Brandon is an analyst at a wealth management firm. One of his clients holds a $7

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: Beta Standard Deviation 23.00% 0.750 Stock Atteric Inc. (AI) Arthur Trust Inc. (AT) Li Corp. (LC) Transfer Fuels Co. (TF) Investment Allocation 35% 20% 15% 30% 27.00% 1.600 1.100 0.400 30.00% 34.00% Brandon calculated the portfolio's beta as 0.868 and the portfolio's expected return as 8.77%. 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? O 0.52 percentage points O 0.83 percentage points 0.67 percentage points O 0.77 percentage points

Explanation / Answer

QUESTION 1

Atteric Stock is being replaced by Transfer Fuels Co. This would change the weight of Transfer Fuels Co to 65% (from current 30%). This is because the weight distributed towards Atteric will also be balanced towards Transfer Fuels Co.. The new Beta of this portfolio would have to be calculated.

Beta of a portfolio is weighted average of the individual components of portfolio.

New Portfolio Beta = (20% * 1.6) + (15% * 1.1) + (65% * 0.4) = 0.745.

Now, we will apply the CAPM equation, according to which

Expected Return on a portfolio/Stock = Risk free rate + Beta * Market risk premium

Expected return on portfolio = 4% + (0.745 * 5.5%) = 8.0975%

Change in Expected Return = 8.0975% - 8.77% = 0.67% --> Answer

QUESTION 2

Let us understand this question with the help of security market line, which is the graphical representation of CAPM, which shows different levels of systematic, or market, risk of various marketable securities plotted against the expected return of the entire market at a given point in time.

When the security is plotted on the SML chart, if it appears above the SML, it is considered undervalued because the position on the chart indicates that the security offers a greater return against its inherent risk. Similary, vice-versa holds true for an overvalued stock.

In our case, SML for the portfolio would have indicated expected return of 8.077%, but it's return at 9.6% will be above the SML. This implies the stock is undervalued.

QUESTION 3

Portfolio beta would INCREASE.

This is because, as previously mentioned, portfolio beta is weighted average of the beta of constituents of portfolio. So, if a stock with higher beta replaces a lower beta stock, by simple mathematics, weighted average (and hence the portfolio beta) would increase.

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