Portfolio Management (Part One)

Question 1

Real Return

Answer 1

= Nominal Return Less Inflation

Question 2

Why is evaluating investments using expected return and variance of returns a simplif ication?

Answer 2

Because returns do not follow a normal distribution; distributions are negatively skewed, with greater kurtosis (fatter tails) than a normal distribution. The negative skew ref lects a tendency towards large downside deviations, while the positive excess kurtosis re flects frequent extreme deviations on both the upside and
downside. These non-normal characteristics of skewness (≠ 0) and kurtosis (≠ 3) should be taken into account when analyzing investments.

Question 3

How does liquidity impact evaluation of investments?

Answer 3

Liquidity can affect the price and, therefore, the expected return of a security. Liquidity can be a major concern in emerging markets and for securities that trade infrequently, such as low-quality corporate bonds.

Question 4

Who is a risk-averse investor?

Answer 4

A risk-averse investor is simply one that dislikes risk (i.e., prefers less risk to more risk). Given two investments that have equal expected returns, a risk-averse investor will choose the one with less risk (standard deviation, σ). Financial models assume all investors are risk averse.

Question 5

Who is a risk-seeking investor?

Answer 5

A risk-seeking (risk-loving) investor would actually prefer more risk to less and, given equal expected returns, would prefer the more risky investment.

Question 6

Who is a risk-neutral investor?

Answer 6

A risk- neutral investor would have no preference regarding risk and would therefore be indifferent between any two investments with equal expected returns.

Question 7

What are an investor’s utility functions?

Answer 7

Investors’ utility functions represent their preferences regarding the tradeoff between risk and return (i.e., their degrees of risk aversion)

Question 8

What is an indifference curve?

Answer 8

An indifference curve is a tool from economics that, in this application, plots combinations of risk (standard deviation) and expected returns among which an investor is indifferent.
In constructing indifference curves for portfolios based on only their expected return and standard deviation of returns, we are assuming that these are the only portfolio characteristics that investors care about.

Question 9

Expected Risk for a 2 Asset Portfolio where one asset is risk free

Answer 9

Wa*SDa
where, a is the risk bearing asset

Question 10

An Indifference curve for a risk averse investor will be (flatter/steeper)

Answer 10

Steeper - as they will require a greater increase in expected return per unit increase in risk reflecting a higher risk aversion coefficient

Question 11

The capital allocation line is a line from the risk-free return through the:

Answer 11

optimal risky portfolio

Question 12

Expected Return for a 2 Asset Portfolio

Answer 12

E(Rp) = WaE(Ra) + WbE(Rb)

Question 13

Sample Variance

Answer 13

S^2 = [Sum of (Rt - R_)]^2 / T-1

Rt = Return for period t
R_ = Mean of Sample
T = Total periods

Question 14

Expected Risk for a 2 Asset Portfolio

Answer 14

SDp = Root of Wa^2SDa^2 + Wb^2SDb^2 + 2WaWbCorrel(A,B)SDa*SDb

Question 15

Capital Allocation Line

Answer 15

The line representing thes possible combinations of risk-free assets and the optimal risky asset portfolio is referred to as the capital allocation line.

Question 16

Two-fund separation theorem

Answer 16

Combining a risky portfolio with a risk-free asset is the process that supports the two-fund separation theorem, which states that all investors’ optimal portfolios will be made up of some combination of the optimal portfolio of risky assets and the risk-free asset.

Question 17

Combination of Capital Allocation Line + Indifference Curve

Answer 17

Gives the Optimal Portfolio that maximises investors expected utility

Question 18

Population Variance

Answer 18

SD^2 = [Sum of (Rt - Mu)]^2 / T

Rt = Return for period t
Mu = Mean of Population
T = Total periods

Question 19

Covariance for Returns of Two Assets (Features)

Answer 19

• extent to which two variables move together over time
• does not indicate strength, only direction
• Cov = 0 - no LINEAR relation (may have non-linear relation)

Question 20

Covariance for Returns of Two Assets (Formula)

