Question

Megan is an analyst at a wealth management firm. One of her 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: Stock Investment Allocation Beta Standard Deviation Atteric Inc. (AI) 35% 0.750 0.53% 20% 1.400 0.57% Arthur Trust Inc(AT) Lobster Supply Corp. (LSC) Baque Co. (BC) 15% 1.300 0.60% 30% 0.300 0.64% Megan calculated the portfolio's beta as 0.828 and the portfolio's expected return as 8.55%. Megan thinks it will be a good idea to reallocate the funds in her client's portfolio. She recommends replacing Atteric Inc.'s shares with the same amount in additional shares of Baque Co. The risk-free rate is 4.00%, and the market risk premium is 5.50%. According to Megan's recommendation, assuming that the market is in equilibrium, the portfolio's required return will change by

Answer 1

New allocations of stocks after reallocation are as follows :

AT = 20%

LSC = 15%

BC = 30% + 35% = 65% (because the shares of AI are replaced with shares of BC)

Revised portfolio beta = sum of weighted beta of stocks in portfolio, with weights being the new allocations of stocks.

Revised portfolio beta = (20% * 1.400) + (15% * 1.300) + (65% * 0.300) = 0.67

Portfolio required return = risk free rate + (revised portfolio beta * market risk premium)

Revised Portfolio required return = 4% + (0.67 * 5.5%) = 0.07685, or 7.685%

Change in portfolio's required return = 7.685% - 8.55% = -0.865%

With the new weights, the portfolio's expected return is 7.71%. Based on the recommended changes, the revised portfolio is overvalued. This is because the revised portfolio's expected return is lower than its required return.

If everything else remains constant, the portfolio's beta would increase and the required return from the portfolio would increase. This is because the portfolio beta is the sum of weighted beta of stocks in portfolio. Hence, replacing AT stock with a higher beta stock would increase the portfolio beta. Due to the increased beta, the portfolio's required return would increase, since required return = risk free rate + (portfolio beta * market risk premium)