0
$\begingroup$

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?

$\endgroup$
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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. $\endgroup$ – Helin Jul 20 '16 at 13:27
  • 1
    $\begingroup$ true I ignored the complexity of delivery options in order to provide a basic explanation. $\endgroup$ – dm63 Jul 20 '16 at 13:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.