Financial Engineering 263
Step 3: The bank determines the amount in the foreign currency required
today (at T 0 ) to hedge X amount of foreign currency at time T. In other
words, what is the present value of X amount of foreign currency given the
expected rate of return? That should be equal to the value of a murabahah
in foreign currency at time T 0 , so that the cost plus the profi t margin in the
foreign market is equal to the required hedge amount of X in foreign cur-
rency at time T. Therefore, the amount required today to hedge X amount
of foreign currency would be equal to x in foreign currency as shown below:
Step 4: Local currency (L) required at time T 0 will be equal to x × spot
exchange rate between the local and the foreign currency. The bank invests
L amount of local currency in foreign murabahah after converting L amount
of local currency into x amount of foreign currency at the spot rate at T 0.
Step 5: The bank agrees with the importer to deliver X amount of for-
eign currency on maturity date T at rate F. The bank determines the rate F
based on the rate - of - return differential between the domestic and foreign
markets. In other words, the future rate F is a function of the expected
rates of return on local and foreign murabahah for time T. The difference
between domestic and foreign murabahah mark - up rates determine the dis-
count/premium on forward rate. This rate F can also be called the unbiased
predictor of the future spot rate, because if this rate is not the equilibrium
rate, there is opportunity for arbitrage where the arbitrageur can make risk -
less profi t by taking offsetting positions in the market creating the arbitrage.
In other words, the forward exchange rate (F) will be determined in such
a way that the forward discount/premium on the currency is equal to the
differential of expected rates of return on murabahah contracts of equal
risk in domestic and foreign capital markets. This rate (F) is not only the
best estimate of the future spot exchange rate, but is also an arbitrage - free
forward rate for the currency.
At the date of delivery (T):
Step 6: The bank receives X amount of foreign currency against the
murabahah investment. The importer buys X amount of foreign currency by
paying X × F amount of local currency to the bank. Since the bank initially
invested L amount, the rate of return to the bank or the investor would be
equal to Rd, or the same as the bank or the investor would have earned by
investing in local murabahah.
This synthetic forward contract is fully backed by an Islamic investment
in the form of a murabahah. As a result, the bank or the investor earns Rd on the
investment. The importer benefi ts from the exchange rate hedge in case
the future exchange rate moves unfavorably.