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Solution Library
Variance of Returns of Securities A, B and C
Question
Risk and return
A. Assume that security returns are generated by the single-index model, Ri = αi + βiRM + εi, 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 |
βi |
E(Ri) |
σ(εi) |
|
A |
0.8 |
10% |
25% |
|
B |
1.0 |
12% |
10% |
|
C |
1.2 |
14% |
20% |
(i) If σM = 20%, help Caillou calculate the variance of returns of securities A, B and C.
(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?
(iii) Is there an arbitrage opportunity in the market? If so, show Caillou the money.
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?
Summary
This question belongs to finance and discusses about risk and returns.
Word count: Excel Format
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