Assume that security returns are generated by the single-index model

a. Assume that security returns are generated by the single-index model, Ri = ?i + ?iRM + ?i, where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also there are 3 securities A, B and C, characterized by the following data:

Security ?i E(Ri) ?(?i)

A 0.8 10% 25%

B 1.0 12% 10%

C 1.2 14% 20%

(i) If ?M = 20%, help Caillou calculate the variance of returns of securities A, B and C. (3 points)

(ii) Now assume there are an infinite number of assets with return characteristics identical to those of A, B and C, respectively. If one forms a well-diversified portfolio of type A securities, what will be the mean and variance of the portfolio’s excess returns? What about portfolios composed only of type B and type C stocks? (2 points)

(iii) Is there an arbitrage opportunity in the market? If so, show Caillou the money. (2 points)

b. Assume the correlation coefficient between the Sid Science Fund and the S&P/TSX index is 0.70. What percentage of Sid Science Fund’s total risk is specific or unsystematic? (3 points)