Q1. A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio?

A)   0.568.

B)   0.725.

C)   0.147.

Q2. A higher Sharpe ratio indicates:

A)   lower volatility of returns.

B)   a lower risk per unit of return.

C)   a higher excess return per unit of risk.

Q3. Claude Bellow, CFA, is an analyst with a real estate focused investment firm. He asks his assistant to gather annual return information on a large office building and on a REIT (real estate investment trust) with diverse holdings. The following tables summarize the information.

Table 1: Annual returns (in %)

Asset        Year 1      Year 2      Year 3      Year 4      Year 5

REIT         25.0          20.0          5.0   -5.0           13.0

Office Building         15.0          5.0   -5.0           -2.0           13.0

Table 2: Mean and Dispersion Information

Asset                Mean Return     Variance

REIT                 11.6%                114.24

Office Building        5.2%             62.56

Calculated using the arithmetic mean.

Determine which of the following statements about the coefficient of variation of the two assets is least accurate.

A)   There is more dispersion relative to the mean in the distribution of the REIT returns when compared to the distribution of the returns for the office building.

B)   The coefficient of variation of the office building returns is approximately 1.52.

C)   The mean of the squared deviations from the arithmetic mean of the office building is less than that of the REIT.

Q4. A partner in the firm asks Bellow to calculate the Sharpe ratio for the REIT. If the risk-free rate is 5.0%, the Sharpe ratio is closest to:

A)     0.62.

B)     1.62.

C)     0.06.

答案和详解如下：

Q1. A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio?

A)   0.568.

B)   0.725.

C)   0.147.

Correct answer is B)

Sharpe ratio = (22% – 7.50%) / 20% = 0.725.

Q2. A higher Sharpe ratio indicates:

A)   lower volatility of returns.

B)   a lower risk per unit of return.

C)   a higher excess return per unit of risk.

Correct answer is C)

The Sharpe ratio is excess return (return − R_f) per unit of risk (defined as the standard deviation of returns).

Q3. Claude Bellow, CFA, is an analyst with a real estate focused investment firm. He asks his assistant to gather annual return information on a large office building and on a REIT (real estate investment trust) with diverse holdings. The following tables summarize the information.

Table 1: Annual returns (in %)

Asset        Year 1      Year 2      Year 3      Year 4      Year 5

REIT         25.0          20.0          5.0   -5.0           13.0

Office Building         15.0          5.0   -5.0           -2.0           13.0

Table 2: Mean and Dispersion Information

Asset                Mean Return     Variance

REIT                 11.6%                114.24

Office Building        5.2%             62.56

Calculated using the arithmetic mean.

Determine which of the following statements about the coefficient of variation of the two assets is least accurate.

A)   There is more dispersion relative to the mean in the distribution of the REIT returns when compared to the distribution of the returns for the office building.

B)   The coefficient of variation of the office building returns is approximately 1.52.

C)   The mean of the squared deviations from the arithmetic mean of the office building is less than that of the REIT.

Correct answer is A)

There is less dispersion relative to the mean in the distribution of the REIT returns (CV = s / mean = 114.24^1/2 / 11.6 = 0.92) when compared to the distribution of the monthly returns for the Office building (CV = 62.56^1/2 / 5.2 = 1.52). The coefficient of variation measures how much dispersion exists relative to the mean of a distribution and allows for direct comparison of dispersion across different data sets. Note: Ignore Table 1! All the information you need is in Table 2.

Both remaining statements are true. The mean of the squared deviations from the arithmetic mean is the definition of the variance, and the variance of the Office Building returns is less than for those of the REIT. Thus, the same relationship holds for the standard deviation.

Q4. A partner in the firm asks Bellow to calculate the Sharpe ratio for the REIT. If the risk-free rate is 5.0%, the Sharpe ratio is closest to:

A)     0.62.

B)     1.62.

C)     0.06.

Correct answer is A)

The Sharpe ratio measures the excess return per unit of risk. The formula is:

Sharpe Ratio = ( r_p − r_f ) / σ_p where: r_p = portfolio return; r_f = risk free return; σ = standard deviation

Sharpe Ratio_REIT = (11.6% − 5.00%) / 114.24^1/2 = 0.62

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