cash and adds liability of bank debt
pre-paid rent and rent deposits are assets; when rent is paid, pre-paid rent asset is decreased by x and logged as an expense of x
anything paid before it is billed is recorded as an asset until such time as the bill is received and the money is recorded as an outflow
wages earned but not paid are recorded in b/s as accrued wages and in income statement as payroll expense
investment gains are logged as unrealised gains under revenue
interest income is revenue and asset (investment)
interest from debt owed is logged as liability (interest payable) and an expense (income statement). If monthly accounts, then annual interest is divided by compounding periods
equipment is logged as an asset (say $120) and then depreciated over time. Say it has a year's usefulness then depreciation will be $10 per month ($120/12) which will be logged as a contra asset (balance sheet) and an expense (income statement) each month

Relationships

Balance sheet contains Assets, Liabilities and Shareholders' Equity
Cash is broken down in the Statement of Cash Flows
Income Statement breaks down all cash flows e.g. net income from Owners' Equity Statement, revenues/expenses on statement of cash flows
Shareholders' Equity is broken down in the Statement of Owners' Equity

Definitions and Purpose of Statements

Balance Sheet is a snapshot of assets, liabilities and b
Income Statement shows profitability over time through details of revenue, expense and resulting net income
Statement of Cash Flows provides info about cash flows over a period from operating, financing and investing activities
Statement of Owners' Equity provides information about the composition and changes in equity during a period

Accruals

Unearned (deferred) revenue

originating recorded as cash receipt and as a liability
adjusting reduce liability while recording revenue

Prepaid Expense

originating record cash payment and establish an asset
adjusting reduce asset while recording the expense

Unbilled (accrued) revenue

originating record revenue, establish an asset
adjusting when billing occrus, reduce unbilled revenue and increase accounts receivable; when cash is collected, eliminate accounts receivable

Accrued Expenses

originating establish a liability and record an expense
adjusting reduce the liability as cash is paid

Accounting Systems

Flow of information in an accounting system:
Journal entries > GL and T-Accounts > Trial Balance > Financial Statements

Cooking books if you want to cook the books, you must find an offset e.g. if you want to report more revenue then you need to create an asset to generate the revenue, if you want to conceal a cost then you need to create a liability to be the cause of that cost

Study Session 5

2010-02-02T16:46:00.000-08:00

Just some quick notes:

MRP = the amount of $ you make from the extra stuff you sell because you hired one more guy. This in turn determines demand for labour (or any other productive input). Therefore, MRP equilibrium will always equal the cost of the input (e.g. wage for the worker day) because any more and you would make a loss.

Physical capital is actual stuff you spend money on which helps you make products. The demand for physical capital is also determined by the MRP of that input (e.g. bulldozer) except that the difference here is that your return on investment in physical capital is seen over many periods. The PV of the MRP's derived from investing in that bulldozer determines the value of investing in that item and determines demand. Kind of like IRR for projects?

SAS vs LAS - Short Run Aggregate Supply and Long Run Aggregate Supply
Aggregate supply is the amt of goods and services produced by an economy and is a function of price level (higher prices increase supply).

General Rules

This is all about regression to the mean. The mean in this case is the level of GDP at full employment.

The swings back and forth are cause by the usual suspects:

higher prices of goods and services cause more supply
higher price of inputs (inc. labour) causes marginal cost to rise, supply to fall
oversupply of labour will cause wages to fall and demand for labour to increase to equilibrium
oversupply of goods/services will cause prices to fall and demand for goods/services to increase to equilibrium
if workers' fears of inflation do not (yet) match actual inflation, we temporarily move along the SAS curve and out of equilibrium until workers' expectations are equal with actual inflation i.e. when workers' fear future inflation, they demand higher wages which increases marginal cost of producing and suppliers will produce less at the same price. Fewer workers employed causes downward pressure on wages as more people compete for fewer jobs and with lower wages come lower marginal cost/higher employment/more supply of product and we return to equilibrium

NB note difference between things that cause a move along a curve and things that cause the whole curve to shift.

SAS is the short term fluctuation either side of the equilibrium supply level (LAS). Movements along this curve are caused by worker expectations about inflation as seen above. Shape of the SAS curve comes from supply at different price levels. Supply increases as price rises so curve is upward sloping.

LAS is level of supply of goods and services when economy is operating at full employment (i.e. only structural and frictional unemployment). This is the natural rate of unemployment and produces the real level of GDP (output). Assumes that workers' view of inflation is in line with reality.

Potential output is positively related to (1) the quantity of labour (2) the quantity of capital and (3) the technology that the economy possesses

In the short run, we are holding money wages (and prices of all inputs) and potential GDP constant.

If the wage rate or prices of other productive inputs increases, the SAS curve will shift to the left, a decrease of aggregate supply in the short run.

Two factors influence change in money wage rates (and cause shift in SAS):

unemployment
inflation expectations

LOS 23b: Explain the components of and the factors that affect real GDP demand, describe the aggregate demand curve and why it slopes downward, and explain the factors that can change aggregate demand.

AD curve shows the relationship between the price level and the real quantity of final goods and services (real GDP) demanded and is made up of:

CIGX = Consumption + Investment + Government Spending + Net eXports

AD is downward sloping as expected because at high price levels, consumption, business investment, and exports will decrease due to the following effects:

when price level rises, real wealth declines so people spend less (wealth effect)
when price level rises, interest rates rise which decrease investment as well as consumption because borrowing cost is higher; consumers delaying purchases in this case is an intertemporal substitution as consumers substitute consumption later (when it is relatively cheaper) for consumption now (which is relatively expensive)

What shifts the AD curve?

Expectations about future incomes, inflation, and profits
Expectations of inflation will cause current spending to increase (inexpensive compared to future); expectations of higher incomes will increase consumption; increase in expected profits will increase investment
Fiscal and monetary policy Gov spending increases G component of demand; decrease in taxes or increase in transfer payments (e.g. Soc Security) will increase demand through increase in consumption (more money in pockets); increase in money supply tends to decrease interest rates and increase consumption and investment
world economy - FX rates and countries' incomes affect their ability to consume other countries' goods and services.

LOS 23c. Differentiate between short-run and long-run macroeconomic equilibrium and explain how economic growth, inflation, and changes in aggregate demand and supply influence the macroeconomic equilibrium

If equilibrium is price = 100 everything is good, full employment, equilibrium output of GDP
At 115, there is excess supply since aggregate supply has outstripped aggregate demand. This is a recessionary gap and will cause downward pressure on prices as suppliers restrict supply and try to shed excess inventory and will move the price back to equilibrium.
At 90, aggregate demand has outpaced aggregate supply = upward pressure on prices and increase of supply - the inflationary gap - as businesses experience unanticipated shortages. return to equilibrium price.

As the price level changes, we move back and forth along the AD curve, regressing toward equilibrium.

Shifts in the short run AS curve are part of the process of moving toward equilibrium i.e. the economy can be in short run equilibrium above or below long term equlibrium.

Economic expansion shift in AD/AS curves = AD outpaces LAS = above full employment = upward pressure on prices. Inflation causes real wages to decline which causes workers to demand more $. More demand for workers (we are above full employment) also causes wages to rise. This increases marginal cost of production which decreases demand for workers (pushing employment back to equilibrium) and decreases supply at the current price (since production is more expensive due to wage increase and fewer employed workers means lower AD) which returns supply to equilibrium.

increase in any input/resource price will cause supply of resulting product to decrease at each price level and causes SAS to decrease.

