Selected Problems


Chapter 3

Problem 4 (page 89 of Eitemann, Stonehill and Moffett): We are told that the spot rate is 110.60 yen/$, the 3-month forward rate is 109.80 yen/$ and the dollar interest rate is currently 4.255 and expected to rise to 4.75%.

Suppose Ayako converted the 400 m. yen into dollars at the spot rate, she would have 400/110.60 or $3.6166365m.  If the dollar interest rate rose to 4.75%, she would have 3.6166365 x (1 + 0.0475/4) = $3.6595841m. in three months time.  If she had bought yen forward at the rate of 109.80 yen/$, she could then use it to convert these dollars into 3.6595841 x 109.80 or 401.82233 m. yen, which works out to a return of 1.82% on an annualized basis.  Obviously, this compares quite well with the 0.5% that she would have had, had she lent out her money at the yen rate.  Of course, it turns out that even if the dollar interest rate had remained at 4.25%, she would still have had a return of 1.32% p.a. after the transaction.  Hence, she is clearly better off converting her yen to dollars and lending in dollars, simultaneously protecting herself against dollar depreciation by selling dollars forward.

If she had not sold the dollars forward, she would make the same amount, on average, perhaps, assuming that the forward rate is an unbiased expectation of the future spot rate.  However, if the rise in dollar rates were not incorporated into current rates, the dollar might well appreciate, leading to an additional profit, when she converted her money back into yen.


Chapter 4

a.

Currency Spot (Bid/Ask) 1-month (Bid/Ask) 3-month (Bid/Ask) 6-month (Bid/Ask)
Mexican peso 9.3850/9.3880 9.3920/9.3960 9.4060/9.4095 9.4260/9.4320
South African Rand 6.1200/6.1300 6.1625/6.1745 6.2300/6.2500 6.3025/6.3200
Pound Sterling 1.6320/1.6335 1.6280/1.6301 1.6215/1.6240 1.6130/1.6165

Keep in mind that the forward rate are quoted not as the foreign exchange rate itself; rather it is the difference between the forward rate and the spot rate.  Hence the forward 1-month bid is 9.3850 + 0.0070 or 9.3920 pesos/$.  The forward ask is similarly calculated off the spot ask.

However, for the pound sterling, note that the forward bid in points is greater than the forward offer in points; hence it is subtracted from the spot rate.

b. If you want to buy Mexican pesos forward with pounds sterling, you'd have to first sell the pounds sterling forward to get dollars forward, and then use the forward dollars to buy the pesos forward.  Hence with 100, you would get $162.15 (using the bid); this would yield 162.15 x 9.4060 = 1525.1829 pesos for a cross rate of 15.2518 pesos/. 

c. If the rate ten years ago were x SR/$, we'd have -0.18 = (x-6.12)/6.12; or x = 5.0184 for the bid and 5.0266 for the ask.

d. From an American perspective, the 1-month forward bid is [(1.628-1.632)/1.632] x 12 x 100 or -2.94118%;  the 3-month forward bid works out to -2.5735%, which is [(1.6215-1.6320)/1.6320] x 4 x 100; the 6-month forward rate works out to a discount of 2.3284%.


Chapter 6

5.a. Receivables: A 4-month (120 day) account receivable means that Chalmers will be receiving foreign currency inflows in the future.  It will therefore need to sell new Mexican pesos forward.  If the sport rate is 10.2400 Pesos/$ and the 120-day forward rate is 11.0400 Pesos/$, the peso is selling forward at a discount relative to the dollar.  Chalmers will therefore receive fewer dollars from forward contracts than it would receive if paid at today's spot rate.  Chalmers is "paying the points forward." 

  1. The amount of required forward cover for paying points forward for 120 days is 50% of the exposure or 1,000,000 pesos.  Chalmers could choose to cover more, but this is the minimum required.
  2. If Chalmers expects the spot rate to be 8.192 pesos/$ in 120 days, Chalmers would likely cover only what is required by company policy and leave the remaining uncovered because the expected spot rate is much more favorable to Chalmers.
  3. If expectations prove correct, the total receivable will result in realized U.S. dollars of the following
  4. 1m. pesos/11.04 = $98,580 from 50% covered position
    1m. pesos/8.1920 = $122,070 from uncovered position, for a total of $212,650.

b. Payables: An eight-week account payable of 3m. pesos would require Chalmers to buy new Mexican pesos forward.  If bought at today's spot rate of 10.2400 pesos/$, as opposed to the forward rate of 11.0400 pesos/$, Chalmers would receive more pesos per dollar.  Once again, Chalmers is "paying the points forward" in the forward market.

  1. The amount of forward cover for paying points forward 60 days is  75% of 3m. pesos or 2.25m. pesos.
  2. The uncovered position is 25% of 3m. pesos or 0.75m. pesos.
  3. If expectations prove correct, the total payable will be the following:
    2.25 pesos/8.8000 = $255,682 from 75% of covered position
    0.75m pesos/10.0000 = $75,000 from uncovered position, for a total of $330,682.