Assume that security returns are generated by the single-index model, Ri=ai+ßiRM+ ei
Where Riis the excess return for security i and RM is the market’s excess return. The risk free rate is 2%. Suppose also that there are three securities A, B, and C, characterized By the following data:
| Security | ßi | E(Ri ) | µ(ei) |
| A | 0.8 | 10% | 25% |
| B | 1 | 12% | 10% |
| C | 1.2 | 14% | 20% |
a.If =M = 20%, calculate the variance of returns of Securities A, B, and C.
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and Crespectively. If one forms a well-diversified portfolio of type Asecurities, what will be the mean and variance of the portfolio’s excess returns? What about portfolios composed only of type Bor Cstocks?
c.Is there an arbitrage opportunity in this market? What is it? Analyze the opportunity graphically.
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