Question

You have been managing a $10 million portfolio that has a beta of 1.15 and a required rate of return of 5.75%. The current risk-free rate is 2%. Assume that you received another $1.5 million. If you invest the money in a stock with beta of 0.85, what will be the required rate of return on your $11.5 million portfolio?

please use excel for your answer.

Answer 1

You have been managing a $10 million portfolio that has a beta of 1.15 and a required rate of return of 5.75%. The current risk-free rate is 2%. Assume that you received another $1.5 million. If you invest the money in a stock with beta of 0.85

Given about a portfolio

Old portfolio value V0 = $10 million

Old portfolio beta B0 = 1.15

Old portfolio required return R0 = 5.75%

Risk free rate Rf = 2%

new assets added of value Va = $1.5 million

Beta of new asset Ba = 0.85

Beta of the new portfolio is weighted average beta of its assets,

So, beta of new portoflio = B0*V0/(V0+Va) + Ba*Va/(V0+Va) = 1.15*10/(10+1.5) + 0.85*1.5/(10+1.5) = 1.11

Using old portfolio beta and required return, Market risk premium is calculated as (CAPM model)

MRP = (R0 -Rf)/B0 = (5.75-2)/1.15 = 3.26%

So, using CAPM model, required return on new portfolio = Rf + beta of new portfolio*MRP

=> required return on new portfolio = 2 + 1.11*3.26 = 5.62%