Question

Consider the following information available in Diamond Bank located in a neighborhood near you.

         Spot Rate for the British Pound Sterling                                                                 $1.60

         90 – day forward rate of the pound                                                                         $1.59

         90 – day UK interest rate                                                                                               4%

         90 – day U.S. interest rate                                                                                             3%

(a)Given this information, would it be a prudent strategy for Diamond Bank to engage in covered interest arbitrage? Explain.

(b)If covered interest arbitrage is profitable how much profit would the Bank earn if it uses $1,000,000?

(c)Briefly discuss the realignment process that will yield interest rate parity.

Answer 1

a) Here the spot rate is given in terms of USD per Pound. Therefore, USD is the domestic currency and Pound is the foreign currency.
Using the interest rate,
90 day forward rate of pound = Forward Price * (1 + Domestic Rate * X/360) / (1 + Foreign Rate * X/360)
= 1.6 * (1+.03*90/360) / (1+.04*90/360)
=1.6*1.0075/1.01
=1.5960
Therefore, forward is priced at a discount and it would be prudent to engage in covered interest arbitrate as opportunity exisits.

b) If bank uses £1,000,000 to exploit the covered interest arbitrage then,
Step 1: Borrow the spot equivanet of £1m in Pound i.e. 1000000/1.6 = £625,000
Step2: Amount payable at end of 90 days = 625000*(1+0.4*90/360) = 631250
Step 3: Convert £625000 spot into Dollars and invest @ 3%
Step 4: Amount receivable after 90 days = 1000000* (1+0.3*90/360) = 1007500
Step 5: Enter into an forward agreement to sell $1007500 @ 1.59
Step6: at the end of 90 days,
The amount received from investment is sold at $1.59 to receive £633,648
Borrowed amount of £631250 is paid and profit is £2398.

c) For interest rate parity, either forward should be priced at $1.596 or spot should be 1.59 * (1.01/1.0075) = 1.594