Risk-free arbitrage profit (currency)

CFA Level I
#1

If we’re given:

Spot rate(GBP/USD) Forward rate (GBP/USD)

USD 1 year interest rate GBP 1 year interest rate

Then we are told the investor is going to short $XXX,XXX of GBP. Find the risk-free abritrage profit.

I understand what we have to do:

-Take the $XXX,XXX GBP and multiply it by the 1 year GBP interest rate (save this number for future reference). -Now, take the same $XXX,XXX and divide by the spot rate to get that amount in current terms of USD. Multiply that amount by the USD 1 year interest rate. Divide that amount by the forward rate to get it in comparable GBP terms. -Subtract the figure from the second step from the figure in the first step to find our profit. What I don’t know is when to subtract what from what. They said he investor shorted GBP, so what exactly does that tell me I need to do in my final step to find the profit?

#2

If the investor sold GBP, he is borrowing that currency at its risk free rate (step one)and investing at risk-free rate of the other currency. You need to reduce your last step by the amount you calculated in step 1

#3

I just think through the transactions:

  1. Borrow GBP at GBP 1-year risk-free rate.
  2. Trade GBP for USD at GBP/USD spot rate
  3. Invest USD at USD 1-year risk-free rate.
  4. Enter into a forward contract to pay USD / receive GBP at the GBP/USD forward rate
  5. Wait patiently. For one year.
  6. Trade USD for GBP at the GBP/USD forward rate.
  7. Pay off GBP loan.
  8. Party with your profit.
#4

S2000magician, what is the formula that tells us this situation should not happen?

Interest rate parity? Do we need to know this for the CFA? I don’t remember reading it

#5

Beautiful, thank you.

#6

You’re welcome.