Question

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For all parts of this question, assume the following: The CAPM holds. The riskless rate of return is 5%. The market portfolio has expected rate of return of 15% and standard deviation of 20%. 1. Burger Inc. stock has an expected rate of return of 4% per year and standard deviation of 30%. Linda Belcher says, “No rational person would hold a risky asset expected to return less than the riskless rate! It must be mispriced.” Is Linda correct? Explain. 2. Consider the following data on two stocks whose returns have a correlation of 0.2 with each other: Walmart Tesla Expected Return 5% 20% Standard Deviation 12% 35% Bob Belcher owns $25,000 worth of Walmart stock, $10,000 worth of Tesla stock, and no other investments. a) Compute expected rate of return (% per year), and standard deviation of Bob's portfolio. b) Mr. Belcher says he cannot tolerate any more standard deviation than her portfolio has now. Given this risk tolerance, is he maximizing her expected return? If he is, explain why? If he is not, explain how she should invest to maximize expected return (give a specific trading and investment strategy).

Answer 1

The CAPM model shows that the points (return and stdv) which are below the capital market line are in infeasible reason. This means no investor, be it risk-taking or risk-neutral, won't invest in such portfolios.

return capital market line 15% risk free rates% not a good investment 4% 20% 30% standard dev

If a risk free asset is giving a return of 5%, then no one would go for an asset with 30% stdv (risky asset) to get 4% return. Hence, Linda is right.

2. Out of 35000 of available funds, 25000 (71.43%) are invested in Walmart and 28.57% are invested in tesla.

Expected return = W1*R1 +W2*R2 where W1 and W2 are the weights and R1 and R2 are the expected returns from each stocks.

hence, the expected return of the portfolio = 0.7143*5% + 0.2857*20%= 9.2858%

portfolio variance = (W1S1)^2 + (W2S2)^2 + 2*W1W2S1S2Cor, where S1 and S2 are stdv of portfolio and Cor is the correlation between these stocks

stdv of portfolio =( (0.7128*0.12)^2 + (0.2857*0.35)^2 + 2*0.7128*0.2857*0.12*0.35*0.2)^0.5 = 14.4%

Return Capital Market Line • Belcher's current portfolio 407 14.4% 20% Stev

We can see from the figure that Bob's investment is not optimal as it lies below the market line.

If he wants to retain the same stdv, we need to find corresponding expected return on Capital market line, which is 12% return.

12% >= W1'*5% + W2'*20%

W1'= 1- W2'

12% = 5% - 5%*W2' +W2'*20%

W2 = 0.466 = 16333

Hence, he should invest 16333 in Tesla and remaining in Walmart