CFA 42: Portfolio Risk & Return I

A portfolio manager creates the following portfolio: Security Security Weight (%) Expected Standard Deviation (%) 1 30 20 2 70 12 If the covariance of returns between the two securities is −0.0240, the expected standard deviation of the portfolio is closest to: 2.4%. 7.5%. 9.2%.

A is correct. σport=w21σ21+w22σ22+2w1w2Cov(R1R2)−−−−−−−−−−−−−−−−−−−−−−−−−−√=(0.3)2(20%)2+(0.7)2(12%)2+2(0.3)(0.7)(−0.0240)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=(0.3600%+0.7056%−1.008%)0.5=(0.0576%)0.5=2.40%.

A portfolio manager creates the following portfolio: Security Expected Annual Return (%) Expected Standard Deviation (%) 1 16 20 2 12 20 If the correlation of returns between the two securities is −0.15, the expected standard deviation of an equal-weighted portfolio is closest to: 13.04%. 13.60%. 13.87%.

A is correct. σport=w21σ21+w22σ22+2w1w2ρ1,2σ1σ2−−−−−−−−−−−−−−−−−−−−−−−−√=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(−0.15)(20%)(20%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√)=(1.0000%+1.0000%−0.3000%)0.5=(1.7000%)0.5=13.04%

An analyst observes the following historic geometric returns: Asset Class Geometric Return (%) Equities 8.0 Corporate Bonds 6.5 Treasury bills 2.5 Inflation 2.1 The real rate of return for corporate bonds is closest to: 4.3%. 4.4%. 4.5%.

A is correct. (1 + 0.065)/(1 + 0.0210) = 4.3%

An analyst observes the following historic geometric returns: Asset Class Geometric Return (%) Equities 8.0 Corporate Bonds 6.5 Treasury bills 2.5 Inflation 2.1 The risk premium for equities is closest to: 5.4%. 5.5%. 5.6%.

A is correct. (1 + 0.080)/(1 + 0.0250) = 5.4%

With respect to an investor's utility function expressed as: U=E(r)−12Aσ2 , which of the following values for the measure for risk aversion has the least amount of risk aversion? −4. 0. 4.

A is correct. A negative value in the given utility function indicates that the investor is a risk seeker.

With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is: the same for all individuals. positive for risk-averse investors. equal to zero for risk seeking investors.

A is correct. A risk-free asset has a variance of zero and is not dependent on whether the investor is risk neutral, risk seeking or risk averse. That is, given that the utility function of an investment is expressed as U=E(r)−12Aσ2 , where A is the measure of risk aversion, then the sign of A is irrelevant if the variance is zero (like that of a risk-free asset).

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence: Asset Outcome 1 (%) Outcome 2 (%) Outcome 3 (%) Expected Return (%) 1 12 0 6 6 2 12 6 0 6 3 0 6 12 6 If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction? Asset 1 and Asset 2. Asset 1 and Asset 3. Asset 2 and Asset 3.

A is correct. An equally weighted portfolio of Asset 1 and Asset 2 has the highest level of volatility of the three pairs. All three pairs have the same expected return; however, the portfolio of Asset 1 and Asset 2 provides the least amount of risk reduction.

The correlation between assets in a two-asset portfolio increases during a market decline. If there is no change in the proportion of each asset held in the portfolio or the expected standard deviation of the individual assets, the volatility of the portfolio is most likely to: increase. decrease. remain the same.

A is correct. Higher correlations will produce less diversification benefits provided that the other components of the portfolio standard deviation do not change (i.e., the weights and standard deviations of the individual assets).

A financial planner has created the following data to illustrate the application of utility theory to portfolio selection: Investment Expected Return (%) Expected Standard Deviation (%) 1 18 2 2 19 8 3 20 15 4 18 30 If an investor's utility function is expressed as U=E(r)−12Aσ2 and the measure for risk aversion has a value of 4, the risk-averse investor is most likely to choose: Investment 1. Investment 2. Investment 3.

A is correct. Investment 1 provides the highest utility value (0.1792) for a risk-averse investor who has a measure of risk aversion equal to 4. Investment Expected Return (%) Expected Standard Deviation (%) Utility A = 4 1 18 2 0.1792 2 19 8 0.1772 3 20 15 0.1550 4 18 30 0.0000

With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all: risky assets. equity securities. feasible investments.

A is correct. The CAL is the combination of the risk-free asset with zero risk and the portfolio of all risky assets that provides for the set of feasible investments. Allowing for borrowing at the risk-free rate and investing in the portfolio of all risky assets provides for attainable portfolios that dominate risky assets below the CAL.

