Question

Exchange rate is currently $1.85 US per 1 British pound. Interest rate is 4% in the US and 3% in the UK. A bank shorts a futures contract to buy 1,000,000 pounds for $1.9 million in one year.

A. Find the expected future spot exchange rate using the interest rate parity

B. What risk is the bank facing?

C. Write the expression for the present value of the bank’s short futures position, as a function of current spot exchange rate S

D. Find the delta of the bank’s position.

Answer 1

(a) Current Spot Exhange Rate = $ 1.85 / 1 BP, UK Interest Rate = rf = 3% and US Interest Rates = rd = 4%

Let the future spot rate be Fs

Then (Fs / S) = [(1+rd) / (1+rf)]

Fs/ 1.85 = (1.04) / (1.03)

Fs = $ 1.868 / 1 BP

(b) The bank has a long position in the futures contract for British Pound.This implies that the bank is willing to purchase 1 million British Pounds after 1 year at the currently determined rate of $ 1.8 / 1 BP as per the futures contract.This might be the case beacuse possibly the bank has a payable amounting to 1 million BP after one year.

The bank faces the risk of BP becoming cheaper, which means that instead of $ 1.8 required to purchase one BP(under the futures contract) it might require a lesser amount say $ 1.75 to purchase one BP in the spot market. By entering into a futures contract the bank has exposed itself to falling value of the British pound. This in practice is however avoided by entering into an opposite position in the futures market (going short as initially bank went long) thereby squaring off the futures position and making the actual purchase of 1 million BPs in the spot market.

Without the futures contract however the bank would have exposed itself to the risk of a rising British Pound value. The two types of risks are bothe examples of currency risks.

(c) The bank will purchase 1 million BP for $ 1.9 million after on year. Therefore, exchange rate under futures contract = $ 1.9 million / 1million BP = $1.9/ 1 BP

The present value of the futures contract is the IRP based current spot exchange rate for a futures rate of $1.9 / 1 BP

Using IRP:

1.9 / S = (1.04) / (1.03)

S = $ 1.882 / 1 BP

Therefore, Present Value of the Futures Contract = S x 1000000 = $ 1.882 million approximately.

(d) The delta of a futures contract is the amount by which the price of the futures contract(the long future position value) changes when the underlying spot price changes by 1 unit. If the bank goes long in the futures position it is paying 1.8$ to gain exposure to an asset (the British Pound) which has future spot value of $ 1.868(from part(a))

Therefore, Delta = Future Spot Rate / Futures Rate = 1.868 / 1.9 = 0.983