Question

You have been managing a $5 million portfolio that has a beta of 1.80 and a required rate of return of 14.415%. The current risk-free rate is 5%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.00, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The required return is computed as follows:

= Risk free rate + Beta x Risk premium

Risk premium is computed as follows:

Required rate of return = Risk free rate + Beta x Risk premium

0.14415 = 0.05 + 1.80 x Risk premium

Risk premium = (0.14415 - 0.05) / 1.80

Risk premium = 0.052305556

Beta is computed as follows:

= Beta of current stock x weight of current stock + Beta of another stock x weight of another stock

= 1.80 x $ 5 million / $ 5.5 million + 1 x $ 0.5 million / $ 5.5 million

= 1.636363636 + 0.090909090909

= 1.727272727

So, the return will be as follows:

= 5% + 1.727272727 x 0.052305556

= 14.03% Approximately

Please ask in case of any doubts.