Deck 13: Performance Evaluation and Risk Management

Question 1

Which one of the following concerns a money manager's control over investment risks, particularly potential short-run losses?

A)Alpha management
B)Normal distribution management
C)Investment risk management
D)Raw return distributions
E)Volatility performance measures

Answer 1

C

Question 2

Which one of the following assesses risk by stating the probability of a loss a portfolio might incur within a stated time period given a specific probability?

A)Sharpe ratio
B)Jensen's alpha
C)Treynor ratio
D)raw return measurement
E)Value-at-Risk

Answer 2

E

Question 3

You are comparing three assets which have differing Treynor ratios. Given this, which one of the following must be true?

A)The assets may all be correctly priced if they have differing betas.
B)The assets have differing rates of return.
C)The assets have differing levels of market risk but equal amounts of total risk.
D)The assets are all mispriced according to CAPM.
E)The preferred investment is the asset with the highest Treynor ratio.

Answer 3

E

Question 4

Tony brags that his portfolio's rate of return is "beating the market". Which one of the following would best substantiate his claim?

A)positive Sharpe ratio
B)negative Treynor ratio
C)positive Jensen's alpha
D)zero Value-at-Risk
E)beta greater than 1.0

Question 5

The Sharpe ratio measures a security's return relative to which one of the following?

A)total risk
B)diversifiable risk
C)market rate of return
D)risk-free rate
E)systematic risk

Question 6

The unadjusted total percentage return on a security that has not been compared to any benchmark is referred to as which one of the following?

A)raw return
B)indexed return
C)real return
D)marginal return
E)absolute return

Question 7

Which one of the following is computed by dividing a portfolio's risk premium by the portfolio beta?

A)raw return
B)Value-at-Risk
C)Jensen's alpha
D)Sharpe ratio
E)Treynor ratio

Question 8

You are considering the purchase of a mutual fund. You have found three funds that meet your basic criteria. Each fund has a different alpha. Which alpha indicates the preferred investment?

A)the most negative alpha
B)the least negative alpha
C)the zero alpha
D)the lowest positive alpha
E)the highest positive alpha

Question 9

Which of the following should generally only be used to evaluate relatively diversified portfolios rather than individual securities?
I. Sharpe ratio
II. Treynor ratio
III. Jensen's alpha

A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III

Question 10

Which one of the following measures a portfolio's raw return against the expected return based on the Capital Asset Pricing Model?

A)Sharpe ratio
B)Treynor ratio
C)Jensen's alpha
D)beta
E)Value-at-Risk

Question 11

The Sharpe ratio is best used to evaluate which one of the following?

A)corporate bonds
B)government bonds
C)Treasury bills
D)individual stocks
E)diversified portfolios

Question 12

Which one of the following is a statistical model defined by its mean and standard deviation that is used to assess probabilities?

A)variance
B)normal distribution
C)efficient frontier
D)Value-at-Risk
E)Jensen's alpha

Question 13

Which one of the following is the best indication that a security is correctly priced according to the Capital Asset Pricing Model?

A)beta of zero
B)beta of 1.0
C)alpha of zero
D)alpha of 1.0
E)alpha of −1.0

Question 14

The risk premium of a portfolio divided by the portfolio's standard deviation defines which one of the following performance measures?

A)raw return
B)Value-at-Risk
C)Jensen's alpha
D)Sharpe ratio
E)Treynor ratio

Question 15

You are comparing three securities and discover they all have identical Treynor ratios. Given this information, which one of the following must be true regarding these three securities?

A)They have identical betas.
B)They have the same rates of return.
C)They earn identical rewards per unit of total risk.
D)They earn identical rewards per unit of systematic risk.
E)They have identical Sharpe ratios also.

Question 16

Which one of the following measures a security's return in relation to the total risk associated with that security?

A)beta
B)Jensen's alpha
C)Sharpe ratio
D)Treynor ratio
E)Value-at-Risk

Question 17

Which one of the following measures returns in relation to total risk?

A)Treynor ratio
B)Sharpe ratio
C)Jensen's alpha
D)Value-at-Risk
E)beta

Question 18

Which one of the following statements is correct in relation to a security that has a negative Jensen's alpha?

A)The security is overpriced and will plot below the security market line.
B)The security is overpriced and will plot above the security market line.
C)The security is underpriced and will plot below the security market line.
D)The security is underpriced and will plot above the security market line.
E)The security is incorrectly priced but you cannot tell if it is underpriced or overpriced based on the information provided.

Question 19

Which one of the following measures risk premium in relation to systematic risk?

