3-Year Treasury Note Futures Synthetic Price History

 3-Year Synthetic Price History

To calculate a synthetic price history for 3-Year Treasury Note futures, we began with five years of cash price data from June 2012 to June 2017, corresponding to the end of zero interest rate policy and return to active rate management by the Federal Open Market Committee.

This period also has a robust set of repo rate data at tenors including 1-14 days, 2-3 weeks, and 2-3 months.  We performed a linear extrapolation for days in between, creating a daily repo curve out a full quarter, capturing financing rates for any given Treasury futures contract based on days remaining until last delivery.

For each 3-Year Futures contract, we estimated the Cheapest To Deliver cash CUSIP based on time remaining to expiry and coupon rates, given the low interest rate environment throughout. This typically corresponded to the 3-Year cash Treasury issued the prior month, ie the March 2012 CUSIP expiring March 2015 for the June 2012 future.

On each trading day in the quarter leading up to a futures contract’s expiry, we calculated the interest accrued since the previous semiannual coupon was paid, the coupon income attributable to the current coupon period (and, where a coupon payment falls in the middle of the delivery window, the next coupon period), and the cost to finance the CUSIP over that same period.

Subtracting the financing cost from the coupon income yielded the total carry, which was subtracted from the cash settlement price before it was converted to the futures equivalent price using the conversion factor. We then consolidated each contract into a full synthetic futures price history².

The 3-Year Synthetic Futures prices tracked appropriately between the 2-Year and 5-Year futures.  Moreover, they exhibited volatilities somewhere between the two, with daily net change correlations closer to the 5-Year than the 2-Year.  Since the latter is much more rangebound, this suggests the 3-Year may be a helpful tool for hedging more volatile instruments in the 2-5 year tenor range.

Looking to Intercommodity spreads, both the 3:2 TYT (2yr vs. 3yr) and 1:1 TOF (3yr vs. 5yr) exhibit similar daily ranges, with average moves around 3.7 and 3.3 ticks, respectively.  This again points to a 3-Year that tracks somewhat more closely to the 5-Year.  The 1:1 TFY (2yr vs. 5yr) index is provided as a comparison.

We assumed the following when calculating the synthetic futures price history:

• Delivery takes place on, and therefore futures price towards, last day of delivery (LDD), i.e. for the March future, the LDD is three business days into April
• The cheapest-to-deliver (CTD) is the closest CUSIP to expiry, one quarter prior to the futures delivery month, i.e. the June futures contract’s CTD is the CUSIP auctioned mid-March
• Futures prices would reflect the total value of the CUSIP most likely to be delivered, including accrued coupons, less the cost of financing, adjusted to a 6% nominal coupon via the conversion factor as occurs at delivery invoicing

¹ 3-Year Futures Update:  https://www.cmegroup.com/trading/interest-rates/us-treasury/3-year-us-treasury-note.html

² 3-Year Synthetic Futures Prices:  https://www.cmegroup.com/trading/interest-rates/us-treasury/3-year-us-treasury-note.html#synthetic