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 (xi − 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. 51.61/2 = 7.2 | 
发表于 2009-1-6 11:43
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