Recession shift in AD and AS curves = AD is less than equilibrium so fewer workers are employed (less than full employment = structural + frictional + cyclical) and output (GDP) is lower than equilibrium = excess supply of labour = wages/input prices fall = marginal cost falls = increase in SAS of goods and services (now cheaper to produce at same price level) = greater supply in short term = lower prices = increase in demand = more demand for labour = return to equilibrium

LOS 23d: Compare and contrast the classical, Keynesian, and monetarist schools of macroeconomic

All are trying to explain deviations from equilibrium.

Classical economists = shifts in both AD and AS driven by changes in technology over time and that economy has a strong tendency toward full employment equilibrium as either recession or over-full employment lead to decreases or increases in the money wage rate. Taxes are impediment and cause inefficiencies in this process.

Keynesian = shifts in AD due to change in expectations and that wages were "downward sticky" (i.e. they refuse to fall at the rate they should) reducing the ability of a decrease in money wages to increase SAS and move econo0my from recession (or depression) back toward full-employment. Keynesians think this can be nudged by increasing money supply (monetary policy) and/or increasing gov spending, decreasing taxes or both (fiscal policy).

Monetarists believe that monetary policy is the key influence over boom and bust i.e. recessions are cause by inappropriate decreases in the money supply so keep the money supply steady with predictable increases.

Monetarists share the Keynesian belief in downward sticky wages and input prices and share the classical view that taxes cause inefficiencies.

LOS 24h: Explain interest rate determination and the short run and long run effects of money on real GDP

In the short run
If the Fed increases the money supply (by buying back treasuries and other securities on the open market), this will decrease the interest rate because there is more cash in the hands of banks who compete to supply this now more abundant cash. Multiplier effect as people spend and more people have cash which banks can then lend again.
Decreased interest rates encourage Investment and Consumption (which increase AD aggregate demand).
Low interest rates cause foreigners to move money out of the country to places where it can earn more which lowers the FX rate for that currency which makes eXports cheaper and increases net eXports.
Long run effect = higher price level, same GDP
Increased demand for goods and services pushes up the price level (inflation) which increases wages and increases MC causing a decrease in SAS to equilibrium GDP of LAS with the price settling at a higher equilibrium price and interest rate returning to equilibrium (because people want to spend less because prices were higher, demand for money is lower).
contractions in the money supply (by Fed selling securities) would have the opposite effect.

Study Session 3 - Reading 12 Technical Analysis

2010-01-12T13:22:00.000-08:00

LOS 12a. explain the underlying assumptions of technical analysis;

Technical analysts believe in the following:

that history repeats itself, so look for trends
trends persist over an appreciable length of time
value and prices are determined by supply and demand
causes are difficult to determine but shifts in supply/demand reveal themselves in market pirce behaviour

Efficient Market Hypothesis (EMH) analysts are opposed and believe:

market prices follow a random (unpredictable) walk
new information gets immediately priced in
that technicians are wasting their time; too subjective and looking for past trends that never reoccur the same way

Fundamentalists are more in the technical camp but they believe that causes for price behaviour can be observed through analysing earnings and publicly available data - that the economic fundamentals such as return vs. risk determine market prices

Technicians look for a price move; expect price move to happen fairly quickly as new data is observed and processed by the market
Fundamentalists look for why the price will move; expect price move to happen slowly
EMH analysts that when price shifts happen, the happen rapidly - instant digesting of new information by the market

LOS 12b. discuss the advantages of and challenges to technical analysis;

Technical analysis pros:

quick/easy
no accounting data needed
incorporates pyschological and economic reasons
tells you when to buy (but not why)

Technical analysis cons:

too subjective
historical relationships may not be repeated
EMH belief that models cannot predict random price walk
technical trading rules would be self-fulfilling
if successful, trading rules would be copied and erase the arbitrage

LOS 12c. list and describe examples of each major category of technical trading rules and indicators.

Four classes of technical trading rules/indicators:

contrarian = opposite of what majority is doing
smart money followers = buy when smart money buys, sell when it sells
momentum indicators = when market moves in a direction, buy/sell with it
price-and-volume = look for significant corresponding movements in both price and volume and act accordingly

Contrarian Opinion Rules

Cash position of mutual funds if mutual fund cash ratio (mut.fund cash/total assets) is high(>11%) then funds are bearish (so contrarians buy). If low (<4%)>
Investor credit balances in brokerage accounts Falling credit balances mean normal investors are bullish and buying (so contrarians sell)
Opinions of investment advisory services if bearish sentiments index is high (>60%) then contrarians buy.
OTC vs. NYSE volume OTC are more speculative. A high ratio of OTC to NYSE means normal investors are bullish (so contrarians sell).
CBOE put/call ratios If ratio is high (>0.6) then most normal investors are trying to sell, so contrarians buy. Low (<0.4)>
Stock index futures When future traders are bullish (>70%) then contrarians sell.

Smart money rules

three indicators:

Confidence Index (CI) by Barrons = ratio of yields on high grade bonds to yields on broader (riskier) bonds. So if CI is high, investors are confident and are selling high grade bonds to buy better earning lower grade bonds. If CI is up, smart money investors are buying.
TED - T-Bill/eurodollar yield spread - spreads widen during crisis, flight to Treasuries. Smart money is bearish.
Debit balances in brokerage accounts (margin debt) - if margin debt is high, smart money is buying (bullish).

Momentum indicators

Breadth of market

indices represent a few, large companies
market has many medium/small companies
index may go one way while smaller issues go the other way
comparing advance-decline line and index - if they move together, then there is a broad market movement

Stocks above their 200 day moving average

if over 80% of stocks trade above their 200 day avg then the market is overbought (therefore bearish). if 20% are above 200 day avg then market is oversold (therefore bullish)

Stock Price and Volume Techniques

Dow Theory = stock prices move in trends: major trends, intermediate trends, short-run movement. Technicians look for reversals and recoveries in major market trends

Volume price changes on high volume tell us whether suppliers or demanders are driving change.
upside/downside volume ratio = vol. of stocks that increased/vol. of stocks that declined
If ratio is 1.75 or more, market is overbought (bearish). If less than 0.75 then market is oversold (bullish)

Support/resistence levels most stock prices are stable; fluctations up hit resistence, flux down receives support
Moving average line trends again. Random flux masks trends. By using moving averages (10 to 200 days) true trends will appears amongst the noise of randomness
Relative strength = stock price/market index value i.e. is a stock outperforming the market (positive trend) or underperforming relative to market

Study Session 3 - Reading 11 Hypothesis Testing

2010-01-12T13:18:00.000-08:00

LOS 11a. define a hypothesis, describe the steps of hypothesis testing, interpret and discuss the choice of the null hypothesis and alternative hypothesis, and distinguish between one-tailed and two-tailed tests of hypotheses;

hypotheses is a statement about the value of a pop parameter developed for the purpose of testing a theory or belief
1. state hypothesis
2. choose test statistic e.g. mean
3. choose level of significance
4. state decision rule
5. collect sample/calculate sample statistics
6. decision on hypothesis
7. investment decision
null hypothesis H₀ is the thing you want to reject and is usually what it would mean to end up outside the confidence interval and might be x = 5 or x > 6
alternative hypothesis H_a is the thing you want to "prove"
use one tailed for greater than or less than
use two tailed for equalities
most are two tailed

OK. I found this a little confusing - usually my problem was that I couldn't quite figure out what I was proving at the end of it all. Must focus on a good rejection rule and applying it well. I'm going to spend some time here and include an example from Schweser because I found this confusing when I read it:

Example (two tailed):
We have data on daily returns on a portfolio of call options over 250 day period. The mean daily return has been 0.1% (0.001) and the sample standard deviation of portfolio returns is 0.25% (0.0025). researcher beleives that the mean daily return is not equal to zero (so our hypothesis is that it is equal to zero):

1. Ho: μ= 0, Ha: μ ≠ 0

Since this is an equality, use two tailed test for mean (#2). At 5% significance, we look up standard deviations in z table for 95% which is ±1.96 (#3). So we can come up with our decision rule:

4. Reject Ho if +1.96 <>

5. Calc. statistic by standardising the test statistic by dividing test stat (mean) by the standard error. This will convert it into standard deviations which we can then compare against our rule. So 0.001/standard error where standard error is 0.0025/sq.rt. 250 and we get 0.001/0.000158 = 6.33

6. Look back at decision rule in #4 and since 6.33 > 1.96 we reject null hypothesis.

7. We can conclude that the mean return is significantly different from zero given sample's standard deviation and size i.e. the two values are different from one another after considering the variation in the sample

Common error - i tend to misread 0.25% as 25 percent instead of 0.0025 etc.

