Suppose a stock fund has an expected return of 12% and standard deviation of 20%. The T-bill rate is 3%, while the borrowing rate faced by investors is 6%.

There are two investors Mary and Michael with coefficients of risk aversion 5 and 1, respectively.

What are the expected returns and standard deviations of their portfolios?

What are the utilities provided by these portfolios?

What are optimal proportions in risky stock fund by each investor?