Valuing Off-the-Run U.S. Treasuries Relative to Liquid Benchmarks
Summary
The note describes practical ways to estimate fair value for off-the-run Treasury securities, which trade less actively than benchmark issues. One approach marks them at spreads to liquid on-the-run securities or futures’ cheapest-to-deliver bonds. Market makers adjust those spreads using observed supply and demand, market conditions, inventory, and the role they want a position to play in the wider book.
Other approaches fit a spline or dynamic term-structure model to liquid curve points, then value less-liquid issues using spreads relative to that curve or model. The response also mentions off-the-run splines and overnight-indexed-swap spreads as related variations. These methods require judgment about appropriate spreads; the answer gives no universal formula or fixed fair-value result. It cautions that supply-demand effects can leave Treasury securities away from estimated fair value for extended periods, limiting the reliability of a purely model-based valuation.
Key ideas
- Off-the-run Treasuries can be marked at spreads to liquid benchmark securities and futures delivery candidates.
- Market makers adjust spreads in response to supply, demand, inventory, and book objectives.
- Spline curves and dynamic term-structure models can provide reference valuations based on liquid points.
- Estimated fair value depends on selecting appropriate spreads and may not match persistent market pricing.
- Reported constant-maturity yields and tradable bonds or futures may represent different instruments and exposures.
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Full text
# How to determine the fair value of "off-the-run" U.S. Treasury securities # How to determine the fair value of "off-the-run" U.S. Treasury securities In the U.S. Treasury securities market, there are seven (7) "on-the-run" coupon-bearing issues: - 2 year - 3 year - 5 year - 7 year - 10 year - 20 year - 30 year I believe the Fed uses a monotone convex method for deriving the official Treasury yield curve (presumably interpolating from the above-mentioned liquid "on-the-run" issues). What is the market convention (i.e. what are the market-makers doing?) to determine the fair value of the so-called "off-the-run" Treasury securities? Thanks! ## Answer by Helin (score 4, accepted) https://quant.stackexchange.com/a/69459 To be honest, this is a complex issue, but there are a few approaches taken in real life trading. The most simplistic approach is to mark the off-the-runs against the liquidly traded points on the curve. We almost always have accurate real-time pricing on benchmark issues and CTDs for bond futures. The off-the-run issues then trade at some spreads to these liquid issues. How are the spreads determined? The hand-waving answer is just supply/demand that shifts the spreads around. You as the market maker will look at the aggregated market information and adjust the spreads based on market conditions, your inventory profile, your objective (e.g., are you purely providing liquidity or are you also exploiting relative value opportunities in conjunction with other positions in the book), etc. A second common approach is to build an on-the-run spline using liquid points and price all the other issues relative to this spline (basically you are determining the most appropriate z-spread relative to this spline). Here's a press release from RiskVal that touts their implementation of this approach; it's rather vague, but might give you a sense for what practitioners actually do (I have no affiliations to them). Yet others use dynamic term structure models. These models are far more likely to be used when relative value opportunities are an important consideration. Similar to the on-the-run spline approach, you'd fit the model using a pretty small number of liquid points on the curve and then price all the other issues based on appropriate z-spreads relative to this model. An example of such a model can be found in the 3rd edition of Bruce Tuckman's Fixed Income Securities. The challenge is again to determine the appropriate z-spreads based on market conditions, etc. Some also reference off-the-run splines, OIS spreads, etc., but these are really just variations of the same theme. At the end of the day, it really just boil down to supply/demand and what makes sense to you as a liquidity provider. If you look at other posts, it's abundantly clear that large chunks of Treasuries can deviate from fair value persistently, but there's just not much you can do. ## Answer by demully (score 3) https://quant.stackexchange.com/a/69447 These are "constant maturity" yields that the Fed reports. Not actual bonds that can be traded. The "US 10yr" bond future is usually a ~8y maturity bond and a ~7yr duration. It usually yields significantly less than the actual Treasury with closest to 10 year maturity. So you are looking at three different "10 year yields" at the outset. Of which two are tradable; but not comparable. Seen thus the "off-the-run" issue is rendered irrelevant. Futures don't continue off-the-run (like CDS can). And STRIPS exist to arb out coupon or principal mispricings in the cash Tsy products... Good question, but no money to made chasing this one ;-( DEM
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