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
... [Show More] 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).
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%.
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%
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.
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.
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].
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 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 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.
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.
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%
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%
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%
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).
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.
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).
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.
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.
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
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
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.
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.
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 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%
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%
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 .
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 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).
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. [Show Less]