LOS 11b. define and interpret a test statistic, a Type I and a Type II error, and a significance level, and explain how significance levels are used in hypothesis testing;
Hypothesis testing involved two statistics: the test statistic calculated from the sample and the critical value of the test stat

The test statistic is the difference between the sample stat (e.g. sample mean) and the
hypothesized stat (the one stated in the null hyp.), divided by the standard error
Type I error: rejection of null when it is actually true
Type II error: Failure to reject null when it is actually false
significance level α is the probability of a Type I error e.g. sig. level = 5% /95% confid.

LOS 11c. define and interpret a decision rule and the power of a test, and explain the relation between confidence intervals and hypothesis tests;

Decision rule is to reject or fail to reject null
decision is based on distribution of the test stat
typical decision rule: if test stat is (greater/less than) the value X, reject the null
power of a test is the prob of correctly rejecting null when it is false
power of test is all about rejecting; if you incorrectly reject then P = α, if you correctly reject then power of test = 1-P e.g. 95%
For any α, you can only descrease the prob of Type II (and increase power of test) by increasing sample size

Confidence Intervals and Hypothesis Tests

confidence levels are about comparing in actual units rather than standard deviations
[sample stat-(crit. value)(stand. error)]≤ pop parameter ≤ [sample stat.+(crit. value)(stand. error)]
this is intuitive: the pop parameter lies in a range of values depending on confidence interval. So if standard error is 0.0158 and sample mean is 0.1 and we want to be 95% confident, we mult. 1.96 (dev's for 95% prob) by the standard error and get 0.030968 which is the percentage deviation from the mean. So we know the pop parameter lies somewhere in the range of 0.1 ± 0.030968

LOS 11d. distinguish between a statistical result and an economically meaningful result;
This concept is basic. Even though you may get a statistically positive return, transaction costs may make erase/diminish it so your investment decision must take this into account

LOS 11e. explain and interpret the p-value as it relates to hypothesis testing;

p-value is prob of obtaining a test stat that would lead to rejection of null when it is actually true (type I)
It is the bit leftover in the tail(s)... so if we find our test stat in the tail past the critical value, the leftover bit(s) is the p-value (in two tailed tests, we sum the leftover bit in each)
If our test stat is found at 99% (at 95% conf., 2.5% in each tail) we would reject the null but there is still that 1% chance in each tail that we are wrong to do so

LOS 11f. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the population mean of both large and small samples when the population is normally or approximately distributed and the variance is 1) known or 2) unknown;

Rule of thumb: when in doubt use t statistic
Use t-test if pop variance is unknown and either small sample but normal or large sample
As we said earlier, small sample and unknown variance with nonnormal means we can't rely on the answer at all
calculate t stat as before in hyp testing i.e. diff between sample stat and hyp stat divided by standard error
the z stat and the t stat are calculated the same way except the t stat includes the degrees of freedom to derive the probability/deviations

Critical Z values - important!

two tailed test significance levels and corresponding critical z values

0.10 is ± 1.65
0.05 is ± 1.96
0.01 is ± 2.58

one tailed test

0.10 is +1.28 or -1.28
0.05 is +1.65 or -1.65
0.01 is + 2.33 or -2.33

LOS 11g. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the population means of two at least approximately normally distributed populations, based on independent random samples with 1) equal or 2) unequal assumed variances;

I sort of skimmed this because the formula is ridiculous but the summary is this:

for two independent samples from two normally dist. pop's, the different in means can be tested (to see if it equals zero i.e. they are the same number) with a z-stat
if variances are assumed equal the denominator is based on the variance of the pooled samples
when variances are assumed unequal, denominator is based on combination of the two samples' variance
otherwise testing of the hypo is done the same way once you have your result i.e. does it lie within or outside the chosen prob range

LOS 11h. identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations (paired comparisons test);

paired comparisons are done when the variables being tested are dependent in some way but the sample distributions are still normal
A t-stat is used in this case
t = avg difference of the n paired observations from hyp value/sample standard error

LOS 11i. identify the appropriate test statistic and interpret the results for a hypothesis test concerning 1) the variance of a normally distributed population, and 2) the equality of the variances of two normally distributed populations, based on two independent random samples;

Chi Square test of variances (normal distribution)

Chi square test is used for hyp tests concerning variance of normally distributed populations i.e. if i believe the variance to be a, my Ho: x ≠ a
chi-squared distribution is asymmetrical and approaches normal as df increases
looks lognormal i.e. bounded by zero, humped to the left
different prob in left tail than right tail - Chi-squared table captures this and is used by matching the df with the prob in the appropriate tail (NB divide sig level by two for two tailed tests)
Chi squared formula = (df * s²)/σ²_hyp
i.e. degrees of freedom mult by sample variance, divided by hypothesized variance

F-test for equality of variances of two normally distributed pops (independent random samples)

F-test is just variance2/variance1
Ratio of the variance in question with the larger one on top
Use F-table to support or reject hypothesis (match degrees of freedom for each sample - numerator df is on the top of the table)
rejection region is in the right side of the table
if you are looking at the difference in divergence/dispersion of earnings between two industries, use greater than in rule

LOS 11j. distinguish between parametric and nonparametric tests and describe the situations in which the use of nonparametric tests may be appropriate.

parametric tests rely on assumptions regarding distribution of population and are specific to pop parameters (hence the name)
non-parametric tests either do not consider a particular pop parameter or have few assumptions about the population that is sample
non-parametric tests are used when there is concern about quantities other than the parameters of a distribution or when the assumptions of parametric tests cannot be supported e.g. ranked observations

Study Session 3 - Reading 10 Sampling and Estimation

2010-01-12T13:15:00.000-08:00

LOS 10a. define simple random sampling, sampling error, and a sampling distribution, and interpret sampling error;

simple random sampling: every item has an equal chance of being selected
can be done by assigning a number to each item and using random numbers to select or by systematically choosing every nth item
sampling error = the difference between the sample stat (e.g. mean) and the corresponding population parameter (e.g. pop mean) i.e. how (un)representative is the sample stat
sampling distribution of the sample stat is probability distribution of all possible sample stats from a set of equal sized samples randomly drawn from same population

LOS 10b. distinguish between simple random and stratified random sampling;

simple random is just random or systematic sampling
stratified random sampling is proportionate - ensuring that the random sample contains a representative number of observations from each category e.g. different stocks

LOS 10c. distinguish between time-series and cross-sectional data;

time-series is looking at one category across multiple time periods
cross-sectional is looking at multiple categories during one single time period

LOS 10d. interpret the central limit theorem and describe its importance;

central limit theorem states that for a large enough sample size n (usually > 30) from a pop with a mean μ and a variance σ², the prob distribution for the sample mean will be approx. normal with a mean μ and a variance of σ²/n
Theory allows us to use normal distribution to test hypotheses about pop mean, regardless of distrib. of the pop
As the sample size grows, the sample stats become closer to the pop parameters
The sample mean will be approximately normally distributed.
The sample mean will be equal to the population mean (μ).
The sample variance will be equal to the population variance (σ2) divided by the size of the sample (n)
Thus the central limit theorem can help make probability estimates for a sample of a non-normal population (e.g. skewed, lognormal), based on the fact that the sample mean for large sample sizes will be a normal distribution.

