Question

Portfolio A has an average return of 13.6 percent, a standard deviation of 17.2 percent, and a beta of 1.38. Portfolio B has an average return of 8.4 percent, a standard deviation of 6.4 percent, and a beta of 0.87. The risk-free rate is 3.3 percent and the market risk premium is 8.5 percent. What is the Treynor ratio of a portfolio comprised of 50 percent portfolio A and 50 percent portfolio B? Select one: a. 0.073 b. 0.054 c. 0.136 d. 0.114 e. 0.068

Answer 1

Answer:

Treynor ratio = 0.068

Explanation:

Given:

For Portfolio A

Average return = 13.6 %

Standard deviation = 17.2 %

Beta of 1.38

For Portfolio B

Average return = 8.4 %

Standard deviation = 6.4 %

Beta of 0.87

The risk-free rate = 3.3 % = 0.033

Market risk premium = 8.5 %

Find:

Treynor ratio on 50% portfolio = ?

Computation:

$Treynor\ ratio=\frac{Portfolio\ return - Risk\ free\ return}{Beta\ of\ portfolio}$

Common Portfolio return = (50%)(Average return for Portfolio A) + (50%)(Average return for Portfolio B)

Common Portfolio return = 50%(13.6%) + 50%(8.4%)

Common Portfolio return = 11%  = 0.11

Common Portfolio beta = (50%)(Beta of Portfolio A) + (50%)(Beta of Portfolio B)

Common Portfolio beta = 50% (1.38) + 50% (0.87)

Common Portfolio beta = 1.125

$TreynorRatio = \frac{0.11 - 0.033}{1.125}$

Treynor ratio = 0.068