Hedging/Arbitrage
The 3-month forward rate equals the spot rate less the discount. Therefore:
RF =.8200 * (.99375) =.814875 b)
Therefore, interest rate parity does not hold.
A c) to take advantage of the arbitrage opportunity I would borrow USD, lend CAD, and sell the CAD on the forward contract. I will receive Canadian interest of 500,000 * (.085/4) = $10,625. I will pay American interest of (410,000) * (.065/4) = $6,662.50. The CAD will be converted back to USD in 3 months to pay the debt at a rate of.814875. Therefore the proceeds from the CAD side will be (10,625)(.814875) = $8,658.05. The profit from the arbitrage will be these proceeds less the cost of the borrowed USD, so:
$6,662.50 = $1,995.55 d) for interest rate parity to hold, the Canadian interest rate would have to be:
1/.82)(1 + Rc (.25))(.8148) = 1.01625
1.2195127(1 + Rc (.25) = 1.01625 / .8148
Rc = 1.2472385 /
Rc =.0227351
Rc = 4 (.0227351)
Rc = 9.09%
a) the spot rate bid/ask is 6.4685-6.4782. The 1-month forward bid/ask is 6.465-6.498. The 3-month forward is 6.435-6.522. The 6-month forward is 6.430-6.561.
A b) the annualized percentage discount from the six-month bid rate is:
(R/2) =.1555209 / .1545953
R/2 =.0059872 c) the ask price for dollars in three months is 1 / 6.435 =.1554001; therefore for FFR 1,000,000 you will receive $155,400.10 d) the bid price for francs in six months is 1 / 6.430 =.1555209; therefore it will cost $77, 760.45 for the FFR 500,000.
3. The bid from the Paris dealer would be.03/.2 =.15.
The ask from the Paris dealer would be.0335 / .202 =.1658415
4. The DEM is undervalued as of December 31, 1999. The PPP calculations for the DEM as follows:
5225 (1.05/1.025) =.5352438;.5252438 (1.045 / 1.02) =.5483624;.5483624 (1.055 / 1.035) =.5589587 should have been the value of the DEM on December 31, 1999.
5. Given the 1% mandatory profit, arbitrage opportunities exist with DEM/FFR exchanges in Frankfurt and Paris. Three point arbitrage opportunities are also possible with transactions beginning with the purchase of FFR in New York; the purchase of FFR in Frankfurt; the sale of FF in Frankfurt; the purchase of dollars in Paris and the sale of $ in Paris. The most profitable arbitrage opportunity is if I sell francs for marks in Paris, then buy marks for francs in Frankfurt.
To sell FFR 1000 in Paris would give me DEM 437.94.
To sell 437.94 DEM in Frankfurt would give me FFR 1031.41, for a return of 3.141%.
6. Given the Japanese information we can calculate the real interest rate:
Rreal = Rnom / Rinf = 1.08/1.03 = 4.85%.
This is then used to determine the nominal rate for France (17.43%) and inflation rate for England (8.72%), given interest rate parity. The expected premium is then the French inflation rate over the English inflation rate. This gives us:
