Reading 7: Statistical Concepts and Market Returns - LOS f style, black

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13、

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 percent during the period 1991-2000, what is the Sharpe ratio for ABC Mutual Fund for the period 1991-2000?

A)   0.52.

B)   0.35.

C)   0.68.

D)   1.12.

14、

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%

What is the arithmetic mean return and the geometric mean return for ABC Mutual Fund for the period 1991-2000?

Arithmetic Mean

Geometric Mean

 

A)            7.2%                        5.6%

B)            28.2%                      7.4%

C)            8.2%                        6.8%

D)            7.2%                        6.8%

15、Assuming a mean of 7.2 percent, what is the sample standard deviation of the returns for ABC Mutual Fund for the period 1991-2000?

A)   7.8%.

B)   9.8%.

C)   10.2%.

D)   9.1%.

16、There is a 40% chance that an investment will earn 10%, a 40% chance that the investment will earn 12.5%, and a 20% chance that the investment will earn 30%. What is the mean expected return and the standard deviation of expected returns?

Mean	Standard Deviation

 

A)   15.0%             5.75%

B)   17.5%             5.75%

C)    17.5%           7.58%

D)       15.0%         7.58%

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jacky_z

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cfaedu

答案和详解如下：

13、

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 percent during the period 1991-2000, what is the Sharpe ratio for ABC Mutual Fund for the period 1991-2000?

A)   0.52.

B)   0.35.

C)   0.68.

D)   1.12.

The correct answer was B)

	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

14、

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%

What is the arithmetic mean return and the geometric mean return for ABC Mutual Fund for the period 1991-2000?

Arithmetic Mean

Geometric Mean

 

A)            7.2%                        5.6%

B)            28.2%                      7.4%

C)            8.2%                        6.8%

D)            7.2%                        6.8%

The correct answer was D)

arithmetic mean = (11+12.5+8+9+13+7+15+2-16.5+11)/10 = 7.20

geometric mean = (1.11 × 1.125 × 1.08×1.09 × 1.13 × 1.07 × 1.15 × 1.02 × 0.835 × 1.11)^1/10 – 1

= (1.932)^0.10 – 1 = 1.068-1 = 0.068 or 6.8%

15、Assuming a mean of 7.2 percent, what is the sample standard deviation of the returns for ABC Mutual Fund for the period 1991-2000?

A)   7.8%.

B)   9.8%.

C)   10.2%.

D)   9.1%.

The correct answer was D)

Standard deviation = [∑ _i (x_i- X)² / (n -1)]^1/2

= √ (744.10 / 9) = √ (82.68) = 9.1%

16、There is a 40% chance that an investment will earn 10%, a 40% chance that the investment will earn 12.5%, and a 20% chance that the investment will earn 30%. What is the mean expected return and the standard deviation of expected returns?

Mean	Standard Deviation

 

A)   15.0%             5.75%

B)   17.5%             5.75%

C)    17.5%           7.58%

D)       15.0%         7.58%

The correct answer was D)

mean = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%

var = (0.4)(10 - 15)² + (0.4)(12.5 - 15)² + (0.2)(30 - 15)² = 57.5

Standard deviation = √57.5 = 7.58