2. Assume that security returns are generated by the single index model 3) (15 points) Consider two assets, A and B. The correlation of returns between asset A and B is equal to zero. Starting with the formula for the variance of a portfolio composed of the two assets, derive an expression for the weight placed in asset A and the weight placed in asset B for the minimum risk portfolio. R; = 2; + BRM + & where R; is the excess return for security i and Ry is the market's excess return. Suppose also that there are three securities A, B, and C characterized by the following data: Security Beta Expected Return A B 0.8 1.0 1.2 0.10 0.12 0.14 o(&) 0.05 0.01 0.10 A.) (5 points) If o?m=0.04 calculate the variance (e.g. the total risk) of returns of securities A, B, and C. B.) (5 points) Now assume there are an infinite number of assets with the 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 variance of the portfolio's return? Similarly, what will the variance of the portfolio's return for portfolios formed only from type B? type C