Please show your work and write solutions in details, including formulas and how you plug numbers, given in each question, into these formulas. Please, write short VERBAL conclusion at the end of each problem summarizing your answer in words. Verbal answers are not substitute for the quantitative solution.

Question 4

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.