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

Beta of the stock is 1.17.

Step-by-step explanation:

The return of this portfolio is Stock Return * 0.5 plus Risk free return * 0.5. So, the return of the stock is
`(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 = (Return - Risk.free)/(market.return - risk free)`

Replacing with numbers

`Beta = (0.1938 - 0.03)/(0.17-0.03) = 1.17`