Question

1. The risk-free rate in the US is 5% and the UK risk-free rate is 8%. The spot quote is $80/£ while the one year forward quote is $78/£. You can borrow either $1,000,000 or £555,556. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

Answer 1

According to IRP,

So, the quoted forward price is not correct. It is quoted higher, so sell forward at the quoted price.

Step 1: Borrow $1,000,000 and convert it into pounds at the spot rate.

1,000,000/80 = 12,500£

Step 2: Deposit 12,500 the UK at 8% per year.

Step 3: Enter the contract to sell euro forward at 78 $/£

After one year

Step 3: Proceeds from the deposit = 12,500 * 1.08 = £13,500

Step 4: Sell £13,500 at the agreed upon rate of 78 $/£ to get 13,500*78 = $1,053,000

Step 5: Repay the borrowed amount with interest: 1,000,000 * 1.05 = $1,050,000

Step 6: You are left with $3,000 which is your profit. This is the difference between the amount you got in step 4 and step 5.

Hope you understand this arbitrage opportunity.

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