Answer 20

Cov1,2 = Sum of [(Rt,1 - R_1)(Rt,2 - R_2)] / n-1

Rt,1 = return on Asset 1 in period t
Rt,2 = return on Asset 2 in period t
R_1 = mean return on asset 1
R_2 = mean return on asset 2
n = number of periods

Question 21

Correlation

Answer 21

• magnitude of covariance
• standardised measure

P1,2 = Cov1,2 / SD1*SD2

P1,2 = Correlation Coefficient
-1 <= P1,2 <= 1
-1 = perfectly negatively correlated
1 = perfectly positively correlated
0 = no LINEAR relationship

Question 22

Portfolio Variance

Answer 22

Varp = Wa^2SDa^2 + Wb^2SDb^2 + 2WaWb*Cov(a,b)

= Wa^2SDa^2 + Wb^2SDb^2 + 2WaWbCorrel(a,b)SDa*SDb

Question 23

Zero-Variance Portfolio

Answer 23

A zero-variance portfolio can only be constructed if the correlation coeff icient between assets is -1

Question 24

Can you get diversification benefits if correlation is less than 1?

Answer 24

Yes

Question 25

Lower the correlation, (lower/greater) the expected benefit of diversification

Answer 25

greater - one stock hedges the other

Question 26

If Correl (1,2) = 1, then Standard Deviation of Portfolio is...

Answer 26

weighted average of Std devs SDp = Root of Varp = Root of W1^2*SD1^2 + W2^2*SD2^2 + 2*W1*W2*SD1*SD2*1 = Root of (W1*SD1 + W2*SD2)^2 = W1*SD1 + W2*SD2

Question 27

Portfolio Risk decreases as correlation....

Answer 27

decreases, thus, diversification benefit

Question 28

minimum variance frontier

Answer 28

For each level of expected portfolio return, we can vary the portfolio weights on the individual assets to determine the portfolio that has the least risk. These portfolios that have the lowest standard deviation of all portfolios with a given expected return are known as minimum-variance portfolios. Together they make up the minimum-variance frontier.

Question 29

Efficient Frontier

Answer 29

Those portfolios that have the greatest expected return for each level of risk (standard deviation) make up the efficient frontier. The efficient frontier coincides with the top portion of the minimum-variance frontier. A risk-averse investor would only choose portfolios that are on the efficient frontier because all available portfolios that are not on the efficient frontier have lower expected returns than an efficient portfolio with the same risk.

Question 30

Global minimum variance portfolio

Answer 30

The portfolio on the eficient frontier that has the least risk is the global minimum-variance portfolio.

Question 31

Homogenous expectations

Answer 31

- simplifying assumption underlying modern portfolio theory and capital asset pricing model - investors have homogeneous expectations (i.e., they all have the same estimates of risk, return, and correlations with other risky assets for all risky assets). Under this assumption, all investors face the same efficient frontier of risky portfolios and will all have the same optimal risky portfolio and CAL.

Question 32

Optimal CAL

Answer 32

- tangent to Efficient Frontier

Question 33

Market Portfolio

Answer 33

Depending on their preferences for risk and return (their indifference curves), investors may choose different portfolio weights for the risk-free asset and the risky (tangency) portfolio. Every investor, however, will use the same risky portfolio. When this is the case, that portfolio must be the market portfolio of all risky assets because all investors that hold any risky assets hold the same portfolio of risky assets.

Question 34

Capital Market Line

Answer 34

Under the assumption of homogeneous expectations, the optimal CAL for all investors is termed the capital market line (CML). Along this line, expected portfolio return, E(RP), is a linear function of portfolio risk, σP. The equation of this line is as follows: E(Rp) = Rf + {[(E(Rm) - Rf)]/SDm}*SDp y intercept = Rf slope = (E(Rm) - Rf)]/SDm An investor who choose no risk ie SDp=0 will earn only Rf

Question 35

Market Risk Premium

Answer 35

The difference between the expected return on the market and the risk-free rate is termed the market risk premium. We can rewrite CML equation as: E(Rp) = Rf + [(E(Rm) - Rf)]*(SDp/SDm)

Question 36

Passive Investment Strategy

Answer 36

Investors who believe market prices are informationally efficient often follow a passive investment strategy (i.e., invest in an index of risky assets that serves as a proxy for the market portfolio and allocate a portion of their investable assets to a risk-free asset, such as short-term government securities)

Question 37

Active Portfolio Management

Answer 37

In practice, many investors and portfolio managers believe their estimates of security values are correct and market prices are incorrect. Such investors will not use the weights of the market portfolio but will invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued. This is referred to as active portfolio management.