With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio? Return on the asset. Standard deviation of the asset. Covariances of the asset with the other assets in the portfolio.

A is correct. The asset's returns are not used to calculate the portfolio's variance [only the assets' weights, standard deviations (or variances), and covariances (or correlations) are used].

Which of the following return calculating methods is best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last five years? Geometric mean return. Arithmetic mean return. Money-weighted return.

A is correct. The geometric mean return compounds the returns instead of the amount invested.

The dominant capital allocation line is the combination of the risk-free asset and the: optimal risky portfolio. levered portfolio of risky assets. global minimum-variance portfolio.

A is correct. The use of leverage and the combination of a risk-free asset and the optimal risky asset will dominate the efficient frontier of risky assets (the Markowitz efficient frontier).

An analyst observes the following annual rates of return for a hedge fund: Year Return (%) 2008 22 2009 −25 2010 11 The hedge fund's annual geometric mean return is closest to: 0.52%. 1.02%. 2.67%.

A is correct. [(1 + 0.22)(1 − 0.25)(1 + 0.11)] (1/3) − 1 = 1.0157(1/3) − 1 = 0.0052 = 0.52%

A portfolio manager creates the following portfolio: Security Expected Annual Return (%) Expected Standard Deviation (%) 1 16 20 2 12 20 If the two securities are uncorrelated, the expected standard deviation of an equal-weighted portfolio is closest to: 14.00%. 14.14%. 20.00%.

B is correct. σport=w21σ21+w22σ22+2w1w2ρ1,2σ1σ2−−−−−−−−−−−−−−−−−−−−−−−−√=(0.5)2(20%)2+(0.5)2(20%)2+2(0.5)(0.5)(0.00)(20%)(20%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√)=(1.0000%+1.0000%+0.0000%)0.5=(2.0000%)0.5=14.14%

An analyst observes the following historic geometric returns: Asset Class Geometric Return (%) Equities 8.0 Corporate Bonds 6.5 Treasury bills 2.5 Inflation 2.1 The risk premium for corporate bonds is closest to: 3.5%. 3.9%. 4.0%

B is correct. (1 + 0.0650)/(1 + 0.0250) = 3.9%

An analyst observes the following historic geometric returns: Asset Class Geometric Return (%) Equities 8.0 Corporate Bonds 6.5 Treasury bills 2.5 Inflation 2.1 The real rate of return for equities is closest to: 5.4%. 5.8%. 5.9%.

B is correct. (1 + 0.080)/(1 + 0.0210) = 5.8%

A portfolio manager creates the following portfolio: Security Security Weight (%) Expected Standard Deviation (%) 1 30 20 2 70 12 If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to: 0.0006. 0.0240. 1.0000.

B is correct. A portfolio standard deviation of 14.40% is the weighted average, which is possible only if the correlation between the securities is equal to 1.0. If the correlation coefficient is equal to 1.0, then the covariance must equal 0.0240, calculated as: Cov(R1,R2) = ρ12σ1σ2 = (1.0)(20%)(12%) = 2.40% = 0.0240.

A financial planner has created the following data to illustrate the application of utility theory to portfolio selection: Investment Expected Return (%) Expected Standard Deviation (%) 1 18 2 2 19 8 3 20 15 4 18 30 If an investor's utility function is expressed as U=E(r)−12Aσ2 and the measure for risk aversion has a value of 2, the risk-averse investor is most likely to choose: Investment 1. Investment 2. Investment 3.

B is correct. Investment 2 provides the highest utility value (0.1836) for a risk-averse investor who has a measure of risk aversion equal to 2. Investment Expected Return (%) Expected Standard Deviation (%) Utility A = 2 1 18 2 0.1796 2 19 8 0.1836 3 20 15 0.1775 4 18 30 0.0900

Compared to the efficient frontier of risky assets, the dominant capital allocation line has higher rates of return for levels of risk greater than the optimal risky portfolio because of the investor's ability to: lend at the risk-free rate. borrow at the risk-free rate. purchase the risk-free asset.

B is correct. The CAL dominates the efficient frontier at all points except for the optimal risky portfolio. The ability of the investor to purchase additional amounts of the optimal risky portfolio by borrowing (i.e., buying on margin) at the risk-free rate makes higher rates of return for levels of risk greater than the optimal risky asset possible.

Two individual investors with different levels of risk aversion will have optimal portfolios that are: below the capital allocation line. on the capital allocation line. above the capital allocation line.

