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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!

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2 Answers 2

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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.

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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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  • $\begingroup$ I'm not looking to make money necessarily (but doing so would be nice!). I'm more interested in how the fair value of the non-benchmark securities is determined. Let's use wsj.com/market-data/bonds/treasuries as an example. Let's take the benchmark 30-year bond to be the 1.875% 11/15/2051. It trades on multiple broker screens in the inter-dealer market and therefore its price and yield are directly observable. Now, let's take a bond that's more seasoned: the 3.00% 2/15/2049. How do the market makers determine that its yield should be 2.078% (for example)? $\endgroup$
    – equanimity
    Jan 12, 2022 at 3:19
  • $\begingroup$ One definition of fair value would be the present value of cash flows using discount factors from a yield curve estimated without looking at the bond in question. However a discrepancy between this fair value and market price could be due to error in curve estimation rather than be a money making opportunity. That's one reason why a lot of work goes into (proprietary) yield curve estimation at any FI desk. $\endgroup$
    – nbbo2
    Jan 12, 2022 at 16:57

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