2. Optimal portfolio choice with one risky asset and one risk-free asset The annual expected return and standard deviation of a stock fund is 10% and 20%, respectively. The annual risk-free rate is 2%. (a) What is the Sharpe ratio of the stock fund? (5 points) (b) Abby plans to invest $1 million in the stock fund and the risk-free asset. If her risk aversion A=3, how many dollars will she invest in the stock fund and how many dollars will she invest in the risk-free asset? (10%) (c) In the next year, Abby again plans to invest $1 million in the stock fund and the risk-free asset. The annual expected return and standard deviation of the stock fund remain the same but the annual risk-free rate increase to 5%. Will Abby invest more or less in the stock fund and why? (10%)