Question

Brandon is an analyst at a wealth management firm. One of his clients holds a $7,500 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	38.00%
Arthur Trust Inc. (AT)	20%	1.600	42.00%
Li Corp. (LC)	15%	1.100	45.00%
Transfer Fuels Co. (TF)	30%	0.300	49.00%

Brandon calculated the portfolio’s beta as 0.838 and the portfolio’s required return as 8.6090%.

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? (Note: Do not round your intermediate calculations.)

1.0776 percentage points

0.8690 percentage points

0.6778 percentage points

0.9994 percentage points

Analysts’ estimates on expected returns from equity investments are based on several factors. These estimations also often include subjective and judgmental factors, because different analysts interpret data in different ways.

Suppose, based on the earnings consensus of stock analysts, Brandon expects a return of 6.24% from the portfolio with the new weights. Does he think that the required return as compared to expected returns is undervalued, overvalued, or fairly valued?

Fairly valued

Overvalued

Undervalued

Suppose instead of replacing Atteric Inc.’s stock with Transfer Fuels Co.’s stock, Brandon considers replacing Atteric Inc.’s stock with the equal dollar allocation to shares of Company X’s stock that has a higher beta than Atteric Inc. If everything else remains constant, the portfolio’s beta would . (Increase/Decrease)

Answer 1

New allocations of stocks after reallocation are as follows :

AT = 20%

LC = 15%

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

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

Revised portfolio beta = (20% * 1.600) + (15% * 1.100) + (65% * 0.300) = 0.68

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

Revised Portfolio required return = 4% + (0.68 * 5.5%) = 0.074, or 7.74%

Change in portfolio's required return = 7.685% - 8.6090% = -0.8690%

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 of 7.74%.

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.