A)Value-at-Risk
B)Jensen's alpha
C)beta
D)Sharpe ratio
E)Treynor ratio

Question 20

Which one of the following values would be the most preferable as a Sharpe ratio?

A)−1.11
B)−.89
C)0
D).10
E)1.02

Question 21

Which of the following measures are dependent upon the accuracy of a security's beta?
I. Sharpe ratio
II. Treynor ratio
III. Jensen's alpha

A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III

Question 22

The Value-at-Risk measure assumes which one of the following?

A)returns are normally distributed
B)portfolios lie on the efficient frontier
C)all portfolios are fully diversified
D)returns tend to follow repetitive patterns
E)the risk premium is constant over time

Question 23

Which one of the following is measured by the Jensen-Treynor alpha?

A)total return relative to systematic risk
B)risk premium relative to systematic
C)risk premium relative to total risk
D)excess return relative to systematic risk
E)excess return relative to total risk

Question 24

The Jensen-Treynor alpha is equal to:

A)the Treynor ratio divided by Jensen's alpha.
B)the Treynor ratio multiplied by Jensen's alpha.
C)Jensen's alpha divided by beta.
D)Jensen's alpha divided by the standard deviation.
E)Jensen's alpha divided by the Treynor ratio.

Question 25

Which of the following measures should be used to determine if a security should be included in a master portfolio?
I. Sharpe ratio
II. Treynor ratio
III. Jensen's alpha

A)I only
B)II only
C)III only
D)I and II only
E)II and III only

Question 26

Which one of the following is the best interpretation of this VaR statistic: Prob (R_p ≤ − .15)= 37%?

A)If your portfolio declines by 15% or more, then that decline is expected to be followed by a 37% increase in value.
B)Your portfolio is expected to lose at least 15%, but not more than 37%, in any given year.
C)There is a 37% chance that your portfolio will decline in value by at least 15% over the next year.
D)Sometime in the future, your portfolio is expected to lose 15% or more in a single year, but have an overall average rate of return of 37%.
E)There is a 37% chance that your portfolio will lose at least 15% of its value over the next 10 years.

Question 27

A Sharpe-optimal portfolio provides which one of the following for a given set of securities?

A)Jensen's Alpha
B)highest possible level of risk
C)highest level of return for a market-equivalent level of risk
D)highest excess return per unit of systematic risk
E)highest risk premium per unit of total risk

Question 28

Which one of the following Value-at-Risk measures would be most appropriate for a portfolio designed for a very risk-adverse investor?

A)Prob (R_p ≤ − .20)= 100%
B)Prob (R_p ≤ − .15)= 50%
C)Prob (R_p ≤ − .10)= 25%
D)Prob (R_p ≤ − .10)= 10%
E)Prob (R_p ≤ − .05)= 1%

Question 29

The Sharpe-optimal portfolio will be the investment opportunity set which lies on a straight line that has which of the following characteristics?

A)the flattest slope when the line intersects the vertical axis at the risk-free rate
B)the steepest slope when the line intersects the vertical axis at the risk-free rate
C)the steepest slope when the line intersects the vertical axis at the origin
D)the flattest slope when the line intersects the vertical axis at the market rate
E)the steepest slope when the line intersects the vertical axis at the market rate

Question 30

A portfolio has a 2.0% chance of losing 15% or more according to the VaR when T = 1. This can be interpreted to mean that the portfolio is expected to have an annual loss of 15% or more once in every how many years?

A)1
B)2
C)25
D)50
E)100

Question 31

You want to create the best portfolio that can be derived from two assets. Which one of the following will help you identify that portfolio?

A)highest portfolio beta
B)market equivalent level of risk
C)highest possible rate of return
D)Treynor-minimal portfolio
E)Sharpe-optimal portfolio

Question 32

Which metric measures how volatile a fund's returns are relative to its benchmark?

A)Jensen's alpha
B)information ratio
C)Tracking error
D)Sharpe ratio
E)Treynor ratio

Question 33

Which one of the following statements is true concerning VaR?

A)VaR ignores time.
B)VaR only applies to time periods of one year.
C)VaR applies only to time periods equal to or greater than one year.
D)VaR values can be computed for monthly time periods.
E)VaR is accurate only for time periods less than one year.

Question 34

Which one of the following correctly states the VaR for a 3-year period with a 2.5% probability?

A)Prob[R_p,T ≤ E(R_p)× 3 − 1.645 × σ_p √3]
B)Prob[R_p,T ≤ E(R_p)× √3 − 1.645 × σ_p 3]
C)Prob[R_p,T ≤ E(R_p)× √3 − 1.645 × σ_p √3]
D)Prob[R_p,T ≤ E(R_p)× 3 − 1.960 × σ_p √3]
E)Prob[R_p,T ≤ E(R_p)× √3 − 1.960 × σ_p 3]

Question 35

Which measure would you use to know whether alpha is truly significant or the result of random chance?

