There are two otherwise identical companies but U is unleveraged and L is leveraged. During a boom both companies make a profit of $250 and $100 when the market is down. The probability of a boom is 60%. The market worth of U is $1500. The risk free debt of L is $700 and with 6% interest on loan the loan expenses are $42. The markets are perfect with no taxes and transaction costs. Investors can borrow and deposit with the risk free interest rate.
a.) What is the market value of L?
b.) You invest $60 into stocks of U. Is there an optional investment that can be made into L (combined with a deposit or loan) that provides you exactly the same profits both when the market is up and when it is down? What are the expected profits?
c.) The other way around: you invest $60 into stocks of L. By combining a stock purchase of U and deposit/loan, provide a optional strategy that provides the same profits.
d.) By using the information in this exercise, prove that MM2 holds.