LOS 10e. calculate and interpret the standard error of the sample mean;

standard error is the standard deviation (of the pop or, if not available, the sample) divided by the square root of the sample size
the sample mean and standard error can be used to calculate approximate confidence intervals for the mean i.e. the actual pop mean will lie between a and b with 95% confidence

LOS 10f. distinguish between a point estimate and a confidence interval estimate of a population parameter;

point estimate is a single sample value used to estimate pop parameters e.g. sample mean representing the pop mean where sample mean is a point estimate of the pop mean
confidence interval gives a range of values within which the actual value of a parameter will lie, given a probability of 1 - α (α is the level of significance)

LOS 10g. identify and describe the desirable properties of an estimator;

unbiased = the expected value of the estimator is equal to parameter you are trying to estimate
efficient = variance of sampling distribution is smaller than all other unbiased estimators
consistent = as sample size grows, estimator accurace increases i.e. standard error decreases

LOS 10h. explain the construction of confidence intervals;

confidence intervals are the point estimate ± (reliability factor * standard error)

LOS 10i. describe the properties of Student’s t-distribution and calculate and interpret its degrees of freedom;

Student's t-distribution is used when sample size is <>
It results in more conservative confidence intervals (curve is platykurtic - fat tails)
t-distribution is symetrical
defines by degrees of freedom (df) calculated by n-1 (sample size minus one)
t distribution converges to z distribution as sample size (degrees of freedom) becomes sufficiently large

LOS 10j. calculate and interpret a confidence interval for a population mean, given a normal distribution with 1) a known population variance, 2) an unknown
population variance, or 3) an unknown variance and a large sample size;

here we are trying to calculate the probability of the pop mean being within a certain range of values based on the sample mean distribution
when available, use population parameters to calculate the confidence interval
the calculation for when distribution is normal with known variance is:
where x is the sample mean,
z_α/2 is the reliability factor i.e. the z-score that leaves α/2 in the upper tail,
e.g. z_α/2 = 1.65 for 90% confidence (sig. level is 10% i.e. 5% in each tail) - might want to just think of this as 10% instead of thinking about the tails bit
and the last part is the standard error

So for example, you have a sample mean test score of 80% with a standard error of 5 at 95% confidence, then the true pop mean would be between 75% and 85% with 95% confidence

when variance is unknown, use t distribution:
here the t_α/2 part is the t-statistic corresponding to a t-distributed random variable with n-1 degrees of freedom

Rules of thumb for when to use t or z

if distribution is non-normal then small sample sizes do not work
if normal w/ known pop variance then use z statistic
if normal w/ unknown variance use t statistic
non-normals only work with large samples, use z or t depending on whether you know variance

LOS 10k. discuss the issues regarding selection of the appropriate sample size, data-mining bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias.

data mining = overestimating significance of a pattern in a data set; test pattern on out of sample data to confirm or deny overestimation of significance
sample selection bias = systematic exclusion of data from analysis, usually because unavailable (creates non-random samples)
survivorship bias = exclusion of samples such as using only surviving mutual funds in sample
look-ahead bias = basing the test at a point in time on data not available at that time
time-period bias = relation does not hold over other time periods

Study Session 3 - Reading 9 Common Probability Distributions

2010-01-12T12:50:00.001-08:00

LOS 9a: Explain a probability distribution and distinguish between discrete and continous random variables

A probability distribution is the probabilities of all possible outcomes for a random variable.
Discrete random variables are finite and countable (e.g. number of days on which it rained) whereas a continuous random variable can be an infinite number (e.g. rainfall for each day - the possible outcomes between 1 and 2 inches is infinite 1.00001, 1.0002, etc.) and is described as ranges instead (e.g. prob. that rainfall will be between 1 and 2 inches or, say, less than 1 inch).

LOS 9b: Describe the set of possible outcomes of a specified discrete random variable

For discrete distribution p(x)=0 when it cannot occur and p(x) > 0 when it can.
p(x) means the prob that rand. variable X=x
For continous distribution p(x)=0 even though x can occur (because x cannot be a single value) so only p(x1 <>
For price changes, generally use continuos e.g. prob. that price will be between $1 and $2

LOS 9c: Interpret a probability function, a probability density function, and a cumulative distribution function

Probability function p(x) is the prob. that a rand. variable = a specific value.
Two key properties:
- 0 ≤ p(x)≤ 1
- Sum of p(x) = 1 ... this makes sense since the sum of all probabilities should be 1
Both the PDF and the CDF are cumulative functions
A probability density function (or pdf) describes a probability function in the case of a continuous random variable. Also known as simply the “density”, a probability density function is denoted by “f(x)”. Since a pdf refers to a continuous random variable, its probabilities would be expressed as ranges of variables rather than probabilities assigned to individual values as is done for a discrete variable. For example, if a stock has a 20% chance of a negative return, the pdf in its simplest terms could be expressed as:
A cumulative distribution function (cdf) is constructed by summing up, or cumulating all values in the probability function that are less than or equal to x and is very similar to the cum. freq. except for probabilities. May be expressed as F(x) = P(x ≤ x)

LOS 9d: Calculate and interpret probabilities for a random variable, given its cumulative distribution function
Take a prob. function for X={1,2,3,4], p(x) = x/10 which means that for the set of the whole numbers 1,2,3,4 the probability of each is 10%, therefore, f(3) is 0.6 which is the sum of 1/10, 2/10 and 3/10 i.e. the cumulative probabilities of all numbers up to and including the number in question. Same process if the prob's are different for each outcome.

LOS 9e: Define a discrete uniform random variable and a binomial random variable

The above function is a discrete uniform random variable i.e. the prob. of each number occuring is equal i.e. for x={a,b,c] the p(a)=p(b)=p(c)
The prob. for a range of outcomes is p(x)k where k is the number of possible outcomes in a range
binomial random variable is the number of "successes" given a number of trials where the outcome is binary ("success" or "failure"). Might be used for the probability of a stock moving up once to $4.55 (the "success" is the up move might be duu where the d and u cancel) after n periods (the number of trials).
Definition of "success" is crucial to this working out.

LOS 9f: Calculate and interpret probabilities given the discrete uniform and the binomial distribution functions

In English, this says multiply the number of combinations that you could have x successes out of n trials by the proportionate prob of success and by the proportionate prob of failure.

Expected value of X for Binomial Random Variable
For a given series of n trials, the expected value is n * p
i.e. if we perform n trials and the prob. of success on each trial is p we expect np successes.

LOS 9g: Construct a binomial tree to describe stock price movement
this is fairly straightforward. Remember: If the up movement is 1.05 it means the price increases by 5% so mult. 1.05 by the stock price. the down movement will be the reciprocal 1/1.05.

LOS 9h: Describe the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform probability distribution

A continuous uniform distribution describes a range of outcomes, usually bound with an upper and lower limit (say a and b), where any point in the range is a possibility.
Since it is a range, there are infinite possibilities within the range. In addition, all outcomes are all equally likely (i.e. they are spread uniformly throughout the range).
To calculate probabilities, find the area under a pdf curve.
Basically, take the range between a and b is 100% of the prob. so the 100 divided by all the values between a and b gives you the prob. for each. Sum the number of values in the range you are looking for and mult. them by the prob. of each.
Technically, this is achieved by the following: P(x1 ≤ X ≤ x2) = (x2-x1)/(b-a) where x1 to x2 is the value range you are looking for and b to a is the range of all values.

