Question

Assume that a bank has assets located in London worth £100 million on which it earns an average of 8% per year. The bank has £150 million in liabilities on which it pays an average of 6% per year. The current spot rate is £1 = $1.25 a) If the exchange rate at the end of the year is £1 = $1.50, will the dollar have appreciated or depreciated against the pound? b) Is the bank net short or net long? Given the change in the exchange rate, will the bank make money or lose money?

Answer 1

Solution:

a) If the exchange rate at the end of the year is £1 = $1.50, the dollar would have depreciated against the pound since the value of a dollar would then be less in terms of pounds i.e 1/1.5 = £ 0.67 versus 1/1.25 = £ 0.80 a year earlier.

b) The bank has assets worth £ 100 million + £ 8 million (accrued interest @ 8%) = £ 108 million and liabilities worth £ 150 million + £ 9 million (accrued interest @ 6%)= £ 159 million. Thus, its net liability would be £ 51 million ( £ 159 - £ 108) a year from now. Since it is a foreign currency (pound) liability, the bank is net short.

The bank will lose money given the appreciation in the pound since while now it has to pay at spot rates $ 1.25 x 50 = $ 62.50 million, a year from now it has to pay $ 1.50 x 50 = $ 75 million on the equivalent pound liability not considering the net accrued interest.

Explanation: The reason is that to repay the pound liability, the bank expects that the pound would depreciate against the dollar a year from now, so that it can repay the liability by buying pounds then at a lower price and thereby not suffer a loss on the transaction. For e.g. the bank would expect that the rate would reduce to say £1 = $ 1.20, so at the spot rate the bank would have to spend $ 1.25 x 50 = $ 62.5 while a year from now it would have to spend $ 1.20 x 51 = $ 61.20 and save $ 1.30 per million.

When a trader buys a currency in the expectation that the currency will rise / appreciate in value, it is a long position and when he sells a currency in the expectation that the currency will fall / depreciate in value, it is a short position. In this problem, if it was a net asset, we would have said the position of the bank is long.