Homework Assignments

All homework solutions are also available on reserve in the library.

Homework 1

Due Monday, September 11

1) The CD$-£ exchange rate is 2.0, the US$-£ exchange rate is 1.8 and the CD$-US$ exchange rate is 1.05. Does and arbitrage opportunity exist? If so, why?

2) Consult the Financial Times (of London) on Wednesday February 10, 1993. At what rate could you change US$ into French Francs on the previous day? How about French Francs (FF) into US$? At what rate could you purchase FF (for US$) 3 months forward? What about 1 month forward? At what rate could you sell FF 3 months forward?

3) Using the spot rates on Tuesday February 9, 1993 (in the same issue of the Financial Times) calculate what rate you would get if you converted a (Canadian) Dollar into Swiss Francs. Do the same for Swiss Francs into German Marks.

Homework 2

Due Monday, September 25

1) Create a spreadsheet in Lotus or Mathematica that generates implied forward rates for all quoted currencies at 1 and 3 month maturities that include transaction costs (i.e. you should generate bid/ask spreads). As usual, use eurocurrency interest rates and do not worry about British pounds. Using U.S. dollars as the domestic currency compare the implied forward rates to actual forward rates on Monday September 16, 1991 (i.e use the quotes in Tuesday's Financial Times.)

2) Using what you learned in question 1, derive the appropriate interest rate parity formulas when transaction costs are included.

Homework 3

Due Monday, October 2

  1. Market Info: Interest rates on pure discount bonds: 
                                                                       Maturity
                 1/2      1        1 1/2       2        2 1/2      3     3 1/2     4    4 1/2    5
Japan           10      10.25  10 1/2    10.75      11        11       11      11      11      11
U.S.		8       8 1/2      9         9.75       10     10 1/2    11      11      11      11
    Spot Exchange Rate: 140

    Assume interest rates are not stochastic for (1)-(4)

    1. Calculate what the 1/2 year rate will be in 1/2,1,11/2,...,4 1/2 years from now. Note that once you have determined these rates, getting the n year rate m years from now simply requires multiplying the 1/2 year rate in years m,m+1/2,..,m+n-1/2 together.
    2. Assume that you can either go long in a 5 year forward contract or a 5 year future contract. What is today's forward and future price.
    3. The exchange rate over the next 5 years (sampled every 6 months) follows the following path: 142,143,139,140,140,140,143,144,141,135. Assuming that in 5 years you execute the contracts and purchase the foreign currencies and then convert the proceeds back to dollars on the spot market, compare the net cash flows of the forward and future contracts over the 5 year period.
    4. Discount the cash flows to the present. What do you know about how much you will be prepared to pay to enter into a forward or a future contract. Explain.
    5. Describe how the analysis would change is interest rates are assumed to be stochastic.
  2. You are currently working at Salomon Bros. Honda has $1 mil Bond outstanding in the US with a 10% coupon, semi-annual payments, for the next 5 years. IBM has a 140mil¥ bond outstanding in Japan, with a 101/2% coupon, semi annual payments also maturing in 5 years. (The coupons are quoted on an annual basis, so each payment is just half the coupon times the principal outstanding, i.e. Honda pays $500,000 every 6 months.) You wish to arrange a swap for these 2 firms.
    1. Calculate (in either $ or ¥) what the semi-annual payments will be between the companies if they agree to do the swap today at no cost to either.
    2. Calculate what one time payment today will allow the companies to exchange their future cash flows at no cost.
    3. For tax reasons IBM would rather enter into the agreement today without exchanging money but Honda does not want to exchange money in the future. With Salomon acting as the intermediary, use an arbitrage argument to explain how you can still effect the deal and ensure that Salomon bears no residual risk.
    Market Info: Interest rates on pure discount bonds: 
                                                                       Maturity
                            1/2      1         1 1/2      2      2 1/2      3       3 1/2      4       4 1/2      5

Japan                    10      10.25        10.5     10.75     11      11        11      11      11         11
U.S.                      8      8 1/2          9        9.75      10      10.5   11      11      11         11

Spot Exchange Rate: 140

Homework 4

Due Monday, October 16

  1. a) Consult the Financial Times on September 21, 1991 (see quote sheet provided). Using the put/call parity relationship, compute the price of the all the Sterling October calls (for which prices are quoted) from the price of the corresponding puts, and the corresponding 1 month eurocurrency rates (see last quote sheet). Compare your results to actual call prices.

    b) Just from the options data provided, calculate the 2 month Sterling - Dollar forward rate to within 2.5¢.

  2. You currently are the chief curator of the Getty Museum. Last year you faced the following decision. The DeLuvan family had decided to sell a very rare Fabergİ egg in London. You and two other anonymous parties were negotiating for the egg. Patric DeLuvan had decided on the following process to sell the egg. On October 16, 1991 he will ask for bids from the three parties. He announced that if all three submitted bids he would sell the egg to the highest bidder, otherwise he would sell the egg at a public auction on December 18, 1991. You decided to submit a bid of £1M Sterling on October 16, and would bid no more than this if forced to go to the public auction. Using the quotes on September 21 , 1991 describe and determine the cost of a hedge that fixes both bids in U.S. Dollar terms, but ensures that if you do not succeed in purchasing the egg you do not lose any money.