Question

You have been managing a $5 million portfolio that has a beta of 0.95 and a required rate of return of 11.175%. 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 1.25, 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

First of all we will calculate Beta of the new portfolio = Beta of $5 million portfolio * portfolio value/Sum of Portfolio + Beta of $500000* portfolio value/Sum of Portfolio

Sum of portfolio = $5 million + $.50 million = $5.50 million

= 0.95*5/5.50 + 1.25*0.50/5.50 = 0.98

Calculation of market risk premium as per CAPM,

Re = Rf + (Rm-Rf)Beta

11.175% = 5% + (Rm-Rf)0.95

Rm-Rf = 6.50%

Rm = Market rate of return

Rf = Risk free rate

Rm-Rf = Market risk premium.

Now return on new portfolio of $5.5 million,

Re = Rf + (Rm-Rf)Beta

= 5% + 6.50%*0.98

= 11.37%

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