Question

You look up a 15-month bond forward contract and find the following: the current price of the bond is $1200, and the forward price is $1250. It will pay a coupon of $50 in 4 months and 10 months. The annualized, continuously compounded risk free rate is 0.5% for 4 months, 1% for 10 months, and 2% for 15 months. Find an arbitrage trade, and show the profit from your trade.

Answer 1

The following arbitrage trade can be made: One can borrow at risk free rate of 2% for 15 months to purchase the bond of $1200. Hence the total cash outflow would be principal = $1200 plus interest = $1200*2% = 24 i.e total outflow would be $1224.

Cash inflow on purchasing the bond would be coupon rate of $50 paid twice i.e. $50*2= $100

Cash inflow at the end of 15 months would be $1250

Total Inflow from Bond would be = Bond forward price + Coupon amt - Bond purchase price

                                                = 1250 + 100 - 1200

                                                = $150

Profit from trade would be = Total inflow from Bond - Total outflow under loan

                                      = $150 - $24 = $126

Pofit from trade would be $26