LOS 9i: Explain the key properties of the normal distribution, distinguish between a univariate and a multivariate distribution, and explain the role of correlation in the multivariate normal distribution

Normal distribution has following properties:

completely described by mean and variance
skewness = 0 and kurtosis = 3
the tails are asymptotic
90% = 1.65
95% = 1.96
99% = 2.58

Univariate = distribution of one variable

Multivariate distribution

is dist. of more than one variable and is meangingful only when the variables are dependent on one another.
If the return of each variable is normally dist. then the distribution of the portfolio will be normal as well.
Want a low correlation among your portfolio assets.
0.5n(n-1) will tell you the number of variances and means you need to describe mult. distribution

LOS 9j: Determine the probability that a normally distributed random variable lies inside a given confidence interval
if μ is $1 and σ is 5% we can say that 66% of the time, the expected return will be ± 5% (one σ) or between $0.95 and $1.05. So the confidence intervals for this example will be:

66% = x±1σ
90% = x±1.65σ
95% = x±1.97σ
90% = x±2.58σ

LOS 9k: Define the standard normal distribution, explain how to standardise a random variable, and calculate and interpret probabilities using the standard normal distribution

Standardise translates the value into a number of standard deviations so it can be compared to confidence intervals and a probability determined. This is called the z-value and is the diff. between the observation and the mean divided by the standard deviation or:

A z value of +1 would mean that the obs is one standard deviation above the mean, a z value of -1 means it falls one standard deviation below the mean.

Calculating Prob's using z-values
Standardise the value and then look up the appropriate prob. in the z-table.

NB watch out for greater than or less than since the z-table is cumulative.
If your z-value is 1.65 and you want to know prob of outcome being less than x then prob. is 90% since 90% of outcomes fall below x.
If you want to know prob of outcome being more than x then prob is 1-0.90 or 10% because this is the small bit that isn't covered in the 90%

LOS 9l: Define shortfall risk, calculate the safety first ratio, and select an optimal portfolio using Roy's safety first criterion

Shortfall risk is focus on both risk and return as opposed to simply the return
Maximise SFR i.e. just like with Sharpe ratios, you want the highest SFR possible as it gives you the best prob. of returns greater than threshold.

LOS 9m: Explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices

Normal dist. are bilaterally symmetric and can take on any value
lognormal is always greater than zero and skews to the right
lognormal is generated by e^x and natural log (ln) of e^x is x
lognormal for asset prices because they cannot be negative
lognormal for modeling price relatives i.e. end of period divided by begin price

LOS 9n: Distinguish between discretely and continuously compounded rates of return and interpret a continuously compounded rate of return, given a specific holding period

use discrete (normal) compounding for interest that compounds during specific times
use continuous (lognormal) compounding for continous
Annual rate (continuous) is ln(1+HPR) or rate of return[2nd][e^x]-1 e.g. if portfolio returned 20% then continuous compounding is found by ln 1.20
Get return from annual rate (or holding period return) by reversing it i.e. 1+annual rate [ln]

LOS 9o: Explain Monte Carlo simulation and historical simulation and describe their major applications and limitations

Monte Carlo

allows for "what if?"
can simulate many possible variables and situations
complex but is only as good as the underlying assumptions

Historical simulation

based on historical data but past performance does not guarantee future results
does not allow "what if?" scenarios

Study Session 2 - Reading 8 Probability Concepts

2010-01-11T12:37:00.000-08:00

LOS 8a - Define a random variable, an outcome, an event, mutually exclusive events, and exhaustive events
These are fairly intuitive, so I'll just deal with the last two:

mutually exclusive = cannot both happen at the same time
exhaustive = includes all possible outcomes (probabilities will sum to 1)

LOS 8b - Explain the two defining properties of probability and distinguish among empirical, subjective and a priori probabilities

Probability is always between 0 and 1
Sum of probabilities of mutually exhaustive and mutually exclusive events will be 1.
empirical probability is established through analysis of past data
a priori probability is deduced or uses logic e.g. 5 out of 10 stocks yesterday were up therefore a random stock from this ten had a 50% probability of going up
subjective = educated guess

LOS 8c - State the probability of an event in terms of odds for or against the event

Here I rely on how i hear this in regular speech. e.g. if the odds are 9 to 1 against an event, I know there is a good chance (90%) that this will not occur.
Only tricky part is remember that the above would not be 10 to 1. e.g. if probability of an event happening is 20% then the odds in favour are 1 to 4 and the odds against are 4 to 1.

LOS 8d- Distinguish between unconditional and conditional probabilities

Unconditional = prob of an event regardless of past or future occurrence of other events
Conditional = occurrence of one event affects the probability of the occurrence of another event

LOS 8d - Define and Explain the multiplication, addition, and total probability rules

mult. rule = P(AB) = P(AB) * P(B) i.e. prob of A and B taking place where A is dependent on B
addition rule = P(A or B) = P(A) + P(B) - P(AB) i.e. prob of A or B taking place is the sum of their probabilities minus the prob of both taking place (to avoid double counting). NB don't forget to subtract the overlap
total prob = P(AB₁)P(B₁) + P(AB₂)P(B₂) +...+ P(AB_n)P(B_n)

LOS 8f: Calculate and interpret (1) the joint probability of two events, (2) the probability that at least one of two events will occur, given a probability of each and the joint probability of two events, and (3) a joint probability of any number of independent events

joint probability of two events A,B is calc. using mult. rule P(AB) = P(AB)*P(B)
if the events are independent, then P(AB) = P(A) so joint prob is P(AB) = P(A)*P(B)
prob. of at least one of two events occuring is addition: P(A or B) = P(A)+P(B)-P(AB)

LOS 8g: Distinguish between dependent and independent events

This is fairly intuitive. Events A and B are independent IFF:
P(AB) = P(A) or vice versa, P(BA) = P(B)
otherwise they are dependent

LOS 8h: Calculate and interpret, using the total probability rule, an unconditional probability

The total probability (unconditional probability) of an event R is calc.:

P(R) = P(RS₁) * P(S₁) + P(RS₂) * P(S₂) +...+ P(RS_n) * P(S_n) where the set of events {S₁), S₂),...S_n)} is mutually exclusive and exhaustive

This is also fairly intuitive in a real world setting. Say you are trying to find the total probability of a rise in interest rates given the state of the economy:

P(Poor Economy) = 0.30
P(Interest Rates Rising Poor Economy) = 0.10
P(Normal Economy) = 0.50
P(Interest Rates Rising Normal Economy) = 0.40
P(Good Economy) = 0.20
P(Interest Rates Rising Good Economy) = 0.70

The total probability is the sum of the joint probability for each event i.e.
(0.30)(0.10)+(0.50)(0.40)+(0.20)(0.70) = 0.03+0.20+0.14 = 0.51 or 51% probability

Note: This will often be structured as a tree diagram which is a good way to visualise it if they do not present it this way and helps visual people like me "get it"

Expected Value

The degree of dispersion of outcomes around an expected value of a random variable is measured using the variance and standard deviation

When pairs of random variables are being observed, the covariance and correlation are used to measure the extent of the relationship between the observed values for the two variables from one obs to the next

The Expected Value is the weighted average of all the possible outcomes of a random variable (e.g. interest rate rise) where the weights are the probabilities that the outcome will occur. Again this is fairly intuitive: it is the sum of the final node results in the tree diagram:

E(X) = P(x1)x1 + P(x2)x2 + ... + P(xn)xn

NB when all probabilities are equally likely, the E(X) is simply the arithmetic mean

LOS 8i: Explain the use of conditional expectation in investment applications

Just like the interest rates example above, conditional expected values are contingent upon the outcome of some other event (e.g. state of the economy). Conditional expected value would be revised using Bayes' formula when new information arrives.

