# What does the conversion factor for Treasury bond futures do in relation to the 6% coupon specification for the contract?

I understand that the specification for say, a 10-year Treasury note futures contract is for a face value of $100,000 with a 6% coupon. However, the eligible securities that may be delivered span across different maturities and may be of different coupons. I also understand that a conversion factor must be applied to the delivered securities. Eg if we have a 3% coupon bond with price 102.45 (chose a random number here), we must multiply this by a conversion factor such that the bond yields 6%. (ie where does the coupon = 6% come into play?) The bit where I am stuck is: how can we compare the price of the futures contract, which may indeed yield below 6%, with that of delivered bond? And how does the conversion factor help? • Not sure I understand your question. Are you trying to look at the relative value between the futures contract and a deliverable cash bond? – user42108 Nov 1 '20 at 16:22 • @user42108 Yes, kind of. I don't understand why you multiply the futures settlement price by the conversion factor? The futures settlement price represents the price for a 6% coupon bond whereas the conversion factor is to make the deliverable bond have a yield to maturity of 6% - how do these link together? – junior_pm Nov 1 '20 at 16:40 ## 1 Answer (This is about U.S. treasury futures. Treasury futures in some other countries, like Germany or the U.K., are somewhat similar with subtle differences. Treasury futures in some other countries, like Australia or Korea are very different.) The conversion factors are determined when the new futures contract is set up and don't change until the contract expires. The goal is to reduce (but not completely eliminate) the difference in coupon and accrued interest among the choices that can be delivered. Imagine if all conversion factors were 1, and you had two eligible instruments, one paying 1% coupon, and another paying 2% coupon, same maturity. You don't need a very sophisticated cheapest to deliver model to see that the 1% coupon is always cheaper to deliver. Throwing in the conversion factor into the mix, so that more of the lower-coupon instrument needs to be delivered, levels the playing field between the choices, so that the cheapest to deliver may not be immediately obvious and may change with time. Every cash note or bond that is eligible for delivery into a Treasury futures contract has a conversion factor that reflects its coupon and remaining time to maturity as of a specific delivery month. A conversion factor is the approximate decimal price at which$1 par of a security would trade if it had a six percent yield-to-maturity.

A common misconception is that the DV01 of a Treasury security remains fixed as the yield of the instrument changes. In truth, the price-yield relationship of a Treasury security is nonlinear; as yields fluctuate, the DV01 of a Treasury security changes.

If there was a U.S. treasury instrument with exactly 6% coupon, then the converson factor for this bond would be 1. But as of this writing, most coupons are much less, and so in order to get 6% yield, the price needs to be below par.

As an aside, according to https://www.risk.net/derivatives/7695186/cme-asks-clients-about-changing-implied-ust-futures-coupon , CME has been asking customers about possibly changing the UST futures implied coupon from 6% to 4%. This would result in higher conversion factors.

• Thanks - the problem I have here is with understanding why you use the conversion factor for 6% YTM, whereas the US Treasury instrument has a 6% coupon . Obviously YTM is not the same as coupon, so how does the deliverable bond and the settlement amount end up being similar? – junior_pm Nov 1 '20 at 17:47
• The futures contract is designed so that when yield is 6% on a 6% coupon bond one future has a notional value of 100,000 USD. – noob2 Nov 1 '20 at 20:17
• @noob2 Sorry - I still don't get it. Why do we want the yield to be 6% (ie equalised) when the actual 6% coupon bond might have a different yield? Please can you elaborate. The way I am thinking about it is: if I have a 4% coupon bond that I want to deliver, that is worth X much compared to the 6% coupon bond, and I will have to apply a conversion factor. But not sure why you want the conversion factor to be the price of \$1 face value of the bond such that the YTM is 6% – junior_pm Nov 1 '20 at 20:25
• Exactly, a 4% coupon with 100,000 in Principal is worth less than the 6% bond so he who delivers it is cheating me. The solution is to require delivery of 100,000*K principal of the 4% bond with K>1 – noob2 Nov 1 '20 at 20:59
• @noob2 Ah, so it goes as follows: If the price that a deliverable bond would trade at if it had a YTM of 6% would be 0.97 USD per 1 USD face value, and the Treasury bond future which would be 1 USD at YTM of 6% (coupon = 6%), and the actual Treasury bond future's price is 124.37, per face value of 100,000 USD, we must multiply this by 0.97, the conversion factor? – junior_pm Nov 1 '20 at 21:04