B is correct. The CAL represents the set of all feasible investments. Each investor's indifference curve determines the optimal combination of the risk-free asset and the portfolio of all risky assets, which must lie on the CAL.

The set of portfolios on the minimum-variance frontier that dominates all sets of portfolios below the global minimum-variance portfolio is the: capital allocation line. Markowitz efficient frontier. set of optimal risky portfolios.

B is correct. The Markowitz efficient frontier has higher rates of return for a given level of risk. With respect to the minimum-variance portfolio, the Markowitz efficient frontier is the set of portfolios above the global minimum-variance portfolio that dominates the portfolios below the global minimum-variance portfolio.

An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information: ETF Time Since Inception Return Since Inception (%) 1 146 days 4.61 2 5 weeks 1.10 3 15 months 14.35 The ETF with the highest annualized rate of return is: ETF 1. ETF 2. ETF 3.

B is correct. The annualized rate of return for ETF 2 is 12.05% = (1.0110 52/5) − 1, which is greater than the annualized rate of ETF 1, 11.93% = (1.0461 365/146) − 1, and ETF 3, 11.32% = (1.1435 12/15) − 1. Despite having the lowest value for the periodic rate, ETF 2 has the highest annualized rate of return because of the reinvestment rate assumption and the compounding of the periodic rate.

As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset's variance to the volatility of the portfolio: increases. decreases. remains the same.

B is correct. The contribution of each individual asset's variance (or standard deviation) to the portfolio's volatility decreases as the number of assets in the equally weighted portfolio increases. The contribution of the co-movement measures between the assets increases (i.e., covariance and correlation) as the number of assets in the equally weighted portfolio increases. The following equation for the variance of an equally weighted portfolio illustrates these points: σ2p=σ¯2N+N−1NCOV¯¯¯¯¯¯¯¯=σ¯2N+N−1Nρ¯ σ¯2 .

An analyst obtains the following annual rates of return for a mutual fund: Year Return (%) 2008 14 2009 −10 2010 −2 The fund's holding period return over the three-year period is closest to: 0.18%. 0.55%. 0.67%.

B is correct. [(1 + 0.14)(1 − 0.10)(1 − 0.02)] - 1 = 0.0055 = 0.55%.

A portfolio manager creates the following portfolio: Security Expected Annual Return (%) Expected Standard Deviation (%) 1 16 20 2 12 20 If the portfolio of the two securities has an expected return of 15%, the proportion invested in Security 1 is: 25%. 50%. 75%.

C is correct. Rp=w1×R1+(1−w1)×R2Rp=w1×16%+(1−w1)×12%15%=0.75(16%)+0.25(12%

A portfolio manager creates the following portfolio: Security Security Weight (%) Expected Standard Deviation (%) 1 30 20 2 70 12 If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is closest to: 10.7%. 11.3%. 12.1%.

C is correct. σport=w21σ21+w22σ22+2w1w2ρ1,2σ1σ2−−−−−−−−−−−−−−−−−−−−−−−−√=(0.3)2(20%)2+(0.7)2(12%)2+2(0.3)(0.7)(0.40)(20%)(12%)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=(0.3600%+0.7056%+0.4032%)0.5=(1.4688%)0.5=12.11%.

A portfolio manager creates the following portfolio: Security Security Weight (%) Expected Standard Deviation (%) 1 30 20 2 70 12 If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to: −1.0. 0.0. 1.0.

C is correct. A portfolio standard deviation of 14.40% is the weighted average, which is possible only if the correlation between the securities is equal to 1.0.

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence: Asset Outcome 1 (%) Outcome 2 (%) Outcome 3 (%) Expected Return (%) 1 12 0 6 6 2 12 6 0 6 3 0 6 12 6 If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation? Asset 1 and Asset 2. Asset 1 and Asset 3. Asset 2 and Asset 3.

C is correct. An equally weighted portfolio of Asset 2 and Asset 3 will have the lowest portfolio standard deviation, because for each outcome, the portfolio has the same expected return (they are perfectly negatively correlated).

An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence: Asset Outcome 1 (%) Outcome 2 (%) Outcome 3 (%) Expected Return (%) 1 12 0 6 6 2 12 6 0 6 3 0 6 12 6 Which pair of assets is perfectly negatively correlated? Asset 1 and Asset 2. Asset 1 and Asset 3. Asset 2 and Asset 3.

C is correct. Asset 2 and Asset 3 have returns that are the same for Outcome 2, but the exact opposite returns for Outcome 1 and Outcome 3; therefore, because they move in opposite directions at the same magnitude, they are perfectly negatively correlated.

