Donald is considering the merits of two securities. He is interested in the common shares of A Co. and B Inc. The expected monthly rate of return of securities is shown below: State of Affair Probability Boom 0.1 Normal 0.5 Recession 0.4 Stock A Stock B 40% -20% 20% 8% -10% 15% At the time of purchase, the market value is $70/share for A and $50/share for B. Donald plans to invest 10,000 shares of Stock A and 6,000 shares in Stock B. (i) Compute the portfolio weights of Stock A and Stock B. (ii) Compute the expected returns of Stock A and Stock B. (iii) Assume that the covariance between Stock A and Stock B is -28%2 (0.0028). Compute the expected rate of return and variance of rate of return of Donald’s portfolio.
Question 4 (Risk & Return and Equity Valuation)
(a) Donald is considering the merits of two securities. He is interested in the common shares of A Co. and B Inc. The expected monthly rate of return of securities is shown below:
State of Affair Probability Boom 0.1 Normal 0.5 Recession 0.4
Stock A Stock B 40% -20% 20% 8% -10% 15%
At the time of purchase, the market value is $70/share for A and $50/share for B. Donald plans to invest 10,000 shares of Stock A and 6,000 shares in Stock B.
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(i) Compute the portfolio weights of Stock A and Stock B.
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(ii) Compute the expected returns of Stock A and Stock B.
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(iii) Assume that the covariance between Stock A and Stock B is -28%2 (0.0028). Compute the expected rate of return and variance of rate of return of Donald’s portfolio.
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(iv) If the risk-free rate is 2%, the market risk premium is 18% and the beta of Stock A is 0.75, estimate the required and expected
rates of return of Stock A. Should Donald invest in Stock A? Show the calculations.
(b) Assume that Stock X is fairly priced today. Stock X just distributed a per share dividend of $1. It is expected that the company will increase its dividend by 20% in the coming year, 15% in the second year, 10% in the third year, and 5% in the fourth year. Starting from the fifth year, the company will maintain the
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