Question 1

The U.S.Treasury bill has a return of 2.84 percent while the S&P 500 is returning 10.84 percent.Your portfolio has an actual return of 14.76 percent and a beta of 1.31.What is the portfolio's Jensen's alpha?
A) −0.47 percent
B) −0.92 percent
C) 1.37 percent
D) 1.44 percent
E) 1.57 percent

Accepted Answer

Jensen's alpha = 0.1476 − [0.0284 + 1.31 (0.1084 − 0.0284)] = 1.44 percent

Question 2

A portfolio has a beta of 1.23 and a standard deviation of 11.6 percent.What is the Sharpe ratio if the market return is 12.4 percent and the market risk premium is 7.9 percent?
A) 0.07
B) 0.11
C) 0.65
D) 0.84
E) 0.90

Accepted Answer

Risk-free rate = 0.124 − 0.079 = 0.045 E(R_P) = 0.045 + 1.23 (0.079) = 0.14217 Sharpe ratio = (0.14217 − 0.045) / 0.116 = 0.84

Question 3

A portfolio has a Treynor ratio of 0.070,a standard deviation of 16.40 percent,a beta of 1.16,and an expected return of 14.3 percent.What is the risk-free rate?
A) 1.32 percent
B) 5.21 percent
C) 5.39 percent
D) 6.18 percent
E) 6.41 percent

Accepted Answer

0.070 = (0.143 - r_f) / 1.16; r_f = 6.18 percent

Question 4

The U.S.Treasury bill is yielding 2.5 percent and the market has an expected return of 9.0 percent.What is the Sharpe ratio of a portfolio that has a beta of 1.25 and a variance of 0.0218?
A) 0.55
B) 0.60
C) 0.69
D) 0.74
E) 0.82

Accepted Answer

E(R_P) = 0.025 + 1.25 (0.90 - 0.025) = 0.1063 Sharpe ratio = (0.1063 − 0.025) / √0.0218 = 0.5503

Question 5

The U.S.Treasury bill is yielding 1.85 percent and the market has an expected return of 7.48 percent.What is the Treynor ratio of a correctly-valued portfolio that has a beta of 1.33 and a variance of 0.0045?
A) 0.056
B) 0.064
C) 0.069
D) 0.082
E) 0.087

Accepted Answer

E(R_P) = 0.0185 + 1.33 (0.0748 - 0.0185) = 0.093379 Treynor ratio = (0.093379 − 0.0185) / 1.33 = 0.056

Question 6

Your portfolio has an expected return of 14.2 percent,a beta of 1.31,and a standard deviation of 15.3 percent.The U.S.Treasury bill rate is 3.48 percent.What is the Sharpe ratio of your portfolio?
A) 0.65
B) 0.67
C) 0.70
D) 0.77
E) 0.83

Accepted Answer

Sharpe ratio = (0.142 − 0.0348) / 0.153 = 0.7007

Question 7

A portfolio has a 2.0 percent chance of losing 15 percent 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 percent or more once in every how many years?
A) 1.0
B) 2.0
C) 25
D) 50
E) 100

Accepted Answer

The 2.0 percent chance of losing 15 percent or more implies that such a loss is expected to occur once in every 50 years (1/0.02 = 50).

Question 8

A portfolio has a beta of 1.30 and an actual return of 15.5 percent.The risk-free rate is 3.5 percent and the market risk premium is 8.2 percent.What is the value of Jensen's alpha?
A) −0.86 percent
B) 1.01 percent
C) 1.14 percent
D) 1.23 percent
E) 1.34 percent

Accepted Answer

Jensen's alpha = 0.155 − [0.035 + 1.30 (0.082)] = 1.34 percent

Question 9

A portfolio has an average return of 9.7 percent,a standard deviation of 8.6 percent,and a beta of 0.72.The risk-free rate is 2.1 percent.What is the Treynor ratio?
A) 0.098
B) 0.106
C) 0.121
D) 0.636
E) 0.884

Accepted Answer

Treynor ratio = (0.097 − 0.021) / 0.72 = 0.106

Question 10

A portfolio has a beta of 1.26,a standard deviation of 15.9 percent,and an average return of 15.07 percent.The market rate is 12.7 percent and the risk-free rate is 3.6 percent.What is the Sharpe ratio?
A) 0.61
B) 0.68
C) 0.72
D) 0.84
E) 0.88

Accepted Answer

Sharpe ratio = (0.1507 − 0.036) / 0.159 = 0.72

Question 11

A portfolio has a beta of 1.16,a standard deviation of 12.2 percent,and an expected return of 11.55 percent.The market return is 10.4 percent and the risk-free rate is 3.2 percent.What is the portfolio's Sharpe ratio?
A) 0.57
B) 0.68
C) 0.73
D) 0.77
E) 0.85

Accepted Answer

Sharpe ratio = (0.1155 - 0.032) / 0.122 = 0.68

Question 12

A portfolio has a variance of 0.031050,a beta of 1.40,and an expected return of 13.3 percent.What is the Treynor ratio if the expected risk-free rate is 4.5 percent?
A) 0.055
B) 0.063
C) 0.367
D) 0.498
E) 0.512

Accepted Answer

Treynor ratio = (0.133 − 0.045) / 1.40 = 0.0629

Question 13

A portfolio has a Sharpe ratio of 0.75,a standard deviation of 17.0 percent,and an expected return of 15.9 percent.What is the risk-free rate?
A) 1.98 percent
B) 2.36 percent
C) 2.48 percent
D) 3.09 percent
E) 3.15 percent

