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

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