Question

You have been managing a $5 million portfolio that has a beta of 1.15 and a required rate of return of 11.625%. The current risk-free rate is 3%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.85, 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

Beta of the portfolio = 1.15

Weight of the portfolio in the new portfolio = Value of the portfolio / Value of the new portfolio = 5 / 5.5

Beta of the stock = 0.85

Weight of the stock in the new portfolio = Value of the stock / Value of the new portfolio = 0.5 / 5.5

np = p*Wp + s.Ws ....beta of the new portfolio after the addition of the stock to the portfolio is the weighted average of the betas of the portfolio and the stock.

np = (1.15*5/5.5) + (0.85*0.5/5.5)

np = (5.75 + 0.425) / 5.5 = 6.175 / 5.5 = 1.122727

The required rate of return on the portfolio is = 11.625%

Risk free rate is = 3%

The required rate of return on the new portfolio is calculated as follows:

Rp = Rrf + (Rm - Rrf) *   np

Rrf = 3%, Rm = 11.625% and  np = 1.122727

So Rp = 3% + (11.625% - 3%) * 1.122727

Rp = 3% + 9.68352% = 12.68352%

Hence, the required rate of return on the new portfolio is 12.68%