You are a portfolio manager, managing a risky portfolio (label P) with expected rate of return of 15% and standard deviation of 20%. The risk-free asset earns 2%. The capital market does not allow borrowing or leveraging.

Your client, Margie, decides to invest in your risky portfolio as well as in the risk-free asset. She has the same utility function as the rational risk-averse investor assumed in the mean-variance portfolio theory.

1. Given her degree of risk aversion, A, is 3, determine the optimal allocation to your risky portfolio (i.e., the optimal proportion of investment allocated to the risky portfolio, P, managed by you). Show all computations. (5 points)

2. Compute the expected return and standard deviation of Margies complete portfolio (please label it as C). (5 points)

3. Calculate the reward-to-variability ratio (s) of Margies complete portfolio (C). Show formulas and inputs for full credit. (5 points)