A)Jensen's alpha
B)information ratio
C)Jensen-Treynor alpha
D)Sharpe ratio
E)Treynor ratio

Question 36

Which one of the following is probably the best measure of the performance of a well-diversified portfolio?

A)Jensen's alpha
B)Value-at-Risk
C)Jensen-Treynor alpha
D)Sharpe ratio
E)Treynor ratio

Question 37

Which of the following are related to VaR analysis?
I. beta
II. standard deviation
III. expected return
IV. time

A)I and III only
B)II and IV only
C)I, III, and IV only
D)II, III, and IV only
E)I, II, III, and IV

Question 38

Which one of the following is the primary purpose of the Value-at-Risk computation?

A)determine the 99% probability range given an abnormal distribution
B)evaluate the risk-return tradeoff for a given mix of securities
C)evaluate the probability of a significant loss
D)determine the portfolio that maximizes the risk premium per unit of total risk
E)determine the portfolio that maximizes the excess return per unit of systematic risk

Question 39

Which metric describes the percentage of a fund's movement that can be explained by movements in the market?

A)Jensen's alpha
B)information ratio
C)Tracking error
D)R Squared
E)Treynor ratio

Question 40

You have computed the expected return using VaR with a 2.5% probability for a 1-year period. How would this expected return be expressed on a normal distribution curve?

A)lower tail starting at the point that is 2.5 standard deviations below the mean
B)lower tail of a 95% probability range
C)the point that corresponds to 2.5 standard deviations below the mean
D)the point that represents the lower end of the 90% probability range
E)the negative range that lies within 2.5 standard deviations of the mean

Question 41

The U.S. Treasury bill is yielding 1.5% and the market has an expected return of 10.2%. What is the Sharpe ratio of a portfolio that has a beta of 1.32 and a variance of .0323?

A).550
B).573
C).639
D).743
E).826

Question 42

A portfolio has an average return of 10.9%, a standard deviation of 9.6%, and a beta of .63. The risk-free rate is 1.8%. What is the Treynor ratio?

A).092
B).106
C).144
D).164
E).283

Question 43

A portfolio has a variance of .0165, a beta of 1.05, and an expected return of 12.65%. What is the Sharpe ratio if the expected risk-free rate is 3.4%?

A).662
B).706
C).720
D).823
E).869

Question 44

A portfolio has a beta of 1.16, a standard deviation of 12.2%, and an expected return of 11.55%. The market return is 10.4% and the risk-free rate is 3.2%. What is the portfolio's Sharpe ratio?

A).574
B).684
C).737
D).770
E).855

Question 45

A portfolio has an average return of 9.9%, a standard deviation of 12.3%, and a beta of 1.23. The risk-free rate is 1.9%. What is the Sharpe ratio?

A).593
B).650
C).679
D).713
E).756

Question 46

The U.S. Treasury bill is yielding 1.85% and the market has an expected return of 7.48%. What is the Treynor ratio of a correctly-valued portfolio that has a beta of 1.33 and a variance of .0045?

A).056
B).064
C).069
D).082
E).087

Question 47

The U.S. Treasury bill has a return of 2.84% while the S&P 500 is returning 10.84%. Your portfolio has an actual return of 14.76% and a beta of 1.31. What is the portfolio's Jensen's alpha?

A)−.47%
B)−.92%
C)1.37%
D)1.44%
E)1.57%

Question 48

A portfolio has a Sharpe ratio of .75, a standard deviation of 17.0%, and an expected return of 15.9%. What is the risk-free rate?

A)1.98%
B)2.36%
C)2.48%
D)3.09%
E)3.15%

Question 49

The U.S. Treasury bill is yielding 3.0% and the market has an expected return of 11.6%. What is the Treynor ratio of a correctly-valued portfolio that has a beta of 1.02 and a standard deviation of 12.2%?

A).074
B).086
C).102
D).619
E).628

Question 50

Your portfolio has an expected return of 12.9%, a beta of 1.52, and a standard deviation of 19.4%. The U.S. Treasury bill rate is 1.35%. What is the Sharpe ratio of your portfolio?

A).595
B).673
C).700
D).773
E).838

Question 51

Your portfolio actually earned 4.39% for the year. You were expecting to earn 6.27% based on the CAPM formula. What is Jensen's alpha if the portfolio standard deviation is 12.1% and the beta is .99?

