Question

12. Portfolio beta and weights Juanita is an analyst at a wealth management firm. One of her dients 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 Standard Deviation Beta Atteric Inc. (AI) 35% 0.750 0.53% 20 % 1.400 0.57% Arthur Trust Inc(AT) Lobster Supply Corp. (LSC) 15 % 1.100 0.60% Transfer Fuels Co. (TF) 30% 0.500 0.64% Juanita calculated the portfolo's beta as 0.858 and the portfolio's expected return as 12.43 % . Juanita thinks it will be a good idea to reallocate the funds in her dlient's portfolio, She recommends replacing Atteric Inc.'s shares with the same amount in additional shares of Transfer Fuels Co. The risk-free rate is 6.00 %, and the market risk premium is 7.50%. According to Juanita'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 sublective and judgmental factors, because different analysts interpret data in different ways. Suppose, based on the earnings consensus of stock analysts, Juanita expects a return of 11.80 % 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? O Fairly valued O Undervalued O Overvalued Suppose instead of replacing Atteric Inc.'s stock with Transfer Fuels Co.'s stock, Juanita 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 required return from the portfolio would

Answer 1

Recommended or modified portfolio would be

Stock	Investment allocation	Beta	Standard deviation
AT	20%	1.4	.57%
LSC	15%	1.1	.60%
TF	65%	.50	.64%

New portfolio beta can be calculated as the sum of the weighted average of securities as

Portfolio beta = w1×b1 + w2×b2 + w3×b3

=.20×1.4 + .15×1.1 + .65×.500

= 0.7700

Old portfolio beta = 0.858

Required return on old portfolio = Rf + Beta(Risk premium)

= 6 + .858 × 7.50

= 12.4350

Required return on modified portfolio = Rf + Beta(Risk premium)

= 6 + .7700 × 7.5

= 11.7750

Change in required return will be = 12.4350 - 11.7750

= .6600

Thus the required return would decline by 0.6600

Since juanita expects the returns to be higher than the required returns, he might have thought the portfolio to be undervalued.

If shares of Atteric Inc. got replaced with the shares of company X with higher beta than Atteric inc., the portfolio required return would increase to compensate investors for the higher risk resulted from higher beta.