Question

A stock has a beta of 0.5 and an expected return of 9.6 percent. A risk-free asset currently earns 3.3 percent. If a portfolio of the two assets has an expected return of 12 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

As per CAPM, expected return of a asset or portfolio can be calculated with following equation -

rf = risk free return

rm = market return

B = Beta

E(r) = Expected return

In above case, Firstly, we need to calculate Market return(rm) with the help a stock details provided.

rf = 3.3% = 0.033

E(ra) = 9.6% = 0.096

Beta = 0.5

Thus,

Market return = 15.9%

We have following details about portfolio -

Expected Return (Ep) = 12% = 0.12

rf = 0.033

rm = 0.159

We can calculate beta of portfolio with CAPM formula -

Beta of Portfolio would be 0.69

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.