A)−5.28%
B)−3.40%
C)−2.34%
D)−2.40%
E)−1.88%

Question 52

Your portfolio has a beta of 1.05, a standard deviation of 14.3%, and an expected return of 14.5%. The market return is 11.3% and the risk-free rate is 3.1%. What is the Treynor ratio?

A).015
B).080
C).109
D).482
E).510

Question 53

A portfolio has a beta of 1.23 and a standard deviation of 11.6%. What is the Sharpe ratio if the market return is 12.4% and the market risk premium is 7.9%?

A).073
B).118
C).655
D).838
E).902

Question 54

A portfolio has a Treynor ratio of .055, a standard deviation of 13.3%, a beta of 1.22, and an expected return of 15.3%. What is the risk-free rate?

A)6.18%
B)7.21%
C)7.39%
D)8.18%
E)8.59%

Question 55

A portfolio has a beta of 1.30 and an actual return of 15.5%. The risk-free rate is 3.5% and the market risk premium is 8.2%. What is the value of Jensen's alpha?

A)−.86%
B)1.01%
C)1.14%
D)1.23%
E)1.34%

Question 56

A portfolio has a variance of .03105, a beta of 1.40, and an expected return of 13.3%. What is the Treynor ratio if the expected risk-free rate is 4.5%?

A).055
B).063
C).367
D).498
E).512

Question 57

A portfolio has a beta of 1.26, a standard deviation of 15.9%, and an average return of 15.07%. The market rate is 12.7% and the risk-free rate is 3.6%. What is the Sharpe ratio?

A).616
B).684
C).721
D).847
E).880

Question 58

A portfolio has an expected return of 13.8%, a beta of 1.14, and a standard deviation of 12.7%. The U.S. Treasury bill rate is 3.2%. What is the Treynor ratio?

A).093
B).138
C).146
D).835
E).951

Question 59

A diversified portfolio has a beta of 1.33 and a raw return of 9.38%. The market return is 10.10% and the market risk premium is 6.58%. What is Jensen's alpha of the portfolio?

A)−3.62%
B)−2.89%
C)−.29%
D)2.89%
E)3.62%

Question 60

A portfolio has a standard deviation of 12.1%, a beta of 1.24, and a Treynor ratio of .094. The risk-free rate is 3.2%. What is the portfolio's expected rate of return?

A)14.86%
B)15.25%
C)15.42%
D)16.41%
E)16.56%

Question 61

Lester has a portfolio with an average return of 10.8% and a standard deviation of 12.3%. He has a 1% probability of losing ________% or more in any given year.
$\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$

A)33.97
B)28.33
C)20.23
D)17.81
E)13.92

Question 62

Your portfolio has an expected annual return of 8.2%. What is the 2-year expected return?

A)11.6%
B)14.6%
C)16.4%
D)21.6%
E)23.2%

Question 63

What is the Treynor ratio of a portfolio comprised of 45% Portfolio A and 55% Portfolio B?
$\begin{array}{lrr}&\text{A}&\text{B}\\\text { Neight } & 45 \% & 55\% \\\text { Avg Return } & 13.60 \% & 8.40 \% \\\text { Std Dev } & 17.20 \% & 6.40 \%\\\text{Beta}&1.38&0.87\end{array}$

The risk-free rate is 3.12% and the market risk premium is 8.5%.

A).041
B).058
C).069
D).114
E).136

Question 64

A portfolio consists of the following two funds:
$\begin{array}{lrr}&\text { Fund A }& \text { Fund B }\\\text { Expected Return } & 13 \% & 9\% \\\text { Standard deviation } & 16 \% & 10\% \\\text { Eortfolio market value } & \$ 6,000 & \$ 14,000\\\text {Correlation}{R}_A,{R}_B&0.54\\\text { Rigk-free rate }&4\%\end{array}$
What is the Sharpe ratio of the portfolio?

A).391
B).453
C).529
D).596
E).640

Question 65

A portfolio has an actual return of 15.17%, a beta of .90, and a standard deviation of 7.2%. The market return is 13.4% and the risk-free rate is 2.8%. What is the portfolio's Jensen's alpha?

A)2.25%
B)2.51%
C)2.67%
D)2.83%
E)3.04%

Question 66

A portfolio consists of the following two funds:
$\begin{array}{lrr}&\text { Fund A }& \text { Fund B }\\\text { Expected Return } & 16 \% & 9\% \\\text { Standard deviation } & 21 \% & 11\% \\\text { Portfolio market value } & \$ 27,000 & \$ 33,000\\\text {Weight}&45\%&55\%\\\text {Correlation}{R}_A,{R}_B&0.21\\\text { Rigk-free rate }&2.5\%\end{array}$
What is the Sharpe ratio of the portfolio?