LOS 8j: Diagram an investment problem using a tree diagram

This is a visual representation of the kind of problem shown above. Say a stock price moves with the state of the economy (up or down). We would have four cases:

good economy, stock up
good economy, stock down
bad economy, stock up
bad economy, stock down

As in the example with interest rates, each comes with its own probability (e.g. prob. of a good economy and then corresponding prob. of stock going up and prob. of stock going down)

**********Must update this to include tree diagram***********

LOS 8k: Calculate and interpret covariance and correlation

Cov(Ra,Rb) = Sum of Prob(x) * (dev from mean for A for scenario x)(dev from mean for B for scenario x)

So this is calculated in four steps:

calculate expected return for A and B
calculate deviations from expected return for A and B for each scenario
multiply the deviations for A and B for each scenario and then multiply the product by the probability for that scenario
sum the resulting products

Correlation
Correlation is an easier to interpret measure of the same relationship between A and B and is found by:

Correlation(A,B) = Cov(A,B)/σA * σB

Correlation properties:
ranges from -1 to +1 (perfect negative correlation to perfect positive correlation with zero being no correlation)

LOS 8l: Calculate and interpret the expected value, variance and standard deviation of a random variable and of returns on a portfolio

Portfolio expected value = weighted average of the assets (or returns)

Portfolio variance took me a while to process because it looks scarier than it actually is. It is simply a way of taking the sum of the weighted variances of each asset's return and the weighted covariance of the assets' returns. So for assets A and B the formula is:

Var(Rp) = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bσ_Aσ_BCorr(A,B)

Note: σ_Aσ_BCorr(A,B) is the covariance(A,B) so if you are not given the Corr, you can find it for the first half of the formula and then substitute the Cov(A,B) after the weights in the second half. Also, this is for a portfolio of only two stocks.
For more stocks, the number of the weighted variances increases by the number of stocks and the number of Cov increases such that all possible pairings of stocks are considered.

LOS 8n: Calculate and interpret an updated probability using Bayes' formula

Well, this one really messed me up. As usual, it was simpler than I assumed by looking at the formula. The definition for the formula is:

updated probability = (prob. of new info for given event/uncond. prob. of new info)*prior prob. of event

This didn't make sense to me because i couldn't tell what the new info was and what the unconditional info was etc.

The way I do it is by thinking of the tree diagram. If we diagram out the possibilities for a stock rising or falling given different probabilities for different states of the economy and then we are told that the stock did rise and we are asked for the probability that the economy was good as a result then my formula would be:

updated probability = probability that stock rose and econ was good/total prob. of economy being good

That is the resulting prob at the end of the node where the stock rose and the econ was good divided by the sum of the resulting probabilities at the end of all the nodes where the econ was good.

Bayes tells us the updated probability now that we know the "answer" to the original question i.e. that the stock rose

LOS 8o: Identify the most appropriate method to solve a particular counting problem and solve counting problems using the factorial, combination and permutation notations

The way this was described was confusing but the bottom line is that you are trying to figure out how many options there are to assigning a set of data to different groups such as if you were trying to assign employees to different development teams.

If the number of groups is the same as the number of people then use n! (n[2nd][x!])
If the number of groups is not the same and order is not important then n [2nd][nCr] r where n is the total number and r is the number of groups n!/(n-r)!r!
If the number of groups is not the same and order is important then n [2nd][nPr]r where n is the total number and r is the number of groups n!/(n-r)!

Study Session 2 - Reading 7 Statistical Concepts and Market Returns

2010-01-08T12:35:00.000-08:00

LOS 7a - Descriptive vs. Inferential Statistics
Descriptive allow one to analyse and summarise large data sets - turns data into information.
Inferential involves making forecasts, estimates/judgments about a larger group from samples and is founded on probability theory.

Nominal Ordinal Interval Ratio

LOS 7b - Frequency Distribution

Define the intervals - must be exhaustive and not overlap
Assign the observations to their relevant intervals
Count the observations

LOS 7c - Relative Frequency, Cumulative Frequency

Absolute frequency = the # of observations in each interval (e.g. 2, 3, 5)
Relative frequency = % of observations in each interval (e.g. 20%, 30%, 50%)
Cum. Abs. Freq. = the cumulative # of obs in each interval (e.g. 2, 5, 10)
Cum. Rel. Freq. = the cum frequency in each interval (e.g. 20%, 50%, 100%)

LOS 7d - Histograms

Graphical representation (either bar or polygon) of frequency distribution. Intervals on x, absolute (usually) frequency on y axis.

LOS 7e - Define, calculate and interpet measures of central tendency, including the population mean, sample mean, arithmetic mean, weighted average or mean, geometric mean, harmonic mean, and mode

All of these are essentially measures of expected returns w/r/t to stocks or portfolios with the exception of harmonic mean which is used largely in dollar cost averaging.

population/sample mean = is simply the arithmetic mean of all the observations and will often be used as Expected Value or Expected Return when referring to stock prices or returns. Sum of all deviations from mean will equal zero.

weighted mean/average is used where the observations have unequal influence on the mean. Multiply the values by their weights and then sum them all. Often used to find Expected Return of a portfolio where different stocks have different weights in portfolio so their returns are averaged using weighted average.

Note: The weighted average in many guises is used in other formulas where values are averaged but they are not equal e.g. variance of a portfolio where stocks have different weights.

median - midpoint. Middle observation. If there are an even number of observations, the median is the average of the middle two observations.

geometric mean is often used when calculating investment returns over multiple periods or when measuring compound growth rates. To calculate, take the nth root of the product of the n observations:

The first is the general formula for geometric mean. The second is used for calculating returns (which is quite a common use).

harmonic mean used for dollar cost averaging. divide the number of obs by the reciprocals of the obs, so...

harmonic mean <>

LOS 7f - Quartiles and other 'iles
These are just intervals. Divide the range by the appropriate number (5 for quintiles, 100 for percentiles) to get the size of the intervals. Remember, no overlapping.

To locate the position of the observation at a given percentile, y, with n data points sorted in ascending order (e.g. find the observation located at the 30th percentile):

LOS 7g - Define, calculate, and interpret 1) a range a mean absolute deviation and 2) the variance and standard deviation of a population and of a sample

Range = (max value - min value)
mean absolute deviation = average of the absolute value of all deviations from the mean.
population/sample variance = measures volatility/risk and is the square root of the average of the squared deviations from the mean. The average can be found arithmetically or using a weighted average as appropriate to the problem.

standard deviation is the most common expression of risk and is simply the square root of the variance. The σ is useful because it is expressed in the same units as the observations i.e. if your observations are in $ and cents then so is your σ.

LOS 7h - Calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev's inequality

Chebyshev's inequality tells you the % of obs that lie within k standard deviations of mean is at least 1-1/k²

Works for any distribution and tells you minimum % and gives the following key markers:

36% = +-1.25 standard deviations of the mean
56% = +-1.50 standard deviations of the mean
75% = +-2 standard deviations of the mean

LOS 7i - Define, calculate, and interpret the coefficient of variation and the Sharpe ratio

Coefficient of variation is a measure of dispersion in a distribution relative to the mean and allows us to make direct comparison of dispersion across different sets of data. Allows us to measure risk (variability) per unit of expected return whereas Sharpe measures return per unit of risk.

CV = standard deviation of x/average value of x

Sharpe Ratio measures excess return per unit of risk and is the risk premium divided by the standard deviation. Portfolios with large Sharpe ratios are preferred because they give more return per unit of risk. To calculate:

Very similar to Safety First Ratio.

