Reading 9: Common Probability Distributions - LOS i ～ Q1-6

答案和详解如下：

1、The mean and standard deviation of four portfolios are listed below in percentage terms. Using Roy's safety-first criteria and a threshold of 4 percent, select the mean and standard deviation that corresponds to the optimal portfolio.

A)             14                           20

B)              8                           10

C)             19                           28

D)              5                            3

The correct answer was

According to the safety-first criterion, the optimal portfolio is the one that has the largest value for the SFRatio (mean – threshold) / Standard Deviation. A mean = 19 and Standard Deviation = 28 yields the largest SFRatio from the choices given: (19 – 4) / 28 = 0.5357.

2、Which of the following portfolios provides the best “safety first” ratio if the minimum acceptable return is 6 percent?

A)   2.

B)   1.

C)   4.

D)   3.

The correct answer was D)

Roy’s safety-first criterion requires the maximization of the SF Ratio:
SF Ratio = (expected return – threshold return) / standard deviation

Portfolio #3 has the highest safety-first ratio at 1.67.

3、If the threshold return is higher than the risk-free rate, what will be the relationship between Roy’s safety-first ratio (SF) and Sharpe’s ratio?

A)   The SF ratio will be lower.

B)   The SF ratio will be higher.

C)   They will be the same.

D)   The SF ratio may be higher or lower depending on the standard deviation.

The correct answer was A)    

Since each ratio has the standard deviation of returns in the denominator, the difference depends upon the effect on the numerator. Since both the risk-free rate (in the Sharpe ratio) and the threshold rate (in the SF ratio) are subtracted from the expected return, a larger threshold rate would result in a smaller SF ratio value.

4、The safety-first criterion rules focuses on:

A)   SEC regulations.

B)   shortfall risk.

C)   IRA guidelines for capital gains.

D)   Margin requirements.

The correct answer was B)    

The safety-first criterion focuses on shortfall risk which is the probability that a portfolio’s value or return will not fall below a given threshold level. The safety-first criterion usually dictate choosing a portfolio with the lowest probability of falling below the threshold level or return.

5、Which of the following portfolios provides the optimal “safety first” return if the minimum acceptable return is 9 percent?

A)   2.

B)   3.

C)   1.

D)   4.

The correct answer was A)    

Roy’s safety-first criterion requires the maximization of the SF Ratio:
SF Ratio = (expected return – threshold return) / standard deviation

Portfolio #2 has the highest safety-first ratio at 0.80.

6、The mean and standard deviation of four portfolios are listed below in percentage terms. Using Roy's safety first criteria and a threshold of 3 percent, select the mean and standard deviation that corresponds to the optimal portfolio.

A)              14                          20

B)               8                              10

C)               5                          3

D)              19                              28

The correct answer was C)

According to the safety-first criterion, the optimal portfolio is the one that has has the largest value for the SFRatio (mean – threshold) / Standard Deviation. A mean = 5 and Standard Deviation = 3 yields the largest SFRatio from the choices given: (5 – 3) / 3 = 0.67.