A).333%
B).425%
C).635%
D).788%
E).838%

Question 67

You have a portfolio which has an average return of 10.3%. In any given year, you have a 2.5% probability of earning either a zero or a negative annual return. What is the approximate standard deviation of your portfolio?
$\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$

A)5.26%
B)6.43%
C)6.94%
D)7.60%
E)8.14%

Question 68

Mike's portfolio has a 2-year expected return of 21.70%. What is the expected return for one year?

A)10.85%
B)12.50%
C)13.33%
D)14.22%
E)15.34%

Question 69

What is the Treynor ratio of a portfolio comprised of 40% Portfolio A, 25% Portfolio B, and 35% Portfolio C?
$\begin{array}{lccrr}\text { Asset } & \text { Weight } & \text { Avg Return } & \text { Std Dev } & \text { Beta } \\\text { A } & 40 \% & 15.30 \% & 17.20 \% & 1.56 \\\text { B } & 25 \% & 10.50 \% & 9.80 \% & .95 \\\text { C } & 35 \% & 13.30 \% & 14.10\% &1.25\end{array}$

The risk-free rate is 2.9% and the market risk premium is 8.6%.

A).054
B).062
C).070
D).081
E).102

Question 70

The Miller Fund's correlation with the market is .648. What percentage of the fund's return can be explained by changes in the overall market?

A)35%
B)42%
C)51%
D)65%
E)71%

Question 71

A portfolio has a standard deviation of 15.8% and an average return of 14.2%. What loss is associated with a 2.5% probability?
$\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$

A)12.03%
B)14.87%
C)16.77%
D)17.38%
E)19.36%

Question 72

Your portfolio has a standard deviation of 12.3% and an average return of 9.6%. You have a 5% probability of losing ________% or more in any given year.
$\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$

A)33.79
B)31.54
C)12.59
D)10.63
E)3.34

Question 73

A fund has an alpha of .89% and a tracking error of 3.8%. What is the fund's information ratio?

A).112
B).135
C).149
D).212
E).234

Question 74

A portfolio has an average return of 14.2% and a standard deviation of 12.85%. Given this, you should expect to lose at least ________% on an annual basis once every century.
$\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$

A)19.53
B)17.24
C)15.69
D)1.710
E)1.550

Question 75

A stock has a return of 16.9%, a standard deviation of 11.7%, and a beta of 1.50. The risk-free rate is 2.89% and the market risk premium is 8.45%. What is the Jensen-Treynor alpha of this stock?

A)−1.37%
B)−1.09%
C)−.48%
D).89%
E)1.05%

Question 76

A stock has a return of 16.18% and a beta of 1.47. The market return is 10.65% and the risk-free rate is 3.20%. What is the Jensen-Treynor alpha of this stock?

A)−1.12%
B)−.17%
C).66%
D)1.38%
E)1.59%

Question 77

A portfolio has a Jensen's alpha of .93%, a beta of 1.45, and a CAPM expected return of 8.8%. The risk-free rate is 2.5%. What is the actual return of the portfolio?

A)5.53%
B)6.17%
C)7.83%
D)9.73%
E)21.9%

Question 78

A portfolio consists of the following two funds:
$\begin{array}{lcr}&\text { Fund A }& \text { Fund B }\\\text {\$ Invested } & \$ 12,000 & \$ 8,000 \\\text { Weight } & 60\% & 40\% \\\text { Exp Return } & 15\% & 12\% \\\text { Std Dev } & 24\% & 14\% \\\text { Beta } & 1.92 & 1.27 \\\text { Corr(A, B) } & .43 &\\\text { Riakfree rate }&3.60\end{array}$
What is the Sharpe ratio of the portfolio?

A).422
B).581
C).645
D).721
E).798

Question 79

What is Jensen's alpha of a portfolio comprised of 40% Portfolio A and 60% of Portfolio B?
$$\begin{array} { c c c r } \text { Portfolio } & \text { Average Return } & \text { Standard Deviation } & \text { Beta } \\\text { A } & 16.3\% & 21.5\% & 1.58 \\\text {B } & 11.1 & 10.6 & 1.15\end{array}$$

The risk-free rate is 1.8% and the market risk premium is 5.3%.

A)1.25%
B)2.47%
C)3.08%
D)4.37%
E)5.38%

Question 80

Angie owns a portfolio which has an expected annual return of 9.76%. What is the 2-year expected return on her portfolio?

A)13.80%
B)19.52%
C)23.40%
D)27.60%
E)29.10%