Question

Suppose you are given the following financial information on January 1, 2020:

Spot $/£ exchange rate (e):                                         $1.20/£

One-year interest rate on dollars (i_US):                       2.0%

One-year interest rate on pounds (i_UK):                      6.0%

Market’s expected spot rate in one year (e^ex):            $1.12/£

1. If a U.K. investor looking for the highest return agrees with the market’s expectation of the future spot rate, should she make an uncovered investment in dollars or simply invest in pounds?
2. If a U.S. firm will be receiving £1,000,000 in one year, and wants to eliminate any foreign exchange risk, what can the firm do in the money markets?
3. A U.S. firm will be receiving £1,000,000 in one year, and discovers that forward contracts are available. Its bank quotes the firm a forward rate of f = $1.15/£? What would the firm do to eliminate any foreign exchange risk using a forward contract?

D. Suppose there is still trading in the spot foreign exchange market today, but the market’s expected spot rate in one year is set at $1.12/£. What is the equilibrium spot rate in the market today at which uncovered interest rate parity holds?

Answer 1

A. Assume investor has 100 pounds

Choice 1: Simply invest in pounds:

Investor will earn one year return of 6% on 100 pound: 106% * 100 = 106 pounds

Choice 2: Uncovered investment in dollars:

Investor will convert 100 pound into dollar at spot rate: 100 * 1.2 = $120

This $120 will fetch interest of 2% = 102% * $120 = $122.4

This $122.4 should get coverted into pound after one year at expected rate: $122.4 / 1.12 = 109.285 pounds

Uncovered investment in dollars will be a better investment option as it yields higher money.

B.

To eliminate against exchange rate fluctuation, the firm needs to do currency hedging in the money market. US firm needs to sells ( go short on) one year dollar/pound futures. This will ensure to lock in exchange rate and eliminate currency risk.

C.

To eliminate against exchange rate fluctuation, US firm needs to sells ( go short on) one year dollar/pound futures in the money market. This will ensure to lock in exchange rate and eliminate currency risk.

This is will be done at the forward rate of 1.15 for 1,000,000 pounds.

Therefore, equivalent notional amount = 1,000,000 * 1.15 = 1,150,000 dollars

After one year: The profit or loss in the spot market will be offsetted by the loss or profit in the futue market. Hence, the currency risk would be eliminated.

D.

This is solved using uncovered interest rate parity formula:

Spot exchange rate = (1+iUK) * expected rate / (1 + iUS)

= (1 + 6%) * 1.12 / (1 + 2%)

= 1.06 * 1.12 / 1.02

Spot Rate = 1.164 dollars/ pound