Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%, and the standard deviation of returns to the market portfolio is 20%, answer the following questions:
a. You have $100,000 to invest. How should you allocate your wealth between the risk free asset and the market portfolio in order to have a 15% expected return?
b. What is the standard deviation of your portfolio in (a)?
c. Suppose that the market pays either 40% or 0% each with probability one half. You alter your portfolio to a more risky level by borrowing $50,000 at the risk free rate and investing it and your own $100,000 in the market portfolio. Give the probability distribution of your wealth (in dollars) next period.