Question 38

Systematic Risk

Answer 38

Because the market portfolio contains all risky assets, it must be a well-diversified portfolio. All the risk that can be diversified away has been. The risk that remains cannot be diversified away and is called the systematic risk (also called nondiversifiable risk or market risk).

Question 39

Unsystematic risk

Answer 39

When an investor diversiies across assets that are not perfectly correlated, the portfolio's risk is less than the weighted average of the risks of the individual securities in the portfolio. The risk that is eliminated by diversification is called unsystematic risk (also called unique, diversifiable, or firm-specific risk).

Question 40

Total Risk

Answer 40

= Systematic Risk + unsystematic risk

Question 41

Equilibrium Security Returns depend on a stock's or a portfolio's

Answer 41

systematic risk (not total risk as measured by standard deviation) as diversifaction is free. The reasoning is that investors will not be compensated for bearing risk that can be eliminated at no cost. Implication: The riskiest stock, with risk measured as standard deviation of returns, does not necessarily have the greatest expected return. Lower systematic risk --> Lower equilibrium rate of return (CMT) Eliminate unsystematic risk by diversification

Question 42

Return generating models

Answer 42

Used to estimate the expected returns on risky securities based on specific factors. For each security, we must estimate the sensitivity of its returns to each specific factor. Factors that explain security returns can be classified as macroeconomic, fundamental, and statistical factors.

Question 43

Multifactor models

Answer 43

Most commonly use macroeconomic factors such as GDP growth, inflation, or consumer confidence, along with fundamental factors such as earnings, earnings growth, firm size, and research expenditures. Statistical factors often have no basis in finance theory E(Ri) - Rf = Bi1 x E(Factor 1) + Bi2 x E(Factor 2) ....

Question 44

Factor sensitivity

Answer 44

AKA Factor Loading Multifactor model states that the expected excess return (above the risk-free rate) for Asset i is the sum of each factor sensitivity or factor loading (the βs) for Asset i multiplied by the expected value of that factor for the period. The first factor is often the expected excess return on the market, E(Rm − Rf).

Question 45

Fama & French Multifactor Model

Answer 45

They estimated the sensitivity of security returns to three factors: firm size, firm book value to market value ratio, and the return on the market portfolio minus the risk-free rate (excess return on the market portfolio).

Question 46

Carhart Multifactor model

Answer 46

Carhart suggests a fourth factor to the F&F Model - measures price momentum using prior period returns.

Question 47

Single Index Model

Answer 47

E(Ri) - Rf = Bi x [E(Rm) - Rf] only excess market returns as a factor

Question 48

Market Model

Answer 48

A simplified form of a single-index model is the market model, which is used to estimate a security's (or portfolio's) beta and to estimate a security's abnormal return (return above its expected return) based on the actual market return. Ri = Alphai + Bi*Rm + ei Ri = Returns of Asset i Alphai = intercept Bi = slope coefficient Rm = Market returns ei = abnormal returns of asset i Alphai, Bi = historical data

Question 49

Beta in Market Model

Answer 49

The sensitivity of an asset's return to the return on the market index in the context of the market model is referred to as its beta. Beta is a standardized measure of the covariance of the asset's return with the market return. Bi = covar(i,m)/Varm

Question 50

Security Characteristic line

Answer 50

In practice, we estimate asset betas by regressing returns on the asset on those of the market index. we represent the excess returns on Asset i as the dependent variable and the excess returns on the market index as the independent variable. The least squares regression line is the line that minimizes the sum of the squared distances of the points plotted from the line (this is what is meant by the line of best it). The slope of this line is our estimate of beta. This regression line is referred to as the asset's security characteristic line.

