How Treasury Futures Conversion Factors Adjust for Coupon Differences

# Answer by Dimitri Vulis (score 1)


# 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?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/59078

(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.

According to CME https://www.cmegroup.com/trading/interest-rates/calculating-us-treasury-futures-conversion-factors.html

> 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.