1. A client has $2m to invest for retirement. She wants to take out $120,000 per year. Her portfolio has an expected return equal to 5% with a standard deviation equal to 8%. Compute the approximation to the geometric mean. Using the geometric mean approximation, how long is it expected to last?
2. Given the following values, compute the Sharpe, Treynor, and Sortino ratios. Average return=9%, risk-free rate=2%, beta=1.1, standard deviation=21%, downside deviation=14%.
3. Unlevered mean and standard deviation: 8%, 15%.
If the borrowing rate is 4%, what is the mean and standard deviation of a portfolio where the investor has $15,000 equity and borrows $10,000 for a total investment of $25,000?