Two bonds make semiannual coupon payments. Bond A is a 5% coupon bond with exactly seven years to maturity, a price of 97.13, and a yield of 5.5%. This bond would have a price of 94.35 if its yield were 6%. Thus, its conversion factor is 0.9435.
Bond B has nine years to maturity and a 7% coupon. Its current price and yield are 109.79 and 5.6%. It would have a conversion factor of 1.0688 since that corresponds to its price at a 6% yield.
Now suppose that the futures contract is close to expiration, the observed futures price is 102.72, and the only two deliverable bonds are Bonds A and B. A trader with a short position in the futures contract can decide which bond to deliver by comparing the market value of the bond to its invoice price if delivered.
Which bond is cheapest to deliver? Why?