Given the following information for the two stocks: Stock Expected Return Standa

Question

Given the following information for the two stocks: Stock Expected Return Standard Deviation Investment Beta 16% 15% 300 10% $30,000 $20,000 0.8 You construct a portfolio composing of stocks A and B according to the above information. Assume that the risk free rate is 6% and the market risk premium (MRP) is 9%. Use the CAPM analysis to numerically determine whether this 2- stock portfolio is fairly priced? What is your investment recommendation on this portfolio? Why? ?E(Re) = 15.6% vs Required(CAPM) RP= 15.36%>

Explanation / Answer

Expected return

Weight of stock A = Amount investment in A / Total investment = $30,000 / $50,000 = 0.60

Weight of stock B = 1 - weight of stock A = 1 - 0.60 = 0.40

Expected return of portfolio E(Rp) = Expected return of A x Weight of A + Expected return of B x Weight of B

or, E(Rp) = 16% x 0.60 + 15% x 0.40 = 15.60%

Required return

First, we need the portfolio beta -

Portfolio beta = Beta of A x Weight of A + Beta of B x Weight of B

or, Portfolio beta = 1.2 x 0.60 + 0.8 x 0.40 = 1.04

Required return as per CAPM can be computed as -

Required Rp = Risk free rate + Portfolio beta x market risk premium = 6% + 1.04 x 9% = 15.36%

The portfolio is expected to perform at 15.6% against the required return of 15.36%. Since expected return is more than the required return, the stock portfolio is underpriced and investment is recommended.

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