LOS 7j - Define and interpret skewness, explain the meaning of a positively or negatively skewed return distribution and describe the relative locations of the mean, median, and mode for a nonsymmetrical distribution

OK. Skew is just like we use it in common speech. If we say that will skew the results it means throw them off in one direction or another. Positive skew says that there are positive outliers and so the distribution is humped to the left. Negative is humped to the right with a long left tail of negative possibilities.

Positive skew = mean > median > mode
Negative skew = mean <>
For a symmetrical distribution, they are equal.

NB put the three measures in alphabetical order and arrows point in the direction of skew.

LOS 7k - Define and interpret measures of sample skewness and kurtosis

kurtosis measures peakness of distribution and normal dist. = 3
leptokurtic is more peaked, mesokurtic is normal and platykurtic is less peaked than normal
lept = leap, meso = same, plat = flat

To calculate skew:

Note: skew is cubed which allows for a positive or negative results. The formula for kurtosis is the same formula but to the fourth power instead of cubed. Excess kurtosis is result minus 3.

To calculate kurtosis:

LOS 7l: Discuss the use of arithmetic mean or geometric mean when determining investment returns

use geometric mean for measures of past performance over multiple years/periods as it gives us the compounded rate
use arithmetic mean as estimator of next year's returns

Notes on Study Session 3

2010-01-06T13:08:00.000-08:00

Don't forget that sample mean is still found by dividing by total number of observations but the variance/standard deviation is divided by n-1
Semivariance and semideviations are covered in the CFAI books but not in Schweser
You are asked to calculate semivariance, semideviations, kurtosis and skew in CFAI books but not in Schweser (although the principles and concepts of kurtosis and skew are covered by Schweser)
Semivariance and semideviation are just calculating the variance and the st. deviation using only the data below the mean - otherwise it is exactly the same. You will still use the sample mean and the sample total number of observations but you only sum the squares of the observations below the mean
don't forget to check whether to divide by n or n-1 i.e. pop or sample
modal interval is the interval with the most number of observations in it
Geometric mean always screws me up because i keep doing some approximation of the standard deviation formula:
Geometric mean = (((1+R₁)(1+R₂)...(1+Rn))^1/n)-1

study session 2 - LOS 5g - 6e - Discounting Cash Flows

2009-12-22T17:43:00.000-08:00

I found this section quite a challenge even though i'm sure many people find it intuitive (esp. if you have been working with Treasury Bills or similar instruments for a while). This section made me start to worry if i can actually finish the readings in the recommended time and if i would actually "get" what was going on. What i've found is that the trick for me is not to memorise the formulas by brute force but actually figure out what the formula does. This turned out to be useful in the questions (which often test the concept more than the execution) and also helped me reconstruct the formulas sometimes when i forgot them.

NPV - is the PV of a series of cash flows based on a discount rate (the firm's cost of capital) minus the initial money the firm put into the investment. Projects with a positive NPV are generally considered worthwhile because they will increase the shareholder's value and makes it worthwhile for them to keep their money in the firm because they will earn more by doing so than by putting the money elsewhere.

IRR - is the discount rate that makes the NPV = 0 (equates the PV of the expected future cash flows to the project's initial cost). I don't get this definition 100% but what i do get is that the IRR is the return on the investment and the higher the number the better.

IRR only shows you the percentage return whereas NPV shows you the actual cash they make on it. If you are choosing between two independent projects, you can use either NPV (must be positive) or IRR (must be greater than the cost of capital).

if you are choosing between two mutually exclusive projects, use NPV because it demonstrates the actual cash they are getting.
You could invest $10 with a 10% IRR and make $1 NPV or invest $100 in a project with a 5% IRR and make $5 NPV. Using only the IRR method, you would pick the first project which would actually make you less money (and the goal is to make the shareholders more money).
So use NPV for mutually exclusive projects because that tells you how much money you are making.

So far so good. Then i hit LOS 6b - 6e. These seemed ok until i tried to put them into practice. Essentially, these are ways of demonstrating the different ways in which returns on investments can be expressed.

LOS 6b - Holding Period Yield

HPY = P1 - P0 + D1
--------------
P0

As the name suggests, this expresses the return that you make on an investment during a particular period. So you are looking at the difference between the final value of the investment and original price of the investment plus any benefits you rec'd from dividends as a fraction of the original value. You divide by the original value to remove that from the equation and leave you with just the money you made/lost at the end of the period.

This was ok and the concept gets used a lot (the HPR is basically the same thing without the Dividends and the total return seems to be pretty much identical to the HPR).

LOS 6c - Money Weighted Returns and Time Weighted Returns
This is where i started to lose the thread a bit but i think i'm getting it.

Money Weighted Returns (MWR) is basically the IRR of a portfolio. One of the confusing things here is that the money that is profit (dividends, selling shares) is considered a withdrawal (a negative sign) and money that is spent buying shares etc. is considered a cash inflow (a positive sign). This does make a kind of sense since we are looking at the value of the portfolio and buying a share puts the value of that share into the portfolio and getting a dividend is money that is leaving the portfolio and going into your pocket.

So basically you group the cash flows for each period and net them out (so buying a share worth $10 and getting a dividend of $1 during the same period leaves you with a net of $9 for that time period). Once you have netted the cash flows for each period, you can use the IRR method on your calculator to solve the MWR.

The MWR assumes that the portfolio manager has control over when money enters or leaves the portfolio which is not often the case unless you are managing your own money.

The Time Weighted Return also took a little getting used to. This method measures the rate at which $1 in the portfolio compounds over a specified performance horizon.

First, break the evaluation period into two (or whatever is appropriate) sub-periods based on timing of cash flows and value the portfolio immediately preceding the influx.

Second, calculate the HPR for each holding period.

Third, find the compound annual rate that would have produced a total return equal to the return on the account over the 2 (or whatever is appropriate) year period by finding the geometric mean.

Geometric mean = (X1*X2*X3*X4 ... *Xn)1/n

When X is 1+ HPR.

Differences between MWR and TMR - TMR is preferred method of measuring a portfolio manager's performance as it removes the distortions caused by invest a lot of money at a fortuitous or unfortuitous time. Since most managers do not have control over the flow of money into the portfolio, this method demonstrates the manager's ability to select good investments regardless of good times or bad times.

If funds are added to a portfolio just before a period of poor performance, the money weighted return will be lower than the TMR. If funds are added just prior to a period of hgih returns, the MWR > TMR.

Valuing Treasuries and Comparing them to Bonds and other securities

OK. This was annoying and is one of the drawbacks of using Schweser. Schweser is great because it distills the knowledge down to the need-to-know facts which probably works out really well if you have a lot of experience in the field but it would be helpful to have a couple of nice-to-know facts that might provide some context. This section was only a few pages long but included four formulas without much context for how to use them or how they relate to one another. I've pieced together what i can by using investopedia's CFA topic articles.

LOS 6d - Calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury Bill

What is this all about?

BDY - T-Bills are quoted differently from U.S. Government Bonds which makes them difficult to compare in value or return with similar assets. T-Bills are quoted using a Bank Discount Yield which is not very usable in this form but through the HPY, EAY and MMY, can be made useable as these each correct some shortcoming of the BDY. The EAY corrects pretty much all of them.

The shortcomings of the BDY are as follows:

It is not a true yield because it is expressed as a fraction of the face value rather than the purchase price of the instrument
It ignores compounding of interest over time (only uses simple interest)
It is based on a short (360) year whereas many instruments are quoted on full 365 year

The BDY is calculated as follows:

D x 360

F t

Where

D = dollar discount (i.e. P1-P0)

F = Face Value (i.e. P1)

t = number of days remaining until maturity

So for a bond with a face value of $100,000 and a purchase price of $98,500 and 120 days left until maturity, the BDY = ($100,000-$98,500/$100,000) * (360/120) = 4.5%

The Holding Period Yield (HPY) is the total return an investor earns between the purchase date and the sale or maturity date. The HPY is simply the HPY of the T-Bill investment so it is just like the HPR above and shows you a non-annualised return for only the holding period and includes dividend payments where they exist. A crucial difference between this and the BDY is that the HPY is expressed as a fraction of the purchase price rather than the face value. So the formula is:

HPY = P1-P0+D1

The HPY is used as a crucial part of the EAY and the MMY coming up next.

