### CFA Practice Question

There are 253 practice questions for this study session.

### CFA Practice Question

The spot rate on the pound is \$1.5005/£, the 360-day forward is \$1.5020/£, the 360-day interest rate in the U.S. is 2.25%, and in the U.K. it is 1.9%. Is covered interest arbitrage possible and if so, what are your profits assuming \$1,000,000 or its equivalent in the other currency?

A. covered interest arbitrage is not possible.
B. covered interest arbitrage is possible with a profit of \$2,481.
C. covered interest arbitrage is possible with a profit of \$1,652.

The interest rate differential and forward premium/discount are such that you want to invest in the U.S. money market. Borrow £666,444.52, then convert it in the spot market to \$1,000,000 (666,444.52 x 1.5005). Invest in U.S. money market at 2.25%. Enter forward contract to deliver \$1,022,500 in 360 days for £680,758.76 (\$1,022,500/1.5020). In 360 days, exercise forward and repay loan of £679,106.96 (£666,444.52 x 1.019), leaving a profit of £1652 or \$2,481. In practice, you would only enter a forward contract for \$1,020,019, the amount necessary to repay the loan, leaving you with the \$2,481.

User Comment
rhardin How do I know that I want to invest in US market? I'm confused...
Allen88 This is what I thought. Calculating the actual forward rate, I did, (\$1.5005/1.019)*(1.0225) and got \$1.506 per pound. Since the forward contract is \$1.502 per pound that means that the dollar appreciated in value compared to the actual forward calculation (\$1.506). This means that the pound depreciated a lot more than expected so we would want to borrow pound and then repay pound.
Offboard You calculate forward rate and get 1,5056\$ per 1 pound (and that should be the rate), but you see the rate 1,5005\$ on the market. You conclude that pound is trading cheap, so you should borrow in pounds and loan in dollars.
tushi123 Is an arbitrage profit possible if I do not take a loan?
davidt876 the point is to show why covered interest parity has a practical application in pricing - it's a hypothetical way to show how an efficient market price correction can occur without the need for any net investment.

but yes tushi you can make money without borrowing and instead making a net investment.

if u start in GBP, convert to USD at the spot, and invest that USD at 2.25% in the US market. at the same time enter into the forward to buy back £ in a year at a price that we've calculated to be lower than the spot rate "should" be in a year. You get access to the higher interest rates without the FX market punishing you by erasing your potential profits by properly pricing forward rates.

or u start in USD invest at 2.25% and contract to convert your USD to GBP at the quoted forward rate. in a year cash out and honour your forward, then convert back to USD at the spot rate (which if covered interest holds should be higher than the forward rate you locked in - i.e. use the mispriced forward to buy pounds cheap, and sell pounds high at the spot rate)

so even if you don't want to borrow money there's an arbitrage opportunity, and so demand for the forward should increase and so the price should increase - until it approached the "correct" forward rate we calculated.

but keep in mind that there are other risks involved in currency trading.. markets with higher interest rates tend to be riskier (try imagine a pair thats not USD/GBP). you may be worried about the counter party honouring their end of the forward contract in a riskier market with higher interest rates... so you'd only enter this trade if the mispricing was substantially more than 30pips. also trading frictions make it impossible for the parity to always hold.

point is that these examples are conceptual. and make a very good argument for why covered interest parity should at the very least be used as a benchmark when pricing currency pairs
Rm178234 I found it easier to just use the covered interest differential equation. Plug in all the numbers here besides foreign interest rate (which is what you want to solve for). The answer ends up being 2.0019%. So if the zero arbitrage point is 2.0019% and the current foreign interest rate is 2.25% you are making a profit of .2481% which is \$2481 on \$1,000,000.