Chapter 8 Assignment e Back to Assignment Attempts: 12. Portfolio beta and weigh

Question

Chapter 8 Assignment e Back to Assignment Attempts: 12. Portfolio beta and weights Kyoko is an analyst at a wealth management firm. One of her dients holds a $10,000 portfolio that consists of four stocks. The investment allocation Average:13 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% 0.900 0.23% 20% 1.600 0.27% Arthur Trust Inc(AT) Li Corp. (LC) 1.300 0.300 15% 0.30% nsfer Fuels Co. (TF) 30% 0.34% Kyoko calculated the portfolio's beta as 0.920 and the portfolio's expected return as 9.06%. Kyoko 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 Transfer Fuels Co. The risk-free rate is 4.00%, and the market risk premium is 5.50% According to Kyoko'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

Explanation / Answer

Expected Return of portfolio = Weighted average of return on constituents.

Beta of portfolio = Weighted average of Beta of constituents.

If funds are reinvested from Atteric to Transfer, new weight of Transfer Co. would be 65%. So, we first need to calculate Beta of portfolio

Beta of portfolio = (20% * 1.6) + (15% * 1.3) + (65% * 0.3) = 0.32 + 0.195 + 0.195 = 0.71

Based on CAPM Equation,

Expected return on stock = Risk free rate + Beta * Market risk premium

Expected return on stock = 4% + 0.71 * 5.5% = 7.905%

Required rate of return = 9.06% - 7.905% = 1.155% ---> Answer 1

Now, if we plot an SML (which is a graphical representation of CAPM). So, based on that and analyst consensus, security would be slightly lower than that on SML. 7.905% is what is on SML and 7.89% is based on analyst consensus. This implies, security is slightly lower than SML.

A security lower than SML --> Overvalued

A security higher than SML --> Undervalued

A security on that on SML --> Fairvalued

So answer is Overvalued. --> Answer 2

As the new stock replacing Atteric has higher beta, if everything else remains constant, portfolio's beta would increase which implies higher systematic risk and hence the portfolio's risk would be HIGHER. --> Answer 3

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