Assume that, in any month, the return on the stock market is either 6% or -2%, and these outcomes occur with equal probabilities. The riskless rate (cash) is 1% per month. The stock/cash mix of a manager who attempts to time the market is either 75/25 or 25/75 in a given month, depending on whether the manager predicts a good or bad market for that month.
- What is the Sharpe measure of the manager's portfolio if in fact he possesses no timing ability?
- Explain how, without timing ability, you could construct a portfolio having the same standard deviation but higher expected return than the manager's portfolio.
- What is the Sharpe measure of your portfolio in b? What is the Sharpe measure of a portfolio that maintains a constant mix of half cash and half stock?