Question

You have an opportunity to borrow 3,000 from X company at the end of year 1 at 6% effective where then you have to repay the loan in one year term. Determine the arbitrage profit you can make at the end of year 1 if the spot rate for 1-year is 7% and 2-year spot rate is 6.5%.

Answer 1

Sell 1 year bond with face value of 3000
Buy 1.0600 (=(3000/1.07)/(3000/1.065^2)) 2 year bonds with face value of 3000

Cash flows
Year 0: =3000/1.07-3000/1.065^2*1.0600
Year 1: -3000 (One year bond matures and we have to return face value to the investor. This we will pay by borrowing at 6%)
Year 2: =+3000*(3000/1.07)/(3000/1.065^2)=+3180.0700935 (Two year bond matures and we get face value which we use to pay off the loan)

Arbitrage profit=3180.0700935-3000*1.06=0.0700935