Question 51

What is the risk measure associated with the capital market line (CML)?

Answer 51

Total risk

Question 52

A portfolio to the right of the market portfolio on the CML is a

Answer 52

Borrowing Portfolio

Question 53

A return generating model is least likely to be based on a security's exposure to:

Answer 53

Statistical factors

Question 54

When you increase the number of stocks in a portfolio, unsystematic risk will...

Answer 54

decrease at a decreasing rate

Question 55

Security Market Line

Answer 55

Given that the only relevant (priced) risk for an individual Asset i is measured by the covariance between the asset's returns and the returns on the market, Covi,mkt, we can plot the relationship between risk and return for individual assets using Covi,mkt as our measure of systematic risk. The resulting line, plotted in is one version of what is referred to as the security market line (SML).

Question 56

Equation of SML

Answer 56

E(Ri) = Rf + Cov(i,mkt)/Var(mkt) x [E(Rmkt) - Rf) Bi = Cov(i,mkt)/Var(mkt) This is also CAPM

Question 57

Capital Asset Pricing Model

Answer 57

This relation between beta (systematic risk) and expected return is known as the capital asset pricing model (CAPM). B = Cov(i,mkt)/var(mkt) Beta measures the relation between a security's excess returns and the excess returns to the market portfolio. CAPM: E(Ri) = Rf + Bi[E(rmkt) - Rf] - same as SML The CAPM holds that, in equilibrium, the expected return on risky asset E(Ri) is the risk-free rate (Rf) plus a beta-adjusted market risk premium, βi[E(Rmkt) − Rf]. Beta measures systematic (market or covariance) risk.

Question 58

SML - Beta

Answer 58

standardised measure of systematic risk B = Cov(i,mkt)/var(mkt)

Question 59

If Ba > 1, E(Ra) >/< E(Rmkt)

Answer 59

E(Ra) > E(Rmkt)

Question 60

Assumptions of CAPM

Answer 60

- Risk Aversion: Greater Risk --> Greater Returns - Utility Maximising Investors - Frictionless Markets: No taxes, not costs or impediments to trading - One-period horizon: all investors have the same one-period time horizon - Homogenous expectations: all investors have same expectations: expected returns, std dev, correl - Divisible assets: all investments are infinitely divisible - Competitive Markets: Investors take the market price as given and no investor can influence prices with their trades.

Question 61

Any stock not on the SML is...

Answer 61

mispriced Forecasted Return > Required Return (E(R)) = undervalued Forecasted Return < Required Return (E(R)) = overvalued Forecasted Return = Required Return (E(R)) = properly valued

Question 62

Performance Evaluation

Answer 62

Performance evaluation of an active manager's portfolio choices refers to the analysis of the risk and return of the portfolio.

Question 63

Attribution Analysis

Answer 63

An analysis of the sources of returns differences between active portfolio returns and those of a passive benchmark portfolio, is part of performance evaluation. Success in active portfolio management cannot be determined simply by comparing portfolio returns to benchmark portfolio returns; the risk taken to achieve returns must also be considered. A portfolio with greater risk than the benchmark portfolio (especially beta risk) is expected to produce higher returns over time than the benchmark portfolio.

Question 64

Sharpe Ratio

Answer 64

The Sharpe ratio of a portfolio is its excess returns per unit of total portfolio risk. Higher Sharpe ratios indicate better risk-adjusted portfolio performance. = E[Rportfolio] - Rf / SDEVportfolio Also the Slope for CAL for that portfolio and can be compared to the slope of the CML which is the Sharpe ration for the portfolios that lie on the CML

Question 65

Ex-Ante / Ex-Post

Answer 65

Ex-Ante: before the fact ie using expected values Ex-Post: after the fact ie. using actual values ie sample mean returns and sample Standard Deviation

Question 66

Use of Sharpe Ratio

Answer 66

The Sharpe ratio is based on total risk (standard deviation of returns), rather than systematic risk (beta). For this reason, the Sharpe ratio can be used to evaluate the performance of concentrated portfolios (those affected by unsystematic risk) as well as well-diversified portfolios (those with only systematic, or beta, risk). The value of the Sharpe ratio is only useful for comparison with the Sharpe ratio of another portfolio.

