Q4. Assuming a mean of 7.2%, what is the sample standard deviation of the returns for ABC Mutual Fund for the period 1991-2000?

A)   7.8%.

B)   9.1%.

C)   9.8%.

Q5. Annual Returns on ABC Mutual Fund

1991    1992        1993        1994        1995        1996        1997        1998        1999        2000

11.0% 12.5%      8.0%        9.0%        13.0%      7.0%        15.0%      2.0%        -16.5%     11.0%

If the risk-free rate was 4.0% during the period 1991-2000, what is the Sharpe ratio for ABC Mutual Fund for the period 1991-2000?

A)   0.52.

B)   0.68.

C)   0.35.

Q6. When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The

A)    variance.

B)    standard deviation.

C)    median.

Q7. Given the following annual returns, what are the population variance and standard deviation, respectively?

2000           2001           2002           2003            2004

15%            2%               5%               -7%              0%.

A)   64.5; 8.0.

B)   32.4; 5.7.

C)   51.6; 7.2.

答案和详解如下：

Q4. Assuming a mean of 7.2%, what is the sample standard deviation of the returns for ABC Mutual Fund for the period 1991-2000?

A)   7.8%.

B)   9.1%.

C)   9.8%.

Correct answer is B)

Standard deviation = [∑_i (x_i − X)² / (n − 1)]^1/2 = √(744.10 / 9) = √(82.68) = 9.1%

Q5. Annual Returns on ABC Mutual Fund

1991    1992        1993        1994        1995        1996        1997        1998        1999        2000

11.0% 12.5%      8.0%        9.0%        13.0%      7.0%        15.0%      2.0%        -16.5%     11.0%

If the risk-free rate was 4.0% during the period 1991-2000, what is the Sharpe ratio for ABC Mutual Fund for the period 1991-2000?

A)   0.52.

B)   0.68.

C)   0.35.

Correct answer is C)

         1991        1992        1993        1994        1995        1996        1997        1998        1999        2000

Annual return 11.0%      12.5%      8.0%        9.0%        13.0%      7.0%        15.0%      2.0%        -16.5%     11.0%      Mean = 7.2

X − mean         3.8   5.3   0.8   1.8   5.8   -0.2           7.8   -5.2           -23.7        3.8  

(X − mean)²     14.44       28.09       0.64          3.24          33.64       0.04          60.84       27.04       561.69     14.44       Sum = 744.10

Variance = (X − mean)² / (n − 1) = 744.10 / 9 = 82.68

Standard deviation = (82.68)^1/2 = 9.1

Sharpe Ratio = (mean return – risk-free rate) / standard deviation = (7.2 – 4) / 9.1 = 0.35

Q6. When creating intervals around the mean to indicate the dispersion of outcomes, which of the following measures is the most useful? The

A)    variance.

B)    standard deviation.

C)    median.

Correct answer is B)

The standard deviation is more useful than the variance because the standard deviation is in the same units as the mean. The median does not help in creating intervals around the mean.

Q7. Given the following annual returns, what are the population variance and standard deviation, respectively?

2000           2001           2002           2003            2004

15%            2%               5%               -7%              0%.

A)   64.5; 8.0.

B)   32.4; 5.7.

C)   51.6; 7.2.

Correct answer is C)

The population variance is found by taking the mean of all squared deviations from the mean.

[ (15 − 3)² + (2 − 3)² + (5 − 3)² + (-7 − 3)² + (0 − 3)² ] / 5 = 51.6

The population standard deviation is found by taking the square root of the population variance.

51.6^1/2 = 7.2

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