Suppose that the current (simple annual) yields on 3-month U.S. (RA) and U.K. T-

Question

Suppose that the current (simple annual) yields on 3-month U.S. (RA) and U.K. T-bills (Rb) are 16 percent and 8 percent, respectively, and that the dollar value of the pound is expected to rise 1 percent during the next three months.

(a) How might the British and American T-bill and foreign exchange markets adjust to this situation? Present and discuss an equilibrium consistent with the concept of interest rate parity (IRP) and discuss the processes by which this equilibrium might be achieved. Should you buy U.S. or U.K. bills? At what U.S. T-bill yield would you be indifferent between U.K. and U.S. T- bills given the expected changes in the exchange rate?

Hints: IRP Condition: (1 + Ra) = (1 + Rb)(1 + Ee) = (1 + Rb)(1 + F/S) where Ra = 3-month U.S. T-bill yield,

• Rb = 3-month U.K. T-bill yield,
Ee = expected proportional change in the dollar value of the British pound, ƒ .

F = forward exchange rate ($/ƒ ), S = spot exchange rate ($/ƒ ).

Explanation / Answer

Let's assume for the sake of simplicity that today $1 = £1

The dollar value of pound is expected to rise 1% during the next three months => $1.01 = £1

Interest Rate Parity: F£/$ / S£/$ = (1 + i£) /(1 + i$)

We know that F£/$ = 1/1.01 = 0.9901£/$ and spot rate S£/$ = 1.0000£/$, now we also know that i£ = 8% (12-months), so for 3-month i£ = 8%/4 = 2%

=>i$ = (1.0000/0.9901) x (1.02) - 1 = 3.02% (3-month). So, 1-year i$ = 3.02% x 4 = 12.08%, which is lower than the current prevailing 16% rate on US T-bills.

Another approach: we know that i$ = 16%, i£ = 8%

Using, F£/$ / S£/$ = (1 + i£) /(1 + i$) => F£/$ / S£/$ = (1+8%/4) / (1+16%/4) = 0.98077

i.e. Pound should appreciate 1/0.98077 = 1.0196 or 1.96% based on interest rate parity

So, markets will sell pounds and buy dollars in spot markets and invest in 3-months US T-bills to fetch more returns. Or, they will buy pounds and sell dollars in futures markets. Basically, the dollar is cheaper or pound is expensive today, so you sell expensive currency and buy cheaper currency.

Also, remember that currency of a higher interest rate country will depreciate more than the currency of the lower interest rate country.

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