Study Session 12 - Portfolio Management

PORTFOLIO MANAGEMENT

The Asset Allocation Decision

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

1. write policy statement = goals, constraints, itemised risks taken to meet goals
2. develop investment strategy to satisfy policy goals
3. implement plan = construct portfolio and allocation of assets
4. 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

1. capital preservation = equal to inflation, little/no risk, no decrease in purchasign power
2. capital appreciation = e.g. saving for retirement, nominal return should exceed rate of inflation
3. 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
4. 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.

1. First, consumers like more to less. In terms of a security or portfolio, consumers prefer more return to less return.
2. 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:

1. the expected return for each asset
2. the standard deviation for each asset
3. 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