Question

Suppose the spot exchange rate between the United States and the
United Kingdom is $1.73/£. The continuously compounded interest
rate in the U.S. is 8%, while the continuously compounded British
pound-denominated interest rate is 3%. Suppose you observe a 9
**-**month forward exchange rate of $1.99/£. What
transactions could you undertake to make money with zero initial
investment and no risk? Please work and show work. Thank you.

Answer #1

Fwd rate = Spot rate * [e^rt for US / e^rt for UK ]

r is int rate per anum

t = Time period in Years

= $ 1.73 * [ e^0.06 / e^0.0225 ]

= $ 1.73 * [ 1.0618 / 1.0228 ]

= $ 1.80

Fair Rate is $ 1.80 & Actual Rate is $ 1.99.

Hence arbitrage gain is possible.

Ex:

Take a loan of 100000 USD

Convert into Pound using spot Rate

Amount in Pound = 100000 / 1.73

= 57803.47

Realize the amount after 9 Months :

= 57803.47 * e^0.06

= 57803.47 * 1.0618

= 61375.72

Amount in USD = 61375.72 * 1.99

= 122137.7

Repay loan in USD = 100000 * e^0.0225

= 100000 * 1.0228

= 102280

Realize the gain of 122137.7 - 102280

= USD 19857.69

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