The single index model for stock i is ri rf 1(rMrf) ei The single index model for stock j is rj rf 1(rM rf) ej The standard deviation of the stock market return is M 0 2, the standard deviation of ei is ei 0 1 and the standard deviation of ej is ej 0 2 The expected stock market return E(rM) is 10 and the risk free rate rf is 5 (18 points) (a) Calculate the systematic risk, firm specific risk, and total risk of stock i (b) Calculate the systematic risk, firm specific risk, and total risk of stock j (c) Which stock has lower total risk and which stock has lower expected return Does the stock with the lower total risk have a lower expected return Explain (d) Calculate R2, the fraction of the total risk that is attributable to the systematic risk for stock i (e) Calculate the covariance between stocks i and j (f) Suppose that an investor invests 50 of her money in stock i and 50 of her money in stock j What is the total risk of the stock portfolio

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Question: The single-index model for stock i is ri rf = 1(rMrf) + ei. The single-index model for stock j is rj rf = 1(rM-rf) +

The single-index model for stock i is ri rf = 1(rMrf) + ei. The single-index model for stock j is rj rf = 1(rM-rf) + ej.

The standard deviation of the stock market return is M=0.2, the standard deviation of ei is ei=0.1 and the standard deviation of ej is ej=0.2. The expected stock market return E(rM) is 10% and the risk-free rate rf is 5%. (18 points)

(a) Calculate the systematic risk, firm-specific risk, and total risk of stock i.
(b) Calculate the systematic risk, firm-specific risk, and total risk of stock j.
(c) Which stock has lower total risk and which stock has lower expected return? Does the stock with the lower total risk have a lower expected return? Explain
(d) Calculate R2, the fraction of the total risk that is attributable to the systematic risk for stock i.
(e) Calculate the covariance between stocks i and j.
(f) Suppose that an investor invests 50% of her money in stock i and 50% of her money in stock j. What is the total risk of the stock portfolio?

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