Question 1

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

Accepted Answer

The Sharpe Ratio formula is:
(Asset Return - Risk-Free Rate) / Asset Standard Deviation

We have the following values:
Asset Return = Expected Market Return = 10.2%
Risk-Free Rate = Treasury Bill Yield = 1.5%
Asset Standard Deviation = Square Root of Portfolio Variance = Square Root of 0.0323 = 0.1796

Using the formula, we get:
Sharpe Ratio = (10.2% - 1.5%) / 0.1796 = 49.5

Therefore, the Sharpe Ratio of the portfolio is 0.639. Thus, the correct answer is option C.

Question 2

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

Accepted Answer

The Treynor ratio is calculated as (Portfolio Return - Risk-Free Rate) / Beta. Here, it is (10.9% - 1.8%) / 0.63 = 0.144.

Question 3

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

Accepted Answer

The Sharpe ratio is calculated as (Expected Return - Risk-Free Rate) / Standard Deviation. First, calculate the standard deviation as the square root of the variance: √0.0165 ≈ 0.128. Then, use the formula: (12.65% - 3.4%) / 0.128 ≈ 0.720.

Question 4

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

Accepted Answer

The answer of A portfolio has a beta of 1.16,...

Question 5

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

Accepted Answer

The Sharpe ratio is calculated as (Portfolio Return - Risk-Free Rate) / Standard Deviation of Portfolio Return. Using the given values: (9.9% - 1.9%) / 12.3% = 8% / 12.3% = 0.650.

Question 6

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

Accepted Answer

The answer of The U.S. Treasury bill is yielding 1.85%...

Question 7

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%

Accepted Answer

Jensen's alpha = Portfolio Return - [Risk-free Return + Beta * (Market Return - Risk-free Return)]
= 14.76% - [2.84% + 1.31 * (10.84% - 2.84%)]
= 1.44%
Therefore, the answer is D) 1.44%.

Question 8

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%

Accepted Answer

The answer of A portfolio has a Sharpe ratio of...

Question 9

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

Accepted Answer

The Treynor Ratio is calculated as (Portfolio Return - Risk-Free Rate) / Beta. For a correctly-valued portfolio, the expected return is the market return. Thus, Treynor Ratio = (11.6% - 3.0%) / 1.02 = 8.43% or .0843, which rounds to option B, .086.

Question 10

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

Accepted Answer

The Sharpe ratio is calculated as (Expected Return - Risk-Free Rate) / Standard Deviation. Here, it is (12.9% - 1.35%) / 19.4% = 0.595.

Question 11

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%

Accepted Answer

Jensen's alpha is calculated as the actual portfolio return minus the expected return based on the CAPM formula. Here, the actual return is 4.39% and the expected return is 6.27%. Therefore, Jensen's alpha = 4.39% - 6.27% = -1.88%. The portfolio's standard deviation and beta are not needed to calculate Jensen's alpha.

Question 12

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

Accepted Answer

The Treynor ratio is calculated as follows:
Treynor ratio = (Expected portfolio return - Risk-free rate) / Portfolio beta
= (14.5% - 3.1%) / 1.05
= 10.4% / 1.05
= 9.90%
Therefore, the Treynor ratio for this portfolio is 9.9%, which is option C.

Question 13

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

Accepted Answer

First, we need to calculate the expected return of the portfolio using the market return and beta:

Expected return = risk-free rate + beta (market risk premium)
Expected return = 0 + 1.23(0.079)
Expected return = 0.09717 or 9.717%

Next, we can calculate the excess return of the portfolio:

Excess return = expected return - risk-free rate
Excess return = 0.09717 - 0
Excess return = 0.09717 or 9.717%

Finally, we can calculate the Sharpe ratio:

Sharpe ratio = excess return / standard deviation
Sharpe ratio = 0.09717 / 0.116
Sharpe ratio = 0.838

Therefore, the best choice is D with the Sharpe ratio of 0.838.

Question 14

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%

Accepted Answer

The answer of A portfolio has a Treynor ratio of...

Question 15

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%

Accepted Answer

The answer of A portfolio has a beta of 1.30...

Question 16

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

Accepted Answer

The Treynor Ratio is calculated as (Expected Return of the Portfolio - Risk-Free Rate) / Beta of the Portfolio. Plugging in the given values: (13.3% - 4.5%) / 1.40 = 8.8% / 1.40 = 0.062857 or approximately .063.

Question 17

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

Accepted Answer

The answer of A portfolio has a beta of 1.26,...

Question 18

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

Accepted Answer

The Treynor ratio is calculated as (Expected Return - Risk-Free Rate) / Beta. Here, it is (13.8% - 3.2%) / 1.14 = 0.093.

Question 19

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%

Accepted Answer

Jensen's alpha is calculated as the portfolio's return minus the expected return based on the Capital Asset Pricing Model (CAPM). The expected return is calculated as the risk-free rate plus the portfolio's beta times the market risk premium. Assuming the risk-free rate is the market return minus the market risk premium (10.10% - 6.58% = 3.52%), the expected return is 3.52% + 1.33 * 6.58% = 12.27%. Jensen's alpha is 9.38% - 12.27% = -2.89%.

Question 20

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%

Accepted Answer

The Treynor ratio is calculated as (Portfolio Return - Risk-Free Rate) / Beta. Rearranging the formula to solve for the Portfolio Return gives us: Portfolio Return = (Treynor Ratio * Beta) + Risk-Free Rate. Substituting the given values: Portfolio Return = (.094 * 1.24) + 3.2% = 11.66% + 3.2% = 14.86%.

Quiz 13: Performance Evaluation and Risk Management

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 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 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 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 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?

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?

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 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?

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%?

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?

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?

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 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 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 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 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 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 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 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 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?