Question 67

M-sqaured (M^2)

Answer 67

Alternative to Sharpe Ratio Expressed in % Given a Portfolio P, we can calculate the return on a Portfolio P* that is leveraged (when σM > σP), or deleveraged (when σM < σP), so that P* has the same risk (standard deviation of returns) as the market portfolio. The return on P* is = Rf + SDEVm/SDEVp (Rp - Rf) and we refer to that as the M2 measure for Portfolio P.

Question 68

M^22 Alpha

Answer 68

The extra return on the Portfolio P* above the return on the market portfolio, (P* - RM), is referred to as M2 alpha. P* - RM

Question 69

If M^2 > Rm, M^2 Alpha (/=) 0

Answer 69

If M^2 > Rm, M^2 Alpha > 0

Question 70

Measures of portfolio performance based on systematic risk

Answer 70

Treynor measure and Jensen's alpha Treynor - slope (like SR) Jensons - % measure of excess returns (like M2)

Question 71

Treynor Measure

Answer 71

= (Rp - Rf) / Bp excess returns per unit of systematic risk Slope of risk/beta graph of portfolio p

Question 72

Jensons Alpha

Answer 72

Ap = Rp - [Rf + Bp(Rm - Rf)] is the percentage portfolio return above that of a portfolio (or security) with the same beta as the portfolio that lies on the SML

Question 73

How to decide if risk adjustment should be based on standard deviation of returns or portfolio beta?

Answer 73

Standard Deviation = using SR/M^2 = when the portfolio bears both systematic & unsystematic risk, single manager Beta = using Treynore & Jensons = well diversified ie. no unsystematic risk, multiple managers

Question 74

Note of Caution

Answer 74

Estimating the values needed to apply these theoretical models and performance measures is often difficult and is done with error. The expected return on the market, and thus the market risk premium, may not be equal to its average historical value. Estimating security and portfolio betas is done with error as well.

Question 75

According to the CAPM, a rational investor would be least likely to choose as his optimal portfolio:

Answer 75

global minimum variance portfolio

Question 76

Stock 1 has a standard deviation of 10. Stock 2 also has a standard deviation of 10. If the correlation coefficient between these stocks is –1, what is the covariance between these two stocks?

Answer 76

-100

Question 77

Which of the following statements best describes an investment that is not on the efficient frontier? A) There is a portfolio that has a lower return for the same risk. B) The portfolio has a very high return. C) There is a portfolio that has a lower risk for the same return.

Answer 77

C The efficient frontier outlines the set of portfolios that gives investors the highest return for a given level of risk or the lowest risk for a given level of return. Therefore, if a portfolio is not on the efficient frontier, there must be a portfolio that has lower risk for the same return. Equivalently, there must be a portfolio that produces a higher return for the same risk.

Question 78

A line that represents the possible portfolios that combine a risky asset and a risk free asset is most accurately described as a:

Answer 78

CAL

Question 79

A line that represents the possible combinations of the market portfolio with the risk-free asset.

Answer 79

CML

Question 80

Portfolios on the capital market line:

Answer 80

are perfectly positively correlated with each other.

Question 81

James Franklin, CFA, has high risk tolerance and seeks high returns. Based on capital market theory, Franklin would most appropriately hold:

Answer 81

the market portfolio as his only risky asset.

Question 82

In the context of the CML, the market portfolio includes:

Answer 82

all existing risky assets The market portfolio has to contain all the stocks, bonds, and risky assets in existence. Because this portfolio has all risky assets in it, it represents the ultimate or completely diversified portfolio.

Question 83

Which of the following pooled investment shares is least likely to trade at a price different from its NAV?

Answer 83

Open Ended

Question 84

Investment Constraints & Objectives

Answer 84

Risk tolerance and return requirements make up the investment objectives. Investment constraints include liquidity needs, time horizon, tax concerns, legal and regulatory factors, and unique circumstances.