Determine the arbitrage profit (spot rates)

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.