Q5. A portfolio has a return of 14.2% and a Sharpe’s measure of 3.52. If the risk-free rate is 4.7%, what is the standard deviation of returns?

A)   3.9%.

B)   2.7%.

C)   2.6%.

Q6. Portfolio A earned a return of 10.23% and had a standard deviation of returns of 6.22%. If the return over the same period on Treasury bills (T-bills) was 0.52% and the return to Treasury bonds (T-bonds) was 4.56%, what is the Sharpe ratio of the portfolio?

A)   1.56.

B)   0.56.

C)   0.91.

Q7. The mean monthly return on U.S. Treasury bills (T-bills) is 0.42%. The mean monthly return for an index of small stocks is 4.56%, with a standard deviation of 3.56%. What is the Sharpe measure for the index of small stocks?

A)  16.56%.

B)  1.16%.

C)  10.60%.

Q8. Which of the following statements regarding the Sharpe ratio is most accurate? The Sharpe ratio measures:

A)   peakedness of a return distrubtion.

B)   excess return per unit of risk.

C)   total return per unit of risk.

Q9. Portfolio A earned an annual return of 15% with a standard deviation of 28%. If the mean return on Treasury bills (T-bills) is 4%, the Sharpe ratio for the portfolio is:

A)   0.54.

B)   0.39.

C)   1.87.

答案和详解如下：

Q5. A portfolio has a return of 14.2% and a Sharpe’s measure of 3.52. If the risk-free rate is 4.7%, what is the standard deviation of returns?

A)   3.9%.

B)   2.7%.

C)   2.6%.

Correct answer is B)

Standard Deviation of Returns = (14.2% – 4.7%) / 3.52 = 2.6988.

Q6. Portfolio A earned a return of 10.23% and had a standard deviation of returns of 6.22%. If the return over the same period on Treasury bills (T-bills) was 0.52% and the return to Treasury bonds (T-bonds) was 4.56%, what is the Sharpe ratio of the portfolio?

A)   1.56.

B)   0.56.

C)   0.91.

Correct answer is A)

Sharpe ratio = (R_p – R_f) / σ_p, where (R_p – R_f) is the difference between the portfolio return and the risk free rate, and σ_p is the standard deviation of portfolio returns. Thus, the Sharpe ratio is: (10.23 – 0.52) / 6.22 = 1.56. Note, the T-bill rate is used for the risk free rate.

Q7. The mean monthly return on U.S. Treasury bills (T-bills) is 0.42%. The mean monthly return for an index of small stocks is 4.56%, with a standard deviation of 3.56%. What is the Sharpe measure for the index of small stocks?

A)  16.56%.

B)  1.16%.

C)  10.60%.

Correct answer is B)

The Sharpe ratio measures excess return per unit of risk. (4.56 – 0.42) / 3.56 = 1.16%.

Q8. Which of the following statements regarding the Sharpe ratio is most accurate? The Sharpe ratio measures:

A)   peakedness of a return distrubtion.

B)   excess return per unit of risk.

C)   total return per unit of risk.

Correct answer is B)

The Sharpe ratio measures excess return per unit of risk. Remember that the numerator of the Sharpe ratio is (portfolio return − risk free rate), hence the importance of excess return. Note that peakedness of a return distribution is measured by kurtosis.

Q9. Portfolio A earned an annual return of 15% with a standard deviation of 28%. If the mean return on Treasury bills (T-bills) is 4%, the Sharpe ratio for the portfolio is:

A)   0.54.

B)   0.39.

C)   1.87.

Correct answer is B)

(15 − 4) / 28 = 0.39

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