Question

Brandon is an analyst at a wealth management firm. One of his clients holds a $5,000 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: Standard Deviation Investment Allocation 35% 53.00% Stock Atteric Inc. (AI) Arthur Trust Inc.(AT) Lobster Supply Corp. (LSC) Transfer Fuels Co. (TF) 20% Beta 0.750 1.400 1.300 0.500 57.00% 15% 60.00% 30% 64.00% Brandon calculated the portfolio's beta as 0.888 and the portfolio's expected return as 8.88%. Brandon 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 Transfer Fuels Co. The risk-free rate is 4%, and the market risk premium is 5.50%. According to Brandon's recommendation, assuming that the market is in equilibrium, how much will the portfolio's required return change? O 0.55 percentage points O 0.37 percentage points O 0.48 percentage points O 0.60 percentage points

Answer 1

Solution: As per CAPM, the expected return of a stock (cost of equity) is calculated as follows: Reuired ROR= Rf + Beta*(Market risk premium) The risk free rate is 4% and market risk premium is 5.5% As per revised allocation of portfolio, it is being considered to replace investment in Atteric with additional investment in Tranfer fuels inc. Post revision, the new weight of Transfer fuel inc. would become 65% (i.e. 30% + 35%). The required rate of return of revised portfolio is as follows: CAPM Cost of equity (Ke) Risk free Market Weights Ke Weights Risk free rate Beta Value risk Formula rate 5.50% (4%1.4* 5.5%) 5.50% (4%1.3* 5.5%) 5.50% (4% 0.5*5.5%) Arthur Trust Inc. 4% 1.4 11.7% 20% 2.34% Lobster Supply Corp Transfer Fuels Co. 11.2% 4% 1.3 15% 1.67% 65% 4% 0.5 6.8% 4.39% Weighted average Ke of revised portfolio 8.40% Required rate of return (Revised portfolio) 8.4% Change in required rate of return after revision of portfolio= 8.88%-8.4%= 0.48% (1) Therefore, change in portfolio's required return would be 0.48% and the correct option is option C If a stock trades at a value higher than its intrinsic value, the expected return of the stock goes below its required rate of return. In the given case, as per the recommendations of stock analysts, the revised portfolio is expected to return 6.8% whereas the required rate of return for the revised portfolio (as (2) calculated above) is 8.4%. This shows that the revised portfolio is overvalued which is based on the fact that the expected return is lower than the required return. hence, the correct option is B and the portfolio is overvalued. Replacing one stock in a portfolio with another stock that has a comparatively higher beta increases the overall beta of the portfolio, because the higher beta of new stock takes the place of lesser beta of replaced stock in the weighted average beta of the portfolio. Therefore, if Atteric Inc. is replaced with (3) equal dollar allocation of company X's stock which has comparatively higher beta, than if everything else remains constant, the portfolio's beta would INCREASE