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AIM 4: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen’s alpha.

1、For a given portfolio, the expected return is 12% with a standard deviation of 22%. The beta of the portfolio is 1.1. The expected return of the market is 10% with a standard deviation of 20%. The risk-free rate is 4%. The Sharpe measure of the portfolio is:

A) 20.00.

B) 0.36. 

C) 7.27.

D) 0.10. 

likaiba

 

The correct answer is B

The Sharpe Measure is the risk premium divided by the standard deviation, σ: Sharpe measure of portfolio “p” = [E(RP) - RF]/σP = [12 - 4]/22 = 0.363

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2、Portfolio A earned a return of 10.23% and had a standard deviation of returns of 6.22%. If the return over the same period on Treasury bills (T-bills) was 0.52% and the return to Treasury bonds (T-bonds) was 4.56%, what is the Sharpe ratio of the portfolio?

A) 0.56.

B) 1.56.

C) 0.91.

D) 7.71.

likaiba

 

The correct answer is B

Sharpe ratio = (Rp – Rf) / σp, where (Rp – Rf) is the difference between the portfolio return and the risk free rate, and σp is the standard deviation of portfolio returns. Thus, the Sharpe ratio is: (10.23 – 0.52) / 6.22 = 1.56. Note, the T-bill rate is used for the risk free rate.

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3、

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)   1.12.

D)   0.35.

likaiba

 

The correct answer is D

	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

 

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

A) 0.147.

B) 0.267.

C) 0.725.

D) 0.568.

likaiba

 

The correct answer is C

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

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

A) 2.6%.

B) 3.9%.

C) 2.7%.

D) 3.1%.

likaiba

 

The correct answer is C

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