Suppose that the only assets available to you are a risk-free Treasury bill yielding 1% per year and an S&P 500 ETF with an expected return of 9% per year and a standard deviation of 18%. Your broker will allow you to buy on margin, but the interest rate on borrowing is 6%.

What is the optimal allocation to the risky asset? Consider three investors, one with a risk aversion (A) of 10, one with A of 1.5, and one with A of 0.5.