You can invest in stocks and T-bills. Stocks pay an expected return of 8% with a volatility of 20%. T-bills are risk-free and pay a return of 2%. Suppose you have mean-variance preferences u(r) = E[r] 1/4 * Var[r].

1. Suppose you can only invest 100% of your wealth in stocks or 100% in T-bills. Do you prefer stocks or T-bills?

2. How large would the risk-free return of T-bills have to be so that you are indifferent between stocks and T-bills?

3. What is the optimal portfolio of stocks and T-bills? Provide the optimal portfolio weights. What utility do you get from this optimal portfolio?

4. What is your optimal portfolio if you cannot short sell T-bills (i.e. you cannot borrow at the 2% risk-free interest rate), but you can borrow at a 5% interest rate? Provide the optimal portfolio weights. What is your utility? Suppose again that you cannot short sell T-bills, but you can borrow at the higher borrowing rate of 5%. In addition, suppose you are not allowed to borrow more than an amount equal to 30% of your (initial) wealth. Provide the optimal portfolio weights.

Problem 3 You can invest in stocks and T-bills. Stocks pay an expected return of 8% with a volatility of 20%. T-bills are risk-free and pay a return of 2%. Suppose you have mean-variance preferences u(r) = E[r] Var[r]. 1 1. Suppose you can only invest 100% of your wealth in stocks or 100% in T-bills. Do you prefer stocks or T-bills? 2. How large would the risk-free return of T-bills have to be so that you are indifferent between stocks and T-bills? 3. What is the optimal portfolio of stocks and T-bills? Provide the optimal portfolio weights. What utility do you get from this optimal portfolio? 4. What is your optimal portfolio if you cannot short sell T-bills (i.e. you cannot borrow at the 2% risk-free interest rate), but you can borrow at a 5% interest rate? Provide the optimal portfolio weights. What is your utility? Suppose again that you cannot short sell T-bills, but you can borrow at the higher borrowing rate of 5%. In addition, suppose you are not allowed to borrow more than an amount equal to 30% of your (initial) wealth. Provide the optimal portfolio weights. Problem 3 You can invest in stocks and T-bills. Stocks pay an expected return of 8% with a volatility of 20%. T-bills are risk-free and pay a return of 2%. Suppose you have mean-variance preferences u(r) = E[r] Var[r]. 1 1. Suppose you can only invest 100% of your wealth in stocks or 100% in T-bills. Do you prefer stocks or T-bills? 2. How large would the risk-free return of T-bills have to be so that you are indifferent between stocks and T-bills? 3. What is the optimal portfolio of stocks and T-bills? Provide the optimal portfolio weights. What utility do you get from this optimal portfolio? 4. What is your optimal portfolio if you cannot short sell T-bills (i.e. you cannot borrow at the 2% risk-free interest rate), but you can borrow at a 5% interest rate? Provide the optimal portfolio weights. What is your utility? Suppose again that you cannot short sell T-bills, but you can borrow at the higher borrowing rate of 5%. In addition, suppose you are not allowed to borrow more than an amount equal to 30% of your (initial) wealth. Provide the optimal portfolio weights