study session 2 - LOS 5g - 6e - Discounting Cash Flows

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:

1. 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
2. It ignores compounding of interest over time (only uses simple interest)
3. 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

          P0

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

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:

1. 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.
2. 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).
3. 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.
4. 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.
5. Maturity Premium - All else being equal, a bond obligation will be more sensitive to interest rate fluctuations the longer to maturity it is.

ethics

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

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:

1. I read the reading on investopedia to get a little more user friendly (and short) version of what I am going to read
2. I read the chapter in Schweser
3. 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
4. I make some notes along the way
5. 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)
6. Write down the problems I had doing the questions
7. Write up my notes on this blog