Suppose the current dollar-pound exchange rate is $1.35/£, and this is also the price trading in the 1-year forward market (i.e. you can agree today to trade currencies in one year at an agreed upon rate of $1.35/£). U.S. 1-year bond yields are currently 2%, and U.K. 1-year bond yields are currently 3%.
A. In a world without transaction costs or other frictions, describe a strategy for generating arbitrage profits.
B. Suppose every transaction has some percentage cost to enact. For example, if the cost is X%, then converting to pounds will cost $1.35(1+X%) per pound, and that to buy a U.S. bond, the true price is not 100.00/1.02 = 98.04 but 100*(1+X%)/1.02. What is the smallest value of X that eliminates your arbitrage opportunity?