# Trying to understand T-Bond futures settlement. What am I missing?

Here's a puzzle I encountered when trying to understand how treasury bond futures (/ZB) are settled.

Supposed I am short 1 September ZB contract at \$170, and on its last trading day the contract settles at \$165. If I were to close the contract at the last minute, my realized P&L will be \$1000 x (\$170 - \$165) = \$5000. That is, for every \$1 difference between my "entry" and "exit" price of /ZB, my final realized P&L is changed by \$1000.

But what happens if I don't close the contract? If I understand it correctly, I will pick a bond to deliver, and be paid an "invoice price" which equals the Settlement Price (\$165) times a Conversion Factor, plus the Accrued Interest. For example if the cheapest to deliver (CTD) bond has a conversion factor of 0.9, then I'll be paid an invoice price of \$1000 x \$165 x 0.9 =$148,500 plus accrued interest. It seems obvious to me that the bond conversion factor (0.9) affects my realized P&L in this case.

So how can it possibly be true that my P&L is not affected by bond conversion factor if I close the contract (because it is always a fixed 1000x multiplier), but is affected by bond conversion factor if I don't?

During the delivery month, the "net basis" defined as $$CTD price - (conversion factor * futures price)$$ trades at around zero, otherwise there is an arbitrage. Therefore daily changes in the CTD price are equal to $conversion factor *$ daily changes in the futures price. Hence it is appropriate that the invoice price change is also multiplied by the conversion factor.

• This is actually not entirely true. Because futures stop trading a week before the last delivery date, the CTD can still switch during the last few days. This creates the so-called end-of-month option. If the EOM option is valuable (rarely happens, but it does), cash and futures will not converge and there's no arbitrage. Jul 20 '16 at 13:27
• true I ignored the complexity of delivery options in order to provide a basic explanation.
– dm63
Jul 20 '16 at 13:59