Question

Jake 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:

Stock	Investment Allocation	Beta	Standard Deviation
Atteric Inc. (AI)	35%	0.750	0.23%
Arthur Trust Inc. (AT)	20%	1.500	0.27%
Lobster Supply Corp. (LSC)	15%	1.300	0.30%
Transfer Fuels Co. (TF)	30%	0.500	0.34%

Jake calculated the portfolio’s beta as 0.908 and the portfolio’s expected return as 10.90%.

Jake 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 5.00%, and the market risk premium is 6.50%.

According to Jake’s recommendation, assuming that the market is in equilibrium, the portfolio’s required return will change by   .

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, Jake expects a return of 10.35% from the portfolio with the new weights. Does he think that the revised portfolio, based on the changes he recommended, is undervalued, overvalued, or fairly valued?

Undervalued

Fairly valued

Overvalued

Suppose instead of replacing Atteric Inc.’s stock with Transfer Fuels Co.’s stock, Jake 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   , and the required return from the portfolio would   .

Answer 1

New portfolio beta =Weighted average beta

= 1.5*20% + 1.3*15%+0.5*65%

= 0.82

New portfolio return = risk free rate + beta*market risk premium

= 5% + 0.82*6.50%

= 10.33%

Hence, change in required return = 10.90% - 10.33%

= 0.57 percentage points

i.e. 0.57 percentage points

He expects return to be 10.35% but CAPM return is 10.33%

Hence, he thinks that revised portfolio is undervalued

Portfolio beta would INCREASE, and required return would INCREASE

Since portfolio beta is equal to weighted average beta. With inclusion of higher beta stock, portfolio beta would increase