# Determine the arbitrage profit (spot rates)

https://i.imgur.com/fBaxybD.png

Can someone walk me through this please?

where does 20 come from?

Treasury bonds pay interest twice per year; ½ × 4% × \$1,000 = \$20.

As for running through it, all of the spot rates are annual (nominal) rates, so you have to divide them by 2 to get the semiannual rates for discounting.

Semi-annual coupon payments: (4% * \$1,000)/2 = \$20

Discount the annual payments with the spot rate. Note that you have to divide the spot rates by two as these are on a semi-annual bond basis.

1. Calculate the PV of the bond at 0 (= arbitrage-free price):

PV= 06m: \$20/(1+0.02/2) + 12m: \$20/(1+0.025/2)^2 + 18m: \$20/(1+0.03/2)^3 + 24m: \$20/(1+0.04/2)^4 + 24m: \$1,020/(1+0.06/2)^5 = \$956.78

Note that this last payment in addition to the coupon also includes the principal value at maturity of 1,000.

1. Compare the arbitrage-free price with the market price of \$976 to determine whether there is mispricing yielding to an arbitrage opportunity:

Mispricing = \$956.78-\$976 = \$19.22 (Answer C) That means that you could by the individual strips (=cash flow streams) for \$956.78, reconstruct the bond with these strips and sell it immediately for the market price of \$975 ensuring an risk-free profit before transaction costs of \$19.22.