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

A)   2.6%.

B)   3.9%.

C)   3.1%.

D)   2.7%.

2、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.

* Calculated using the arithmetic mean.

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

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

B)   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.

C)   The standard deviation of returns for the office building is less than that of the REIT.

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

3、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)   0.06

C)   0.24

D)   1.62

4、A higher Sharpe ratio indicates:

A)   a lower risk per unit of return.

B)   greater diversification in the portfolio.

C)   lower volatility of returns.

D)   a higher excess return per unit of risk.

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

A)   0.725.

B)   0.147.

C)   0.267.

D)   0.568.

答案和详解如下：

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

A)   2.6%.

B)   3.9%.

C)   3.1%.

D)   2.7%.

The correct answer was D)

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

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

B)   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.

C)   The standard deviation of returns for the office building is less than that of the REIT.

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

The correct answer was B)

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.

The other 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.

3、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)   0.06

C)   0.24

D)   1.62

The correct answer was 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

4、A higher Sharpe ratio indicates:

A)   a lower risk per unit of return.

B)   greater diversification in the portfolio.

C)   lower volatility of returns.

D)   a higher excess return per unit of risk.

The correct answer was D)

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

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

A)   0.725.

B)   0.147.

C)   0.267.

D)   0.568.

The correct answer was A)

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