Perform an analogous argument to the one in Example 2.12, for an investor who wishes to have the investment risk equal to a given s (instead of requiring that the expected return is m). Example2.12:...

Perform an analogous argument to the one in Example 2.12, for an investor who wishes to have the investment risk equal to a given s (instead of requiring that the expected return is m). Example2.12: Assume that the covariance matrix C, the vector of expected returns µ, and the risk-free return R are given. Assume also that an investor wishes to spend V and that the aim is to achieve an expected return equal to a given rate m. The question is how much he should spend on the risky assets, and how much he should invest risk-free. First we compute m using (2.16). We can then compute the expected return of the market portfolio using (2.9) µ m = m T µ . Optimal investments lie on the capital market line. The investor needs to hold a combination of the market portfolio and the risk-free security. We assume that he spends ?V on the market portfolio and invests (1 - ?) V risk-free. The desired ? can be computed from the expected return of the position ? µm + (1 - ?) R = m, gives us the amount v1 invested in the first asset, and v2 invested in the second asset. As mentioned above, (1 - ?) V is invested risk-free.