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Implications from the Treasury Yield Curve

Submitted by scriabinop23 on 08/14/2010 19:37 -0400

Here is a derivation of implied 1 year forward rates on treasuries. A 1 year treasury forward is close enough (for government work) to get an idea of when the market projects the Fed will start moving rates upward. If you imply the Fed responds with hikes because a recovery is already happening, this data tells a little more where general sentiment is at.

For the sake of robustness, I purposefully designed this to work with very few input points, necessitating a basic a smoothing mechanism. From this, there is a small amount of error, but nothing meaningful.

The obvious interpretation here is that the treasury markets as of today do not project a meaningful recovery will start until 2012, with the end of cycle not happening until 2017. Post 2017, I'll venture to say 25 basis points of 1 year treasury forward movement per year is not actually projected Fed Funds policy change, but instead accounting for normal upward sloping yield curve behavior, where investors want to be paid extra for taking more interest rate risk from longer duration bonds.

And a snapshot of the treasury curve from November 2006, the "golden age" of securitization:

For more analysis, go to http://scriabinop23.blogspot.com.

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Sun, 08/15/2010 - 11:14 | 522369 Bohica

For what it’s worth, 5-yr 5-yr forward implied inflation was 2.26% as of July (using H.15 monthly data), after 3 monthly declines from 2.94% in April. Despite those declines, it’s only 18 bps below its average over the 115 months that inflation-indexed TCM data has been available (since Jan 2003). With a few exceptions, like around Dec ‘08, the 5-yr number has been remarkably flat since 2003.

I haven’t found the bond market to be particularly good at anticipating inflation, despite the reputation of the bond vigilantes, but I watch the 5-year number because I understand it’s one of the Fed’s preferred market-based predictors.

Sun, 08/15/2010 - 06:29 | 522274 tom

your math is right and your theory as applied in the chart is the standard, but i agree more with what you say for the 2017 and out "projections", except applied to the whole curve: "not actually projected Fed Funds policy change, but instead accounting for normal upward sloping yield curve behavior, where investors want to be paid extra for taking more interest rate risk from longer duration bonds". That said, there is some projection of Fed Funds policy change in there, but it's hard to single out, and it's likely to be mostly herd adherence to standard assumptions of reversion to historical averages, not particularly seriously thought out projections.

Sun, 08/15/2010 - 11:47 | 522416 masterinchancery

The curve may not be projecting economic recovery in future years, just reversion to the mean and then some as treasury debt becomes unwieldy.

Sun, 08/15/2010 - 10:25 | 522340 knukles

Not only is the math right and the theory soundly and faithfully expounded upon, as a practitioner I can verify the sad fact of the matter that forward rates have virtually no predictive capacity whatsoever.
Nonetheless, they are utilized in part explicitly or implicitly in the pricing formulations for options, swaps, futures, forwards and the like (in part as time value of money/present value/discount rates) as no other tool has established itself as a market based standard.
But if anyone thinks that a 30 year bond's true value 15 years hence will in fact be exactly as forecast by two serial 15 year rates, they'll not need to worry about markets being irrational longer than they can remain solvent.

Thanks to tom and predecessor comments. Love it when the threads are sound and fundamentally consistent.

Mon, 08/16/2010 - 12:57 | 524051 Greater Fool

+Actual/360

But...does the same hold of curves bootstrapped from swaps? Since multiple points are liquid, and it's relatively easy to construct forward-starting swaps from scratch, I'd expect forward rates from those curves to do a better job of representing current expectations than a Treasury curve.

Now, whether current expectations are realized when the time comes is another question entirely....

Sun, 08/15/2010 - 02:15 | 522244 Fishhawk

Your explanation is quite clear, and makes the point well. my question is, is this expectation of higher yields coming to a Treasury note near you even reasonable, given that the Fed will be buying up $1 to 3T in that same market for years? Japan has seen 0.5% bond rates for 10 or 12 years now. Can the market stay oversold for longer than you can stay solvent?

Sun, 08/15/2010 - 09:58 | 522327 bonddude

Yes.

Sun, 08/15/2010 - 00:41 | 522224 scriabinop23

Very simplified, a 2 year note with 5% yield pays 5% each year. If the 1 year note has a 3% rate, upon buying the 1 year note and receiving the principal to reinvest at its maturity, you could buy another 1 year maturity note. The market rate of that second 1 year note is implied by the yield on the 2 year note versus the first1 year note. The math: 1.05*1.05=1.03*(1+x). x is the annual interest rate on that bond. x=7.0388%. An investor would be indifferent to buying 1 year note the first year at 3% yield, then another 1 year note starting the second year at a 7.0388% yield --- compared to just buying a 5% two year bond. The net returns are the same. So given a few points on the treasury yield curve, you can figure out the implied forward rates. Given our current steep curve, it means expectations are quite a bit higher for future rates to compensate for near term near zero rates.

Sun, 08/15/2010 - 17:35 | 522873 chrisd

That's helpful, thanks

Sat, 08/14/2010 - 22:04 | 522156 chrisd

Could you help me understand the math behind calculating this information?

Implications from the Treasury Yield Curve

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