Question

An investor has a portfolio with an expected return of 11.19%. The portfolio is evenly invested in a stock and a risk-free asset. The market has an expected return of 17% and the risk-free asset has an expected return of 3%. What is the beta of the stock?

Answer 1

Answer:

Beta of the stock is 1.17.

Explanation:

The return of this portfolio is Stock Return * 0.5 plus Risk free return * 0.5. So, the return of the stock is $\frac{0.1119 - 0.03 * 0.5}{0.5} = 0.1938$

The expected return of a stock is determined:

$Return = Risk.free + Beta * (market.return - Risk.free)$

So, if we clear Beta from that equation

$Beta = \frac{Return - Risk.free}{market.return - risk free}$

Replacing with numbers

$Beta = \frac{0.1938 - 0.03}{0.17-0.03} = 1.17$