Question

The risk-free rate, average returns, standard deviations, and betas for three funds and the S&P 500 are given below. Fund Avg Std Dev Beta A 17.5 % 26.5 % 1.35 B 12.5 % 23.5 % 1.10 C 13.5 % 20.5 % 1.15 S&P 500 10 % 15 % 1 rf 4.0 % If these portfolios are subcomponents that make up part of a well-diversified portfolio, then portfolio ______ is preferred.

Answer 1

Answer:

Portfolio A is preferred.

Explanation:

Given the following sorted data from the question:

Fund        Avg         Std Dev         Beta

A                17.5%        26.5%         1.35

B                 12.5%       23.5%          1.10

C                 13.5%       20.5%          1.15

S&P 500     10%          15%               1

rf                  4.0%

To determine the preferred portfolio, the Treynor measure for each portfolio is estimated as follows:

Treynor measure = (Avg - rf rate) / beta

Therefore, we have:

Treynor measure of Portfolio A = (17.5% - 4.0%) / 1.35 = 10.00%

Treynor measure of Portfolio B = (12.5% - 4.0%) / 1.10 = 7.73%

Treynor measure of Porfolio C = (13.5% - 4.0%) / 1.15 = 8.26%

Since the 10% Treynor measure of Portfolio A is the highest, Portfolio A is preferred.