The U.S. three-month interest rate (unannualized) is 2%. The British pound three
ID: 2778732 • Letter: T
Question
The U.S. three-month interest rate (unannualized) is 2%. The British pound three-month interest rate (unannualized) is 3.5%. Assume interest rate parity exists. The expected inflation over this period is 6% in the U.S. and 2% in England. A call option with a three-month expiration date on British pounds is available for a premium of $.02 and a strike price of $.63. The spot rate of the British pound is $.61. Assume that you believe in purchasing power parity.
Determine the dollar amount of your profit or loss from buying a call option contract specifying $104,000 British pounds.
ANSWER: The expected change in the British pound’s spot rate is: ______________________
PLEASE BREAKDOWN YOUR SOLUTION IN DETAL
Explanation / Answer
According to purchasing power parity,
The expected spot rate of the British pound in 3 months=($.61/pound)*(1+exp inflationUS/1+exp inflationUK)3/12
The expected spot rate of the British pound in 3 months=($.61/pound)*(1.06/1.02).25
The expected spot rate of the British pound in 3 months=$1.009663/pound
You believe according to purchasing power parity that spot rate for British pound shall rise in 3 months to $1.009663/pound and you purchase call options on British pounds at strike price of $.63.
According to interest rate parity,
The expected spot rate of the British pound in 3 months=($.61/pound)*(1+U.S. three-month interest rate/1+ pound three-month interest rate)= ($.61/pound)*(1.02/1.035)=$0.60116/pound
But expected spot rate of the British pound in 3 months declines to $0.60116/pound as interest rate parity exists thus you lose all the premium paid in purchase of the options.% drop=(0.60116-.61)/.61=-0.00884/.61
total call options on pound=104,000/.61=170491.80=~170492
dollar amount of your loss from buying a call option contract specifying $104,000 British pounds= premium of $.02*total call options on pound=.02*170492=$3409.84
The expected change in the British pound’s spot rate is: $1.009663/pound-$.63/pound = $0.379663/pound as expected by purchasing power parity.
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