Rafael is an analyst at a wealth management firm. One of his clients holds a $10
ID: 2779706 • Letter: R
Question
Rafael is an analyst at a wealth management firm. One of his clients holds a $10,000 portfolio that consists of four stocks. The investment allocation in the portfolio along with the contribution of risk from each stock is given in the following table: Investment Allocation 35% 20% 15% 30% Beta 0.750 1.600 1.100 0.500 Standard Deviation 23.00% 27.00% 30.00% 34.00% Stock Atteric Inc. (AI) Arthur Trust Inc. (AT) Lobster Supply Corp. (LSC) Baque Co. (BC) Rafael calculated the portfolio's beta as 0.898 and the portfolio's expected return as 12.74% Rafael thinks it will be a good idea to reallocate the funds in his client's portfolio. He recommends replacing Atteric Inc.'s shares with the same amount in additional shares of Baque Co. The risk-free rate is 6%, and the market risk premium is 7.50%.Explanation / Answer
Portfolio beta is given by the weighted average of beta of individual stocks in the portfolio using percentages of individual stocks as weights.
Given old portfolio beta= 0.898
New Portfolio beta= (0.2*1.6+0.15*1.1+0.65*0.5)= 0.81
The required return of the portfolio is thus given by= Risk free rate + Beta*Risk Premium
=6+0.81*7.5 = 12.075%
So change in the required rate of return= 12.74%-12.075%= 0.66%
It is given that Rafael expects a return of 10.58% from the portfolio with the new weights. As the expected return is 12.075% as per CAPM model, so the portfolio is undervalued.
Stock Previous Investment Allocation New Investment Allocation Beta Atteric Inc. 35% 0% 0.75 Arthur Trust Inc. 20% 20% 1.6 Lobster Supply Corp. 15% 15% 1.1 Baque Co. 30% 65% 0.5Related Questions
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