Accepted Answer

0.75 = (0.159 - r_f) / 0.17; r_f = 3.15 percent

Question 14

A portfolio has a standard deviation of 12.1 percent,a beta of 1.24 and a Treynor ratio of 0.094.The risk-free rate is 3.2 percent.What is the portfolio's expected rate of return?
A) 14.86 percent
B) 15.25 percent
C) 15.42 percent
D) 16.41 percent
E) 16.56 percent

Accepted Answer

0.094 = (R_p - 0.032) / 1.24; R_p = 14.856 percent

Question 15

Your portfolio has a beta of 1.05,a standard deviation of 14.3 percent,and an expected return of 14.5 percent.The market return is 11.3 percent and the risk-free rate is 3.1 percent.What is the Treynor ratio?
A) 0.015
B) 0.080
C) 0.109
D) 0.482
E) 0.510

Accepted Answer

Treynor ratio = (0.145 − 0.031) / 1.05 = 0.1086

Question 16

A portfolio has a variance of 0.0165,a beta of 1.05,and an expected return of 12.65 percent.What is the Sharpe ratio if the expected risk-free rate is 3.4 percent?
A) 0.66
B) 0.70
C) 0.72
D) 0.82
E) 0.86

Accepted Answer

Sharpe ratio = (0.1265 − 0.034) / √0.0165 = 0.7201

Question 17

The U.S.Treasury bill is yielding 3.0 percent and the market has an expected return of 11.6 percent.What is the Treynor ratio of a correctly-valued portfolio that has a beta of 1.02,and a standard deviation of 12.2 percent?
A) 0.074
B) 0.086
C) 0.102
D) 0.619
E) 0.628

Accepted Answer

E(R_P) = 0.03 + 0.92 (0.116 - 0.03) = 0.11772 Treynor ratio = (0.11772 − 0.03) / 1.02 = 0.086

Question 18

A portfolio has an expected return of 13.8 percent,a beta of 1.14,and a standard deviation of 12.7 percent.The U.S.Treasury bill rate is 3.2 percent.What is the Treynor ratio?
A) 0.093
B) 0.138
C) 0.146
D) 0.835
E) 0.951

Accepted Answer

Treynor ratio = (0.138 − 0.032) / 1.14 = 0.093

Question 19

Your portfolio actually earned 6.2 percent for the year.You were expecting to earn 8.6 percent based on the CAPM formula.What is Jensen's alpha if the portfolio standard deviation is 12.1 percent and the beta is 0.93?
A) −3.91 percent
B) −3.40 percent
C) −2.96 percent
D) −2.40 percent
E) −1.87 percent

Accepted Answer

Jensen's alpha = 6.2 percent − 8.6 percent = − 2.4 percent

Question 20

A portfolio has an average return of 12.4 percent,a standard deviation of 15.8 percent,and a beta of 1.35.The risk-free rate is 2.6 percent.What is the Sharpe ratio?
A) 0.49
B) 0.52
C) 0.62
D) 0.71
E) 0.75

Accepted Answer

Sharpe ratio = (0.124 − 0.026) / 0.158 = 0.62

Quiz 13: Performance Evaluation and Risk Management

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

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

A portfolio has a Treynor ratio of 0.070,a standard deviation of 16.40 percent,a beta of 1.16,and an expected return of 14.3 percent.What is the risk-free rate?

The U.S.Treasury bill is yielding 2.5 percent and the market has an expected return of 9.0 percent.What is the Sharpe ratio of a portfolio that has a beta of 1.25 and a variance of 0.0218?

The U.S.Treasury bill is yielding 1.85 percent and the market has an expected return of 7.48 percent.What is the Treynor ratio of a correctly-valued portfolio that has a beta of 1.33 and a variance of 0.0045?

Your portfolio has an expected return of 14.2 percent,a beta of 1.31,and a standard deviation of 15.3 percent.The U.S.Treasury bill rate is 3.48 percent.What is the Sharpe ratio of your portfolio?

A portfolio has a 2.0 percent chance of losing 15 percent 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 percent or more once in every how many years?

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

A portfolio has an average return of 9.7 percent,a standard deviation of 8.6 percent,and a beta of 0.72.The risk-free rate is 2.1 percent.What is the Treynor ratio?

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

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

A portfolio has a variance of 0.031050,a beta of 1.40,and an expected return of 13.3 percent.What is the Treynor ratio if the expected risk-free rate is 4.5 percent?

A portfolio has a Sharpe ratio of 0.75,a standard deviation of 17.0 percent,and an expected return of 15.9 percent.What is the risk-free rate?

A portfolio has a standard deviation of 12.1 percent,a beta of 1.24 and a Treynor ratio of 0.094.The risk-free rate is 3.2 percent.What is the portfolio's expected rate of return?

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

A portfolio has a variance of 0.0165,a beta of 1.05,and an expected return of 12.65 percent.What is the Sharpe ratio if the expected risk-free rate is 3.4 percent?

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

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

Your portfolio actually earned 6.2 percent for the year.You were expecting to earn 8.6 percent based on the CAPM formula.What is Jensen's alpha if the portfolio standard deviation is 12.1 percent and the beta is 0.93?

A portfolio has an average return of 12.4 percent,a standard deviation of 15.8 percent,and a beta of 1.35.The risk-free rate is 2.6 percent.What is the Sharpe ratio?