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.
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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