Bla Bla

RISK MODELING

EXAM

Answer the following requirements in handwriting and then scan the answers. Use the Excel wherever necessary (at least for questions 3 and 6). Build an archive with everything that you worked, name with your FirstName_LastName and send the file to the e-mail address homework.mpi@gmail.com before 23.59, Sunday 11th of December 2011.

1. Consider a futures contract to purchase a coupon-bearing bond whose current price is $875. The futures contract matures in 15 months and the bond matures in 4 years. The bond holder receives an annual coupon of $60 paid semiannually and the next coupon will be paid in 3 months. Thus, if we want to take a long position in the futures on this bond we will have to take into account three coupons until the maturity of the futures (the last coupon will be paid immediately prior to the delivery date). We can borrow and lend money at the following continuously compounded interest rates:
    • R3 = 7%   per annum for 3 months
    • R9 = 9%   per annum for 9 months
    • R10 = 10%   per annum for 10 months
    • R15 = 11%   per annum for 15 months
Assume that the futures price and the spot price follow the futures-spot parity condition.
  a) If the futures price is $905 will you be able to benefit from these prices? If a profit is possible then present the strategy that you can use to obtain this profit.
  b) What if the futures price is $910? Can you make any profit? Explain how.

2. Nearby Bank has the following balance sheet (in millions):

Assets Liabilities and Equity
Cash $60 Demand deposits $140
5-year treasury notes $60 1-year Certificates of Deposit $160
30-year mortgages $200 Equity   $20
Total Assets $320 Total Liabilities and Equity $320

  What is the maturity gap for Nearby Bank?   Is Nearby Bank more exposed to an increase or decrease in interest rates?   Explain why?

3. Consider the following prices of the stock and the futures at the end of the month.

|month         |spot...