MEDIDA DE JENSEN (ALPHA DE JENSEN)

Instructions: Do the following calculations according to the information given.

Question 1

Given the following investment characteristics of four different portfolios, calculate the

Sharpe ratio, the Treynor ratio and the Jensen’s alpha performance for each one of them.

Portfolio

A 12% 40% .5

B 15% 30% .75

C 20% 22% 1.4

Market 15% 15% 1

Risk Free Asset 5% 0% 0

MEDIDA DE SHARPE

A= 12%-5%/ 40%= 0.175

B= 15%-0%/ 30% =0.5

C= 20%- 0/22%=0.9090

MEDIDA DE TREYNOR

A= 12%-5%/0.005= 14%

B= 15%-0%/ 0.0075=20%

C= 20%-0/1.4= 14.28%

MEDIDA DE JENSEN (ALPHA DE JENSEN)

(12%-5%)-(0.005x (15%-5%))= 0.0695= 6.95% (.5X 14%)=0.07-0.0695=0.05

(15%-0%)-(0.0075x (15%-0%)) = 0.148875= 14.88%=(.75X 20%)=0.15- 0.1488=0.12

(20%-0)- (1.4x (7-0)) = -9.6%= (1.4X 14.28) = -9.6-+19.99= -29.59

Question 2

A portfolio has an actual return of 16.7 percent, a beta of .93, and a standard deviation of

7.2 percent. The market return is 13.4 percent and the risk-free rate is 2.8 percent. What is the portfolio's Jensen's alpha?

(16.7%-2.8%)-(0.93x (13.4%-2.8%)) =0.04042

Question 3

A portfolio has a variance of .027556, a beta of 1.54, and an expected return of 11.2 percent. What is the Treynor ratio if the expected risk-free rate is 2.7 percent?

11.2%- 2.7%/1.54= 5.52%

Question 4

A Sharpe-optimal portfolio provides which one of the following for a given set of securities?

A. highest level of return for a market-equivalent level of risk

B. highest possible rate of return

C. highest possible level of risk

D. highest excess return per unit of systematic risk

e. highest risk premium per unit of total risk

Question 5

A portfolio has a beta of 1.26, a standard deviation of 15.9 percent, and an average return of 15.07 percent. The market rate is 12.7 percent and the risk-free rate is 3.6 percent. What is the Sharpe ratio?

15.07%- 3.6%/15.94%=11.66%

Question 6

A portfolio has a Sharpe ratio of .80, a standard deviation of 17.4 percent, and an expected return of 15.9 percent. What is the risk-free rate?

17.4%X 15.9= 2.7%

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