1. Consider R one-period model for the price of a stock s: suppose Its time-0 value S0 is known, and it is known that at t i11w 7’, its value is either Su or Sd. Assume further that V is a derivative on S expiring at time T; suppose it’s time-0 value is l4. and that at time T, it has value U if the stock price is Su or D if the stock price is Sd. Use the arbitrage theorem to prove that the risk-neutral probability is given by

And

2. Carey Company is borrowing $150,000 for one year at 8.0 percent from Second Intrastate Bank. The bank requires a 15 percent compensating balance. The principal refers to funds the firm can effectively utilize (Amount borrowed − Compensating balance).

a. What is the effective rate of interest? (Use a 360-day year. Input your answer as a percent rounded to 2 decimal places.)

b. What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? (Use a 360-day year. Input your answer as a percent rounded to 2 decimal places.)

3. Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that expectations theory holds and the real risk-free rate is r* = 2.75%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2.75%, what inflation rate is expected after Year 1?

4. The skipper wants to buy a beach house. The house costs $250,000. What is the monthly payment on a 30 year loan with a 6% nominal interest rate?

5. The market portfolio has a standard deviation of 20 percent, and the covariance between the returns on the market and those on a stock Z is 0.08.

1. What is the beta of stock Z.?

2. What is the standard deviation of a fully diversified portfolio of such stocks?

3. What is the average beta of all stocks?

4. If the market portfolio gave an extra return of 5%, how much extra return can you expect from stock Z?