Question

What is Jensen's alpha of a portfolio comprised of 45 percent portfolio A and 55 percent of portfolio B?

Portfolio Average Return Standard Deviation Beta
A 18.9 % 21.6 % 1.92
B 13.2 12.8 1.27

The risk-free rate is 3.1 percent and the market risk premium is 6.8 percent.
2.04 percent

0.47 percent

1.08 percent

1.46 percent

−1.25 percent

Answer 1

Alpha of the overall portfolio = 2.04%

Step-by-step explanation:

The alpha or abnormal return is the excess return given by a stock or a portfolio over its required rate of return. To calculate the alpha of a portfolio containing two portfolios, we first need to calculate the alpha of each individual portfolio and then take a weighted average of these alphas to determine the overall portfolio alpha.

First we need to calculate the required rate of return of each portfolio and deduct it from the Average return of portfolios to calculate individual portfolio alpha.

Using the CAPM, we can calculate the required rate of return on a stock. This is the minimum return required by the investors to invest in a stock based on its systematic risk, the market's risk premium and the risk free rate.

The formula for required rate of return under CAPM is,

r = rRF + Beta * rpM

Where,

• rRF is the risk free rate

• rpM is the market risk premium

r of A = 0.031 + 1.92 * 0.068 = 0.16156 or 16.156%

Alpha of portfolio A = 18.9 - 16.156 = 2.744%

r of B = 0.031 + 1.27 * 0.068 = 0.11736 or 11.736%

Alpha of portfolio B = 13.2 - 11.736 = 1.464%

Alpha of the overall portfolio = 0.45 * 2.744% + 0.55 * 1.464%

Alpha of the overall portfolio = 2.04%