The Effective Annual Yield (EAY) expresses the return on the investment on a 365 annualised basis including the compounding of the interested involved. So the formula is:

EAY = (1+HPY)^356/t - 1

I sort of got this at first but didn't understand how the 1's were involved mathematically. You cannot take the nth root of a fraction so the 1 is added to allow us to calculate the return based on the compounding of $1. The last step of the equation is to subtract this $1.

The Money Market Yield is the holding period annualised assuming simple interest and a 360 day year. The MMY makes the quoted yield on a T-bill comparable to yield quotes for interest bearing money market instruments that pay interest on a 360 day basis. The formula is therefore:

MMY = HPY * 360/t

the HPY is the actual return an investor will receive if the money market instrument is held until maturity
The EAY is the annualised HPY using compound interest and a 365 day year
The MMY is the annualised HPY using simple interest and a 360 day year

LOS 6e - You should be able to convert among EAY, HPY and MMY which I am going to do by reversing the formulas. So if i get an EAY and i am asked to find the HPY i will work backwards through the equation for the EAY. I will first add one to the EAY then instead of 365/t for the exponent, i will use t/365 and then subtract one which should "undo" the EAY equation and leave me with the HPY.

Same principle for getting HPY if i know the MMY. I will multiply by t/360.

Bond Equivalent Yield

The BEY is 2x the semi-annual discount rate. Yields on US Bonds are quoted as twice the semi-annual rate because the coupon interest is paid in two semi-annual periods. The BEY allows us to compare US Bonds and other instruments such as corporate debt.

To find the BEY, you need to know the interest rate and the frequency of the payments. We need to set 1+ Interest Rate to an exponent that will give us a six month yield and then multiply the answer by 2. So if you have a loan that pays out every three months, you would convert it by (1 + I/R)² and if you had a loan that pays out annually, you would use (1 + I/R)^1/2

study session one - LOS 5a - 5f - Time Value of Money

2009-12-22T17:23:00.000-08:00

mostly Time Value of Money. i read most of this in CFA Fundamentals (which i recommend - by Schweser).

Constructing a timeline does actually help you work this out
If you know all but one of PV, FV, Number of compounding periods (N), Interest per year (I/Y) you can work out the rest using a financial calculator pretty easily
Watch out for questions where the investment compounds several times per year; in this case, divide the interest rate by the number of compounding periods per year and use the result as the I/Y
Maturity payments at the end of an investment (e.g. T-Bills) are calculated as the FV of that investment
FV or PV must be negative or your calculator will throw an error
To calculate growth, use start and end payments as PV and FV respectively
I often transpose numbers or just make stupid mistakes when inputting - must double check that what i have inputted is the actual number
perpetuities are present valued by dividing the payment by the interest rate
PV
FV
Annuity Due
Ordinary Annuities
For finding the PV of a series of uneven cash flows it is the sum of the PV of each cash flow; i do this using the NPV function and entering the cash flows and the interest rate (but this assumes interest rate is constant)
For things like saving up for retirement plans, you have to work out the PV of the future sum needed to support the required payments
For finding the FV/PV of a lump sum which receives coupons or payments, add the payments as PMT when calculating the value
NOTE: Questions involving annuity due do not tell you explicitly but often use phrases like "Bob invests $10 now" or "If Mary invests $10 today" to imply that the compounding starts from the beginning of the period
NB Don't forget to set your calculator to BGN for the compounding period and to switch it back when you are done.

I don't know most of these formulas but i do know how to calculate them using a Texas Instruments BA II Plus calculator - YouTube has some good videos on how to do this.

One note on interest rates:

Real Risk-Free Rate - This assumes no risk or uncertainty, simply reflecting differences in timing: the preference to spend now/pay back later versus lend now/collect later.
Expected Inflation - The market expects aggregate prices to rise, and the currency's purchasing power is reduced by a rate known as the inflation rate. Inflation makes real dollars less valuable in the future and is factored into determining the nominal interest rate (from the economics material: nominal rate = real rate + inflation rate).
Default-Risk Premium - What is the chance that the borrower won't make payments on time, or will be unable to pay what is owed? This component will be high or low depending on the creditworthiness of the person or entity involved.
Liquidity Premium- Some investments are highly liquid, meaning they are easily exchanged for cash (U.S. Treasury debt, for example). Other securities are less liquid, and there may be a certain loss expected if it's an issue that trades infrequently. Holding other factors equal, a less liquid security must compensate the holder by offering a higher interest rate.
Maturity Premium - All else being equal, a bond obligation will be more sensitive to interest rate fluctuations the longer to maturity it is.

ethics

2009-12-22T17:14:00.000-08:00

the ethics is kind of common sense:

don't guarantee any performance of your investments in any form
don't accept any gift that could reasonably be considered to compromise your integrity or your loyalty to your company or make you consider one client over another
don't front run trades for yourself or family members ahead of your clients (family members who are clients, however, should be treated like any other client)
don't deprive your company of your services
if you accept outside work, get approval from your company first
if you supervise people, you are responsible for their actions - make sure they adhere to the same standards you set yourself
don't let your research be compromised - if you are paid to conduct research, disclose the relationship
don't get involved in IPO's for any kind of personal gain
don't mess with the market or allow others to do the same e.g. buying and selling a stock to increase volume of trade artificially
you should consider the suitability and appropriateness of investments for your clients through consultation and discussion with them
CFA is an adjective not a noun
you cannot claim any superiority for having passed the CFA in the minimum amount of time or because you hold the charter
Don't misuse the logo for CFA - it cannot be part of a company name
GIPS is an investment standard that primarily focuses on how investment managers report earnings; do not cherry pick performance of investments but give representative composites within sectors; do not omit accounts which were ended before the presentation date
Firms can be independently verified as being GIPS compliant but this is not required and must be for the whole firm and not just some funds/accounts
History of investments should be for five to ten years
Real estate is a special case
Basically, if it feels wrong, it probably is.

the cfa with no experience

2009-12-22T17:11:00.000-08:00

so i'm signed up for the CFA Level 1 for June 2010 and i have no financial background. i have a BA in English and Modern Languages and a Masters in Economic History. The latter gave me an understanding of basic economics but other than that i've been working in web development for the decade since college. I've run web design agencies and taught web development at a local college. i did badly in math in high school and avoided it as much as possible during college. i haven't really touched math in ten years aside from basic algebra for programming. Now i have a job working for a large bank and i thought the CFA would be a good way to fast forward my investment knowledge. i looks like a very rough road ahead for me for this exam and i'm sure i am not alone so these are my thoughts.

being a teacher, i've found the best way to learn is to teach it because you must know it cold. these posts are intended (at this point) to be my way of explaining the material to myself. who knows, maybe someone will learn the way i do or maybe someone who is better at this than i am might correct my mistakes. Either way, it will selfishly help me cement some concepts.

Process: Took me a while to find my method. What i've found is that I do the following:

I read the reading on investopedia to get a little more user friendly (and short) version of what I am going to read
I read the chapter in Schweser
Any problems, I do a search on the term or concept or watch a YouTube video on the subject or read the version in the CFAI text
I make some notes along the way
I do the problem sets at the end of the chapter in Schweser (and try to do the CFAI ones but they tend to be incredibly long... but i recommend them as they really test you)
Write down the problems I had doing the questions
Write up my notes on this blog