With respect to trading costs, liquidity is least likely to impact the: stock price. bid-ask spreads. brokerage commissions.

C is correct. Brokerage commissions are negotiated with the brokerage firm. A security's liquidity impacts the operational efficiency of trading costs. Specifically, liquidity impacts the bid-ask spread and can impact the stock price (if the ability to sell the stock is impaired by the uncertainty associated with being able to sell the stock).

With respect to the mean-variance theory, the optimal portfolio is determined by each individual investor's: risk-free rate. borrowing rate. risk preference.

C is correct. Each individual investor's optimal mix of the risk-free asset and the optimal risky asset is determined by the investor's risk preference.

Evidence of risk aversion is best illustrated by a risk-return relationship that is: negative. neutral. positive.

C is correct. Historical data over long periods of time indicate that there exists a positive risk-return relationship, which is a reflection of an investor's risk aversion.

A financial planner has created the following data to illustrate the application of utility theory to portfolio selection: Investment Expected Return (%) Expected Standard Deviation (%) 1 18 2 2 19 8 3 20 15 4 18 30 A risk-neutral investor is most likely to choose: Investment 1. Investment 2. Investment 3.

C is correct. Investment 3 has the highest rate of return. Risk is irrelevant to a risk-neutral investor, who would have a measure of risk aversion equal to 0. Given the utility function, the risk-neutral investor would obtain the greatest amount of utility from Investment 3. Investment Expected Return (%) Expected Standard Deviation (%) Utility A = 0 1 18 2 0.1800 2 19 8 0.1900 3 20 15 0.2000 4 18 30 0.1800

A financial planner has created the following data to illustrate the application of utility theory to portfolio selection: Investment Expected Return (%) Expected Standard Deviation (%) 1 18 2 2 19 8 3 20 15 4 18 30 If an investor's utility function is expressed as U=E(r)−12Aσ2 and the measure for risk aversion has a value of −2, the risk-seeking investor is most likely to choose: Investment 2. Investment 3. Investment 4.

C is correct. Investment 4 provides the highest utility value (0.2700) for a risk-seeking investor, who has a measure of risk aversion equal to −2. Investment Expected Return (%) Expected Standard Deviation (%) Utility A = -2 1 18 2 0.1804 2 19 8 0.1964 3 20 15 0.2225 4 18 30 0.2700

With respect to an equally-weighted portfolio made up of a large number of assets, which of the following contributes the most to the volatility of the portfolio? Average variance of the individual assets. Standard deviation of the individual assets. Average covariance between all pairs of assets.

C is correct. The co-movement measures between the assets increases (i.e., covariance and correlation) as the number of assets in the equally weighted portfolio increases. The contribution of each individual asset's variance (or standard deviation) to the portfolio's volatility decreases as the number of assets in the equally weighted portfolio increases. The following equation for the variance of an equally weighted portfolio illustrates these points: σ2p=σ¯2N+N−1NCOV¯¯¯¯¯¯¯¯=σ¯2N+N−1Nρ¯ σ¯2

The portfolio on the minimum-variance frontier with the lowest standard deviation is: unattainable. the optimal risky portfolio. the global minimum-variance portfolio.

C is correct. The global minimum-variance portfolio is the portfolio on the minimum-variance frontier with the lowest standard deviation. Although the portfolio is attainable, when the risk-free asset is considered, the global minimum-variance portfolio is not the optimal risky portfolio.

Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the: highest expected return for a given level of risk. lowest amount of risk for a given level of return. highest expected return relative to the risk-free rate.

C is correct. The minimum-variance frontier does not account for the risk-free rate. The minimum-variance frontier is the set of all attainable risky assets with the highest expected return for a given level of risk or the lowest amount of risk for a given level of return.

With respect to utility theory, the most risk-averse investor will have an indifference curve with the: most convexity. smallest intercept value. greatest slope coefficient.

C is correct. The most risk-averse investor has the indifference curve with the greatest slope.

An investor purchased 100 shares of a stock for $34.50 per share at the beginning of the quarter. If the investor sold all of the shares for $30.50 per share after receiving a $51.55 dividend payment at the end of the quarter, the holding period return is closest to: −13.0%. −11.6%. −10.1%.

C is correct. −10.1% is the holding period return, which is calculated as: (3,050 − 3,450 + 51.55)/3,450, which is comprised of a dividend yield of 1.49% = 51.55/(3,450) and a capital loss yield of −11.59% = -400/(3,450).