Question: There is a risk-free asset with return rf = 1% and a risky asset (stocks) with expected return S = 7% and volatility S =

There is a risk-free asset with return rf = 1% and a risky asset (stocks) with expected return S = 7% and volatility S = 15%. 1. What are expected return, volatility and Sharpe ratio of a portfolio with some fraction w invested in the risky asset and fraction 1 w invested in the risk-free asset? 2. Provide an expression for the Capital Allocation Line (CAL) (p as a function of p). Draw the CAL. 3. Suppose your preference is u(r) = E[r] 1 2V ar[r]. What is the optimal portfolio? 4. What are expected return, volatility, Sharpe ratio and utility of the optimal portfolio? 5. Draw the optimal portfolio and an indifference curve in the picture of (b). 6. Suppose you can only lend at the risk free rate rf = 1%, but if you borrow you have to pay interest rb = 4%. Draw a new CAL. What is now the optimal portfolio? Calculate expected return, volatility, Sharpe ratio and utility. Draw the new optimal portfolio and a new indifference curve.

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