What if breakeven inflation and the “term premium” are measuring the same thing?

There are two simple ways to think about long-term bonds yields:

Traders’ best guesses about future short-term interest rates plus something extra — the “term premium” — to compensate for the risk that those guesses are wrong
A long-term real interest rate plus something to compensate you for inflation

So here’s a surprising chart:

The change in the Federal Reserve Bank of New York’s estimate of the “term premium” is, apparently, closely related to the change in the spread between US Treasury bonds and their inflation-indexed equivalents. For a given move in the five-year forward “term premium”, there is a corresponding move about half as big in the five-year forward breakeven inflation rate.

The only serious exceptions are a few months in the second half of 2008 during the financial crisis and the summer of the “taper tantrum” in 2013. Take those out and the relationship gets even tighter, with an r-squared of 0.43.

(Interestingly, the relationship looks much less tight if you use forward inflation swap rates instead of forward breakeven inflation rates. It looks about the same when using different time horizons for measuring changes.)

There is no obvious reason why the claret and pink lines should move together so tightly. To understand why, consider what each thing is supposed to be measuring.

Start with the claret line. No one can see the “term premium”, only estimate it by looking at the difference between actual interest rates and some guess about where they “should be”.

The NY Fed’s model isn’t perfect. It implies there was little change in the uncertainty surrounding ultra-long-term inflation forecasts between 1960 and 2000, and that the yield curve should usually be inverted, for example. But many in the markets take it seriously. And as Alex has noted, this measure of the “term premium” tends to move in interesting ways in response to certain kinds of news events.

The key thing for our purposes, however, is that it’s derived entirely from changes in the level and shape of the yield curve. Not included: options prices, inflation-indexed bond yields, survey data, and macro data.

Then there is the pink line. The breakeven inflation rate can be divided into traders’ best guess of what inflation will be, plus some premium to compensate for the danger that guess is wrong. The split between what counts as actual expectations versus the uncertainty surrounding those expectations is tough to measure from bond yields alone, but it’s possible to get a sense of changes in the inflation risk premium by looking at the prices of certain kinds of derivatives.

Another way of thinking about all this is that Treasury Inflation-Protected Securities and regular Treasury bonds both have risk premiums built into their yields.

For regular USTs this is the “term premium”. For TIPS it should be the “term premium” minus the inflation risk premium — the whole point of TIPS is you don’t have to worry about inflation! — plus some premium to compensate for the fact that TIPS are somewhat more difficult to trade than their inflation-unprotected counterparts.

The breakeven inflation rate should therefore be the same as the expected inflation rate plus the inflation risk premium minus the TIPS liquidity premium. It shouldn’t be affected by the risk premium compensating investors for uncertainty about long-term real interest rates.

So why does the breakeven rate — which excludes a risk premium to compensate for uncertainty around real interest rates — seem to move so tightly with the NY Fed’s estimate of the “term premium”?

There is one way to explain this, although it’s not very satisfying.

First, assume inflation expectations basically never move, which is in fact the position of the same team of NY Fed economists. Second, assume (reasonably) that changes in the TIPS liquidity premium are generally small. Changes in breakeven inflation rates could therefore be simplified in most cases to changes in the inflation risk premium. That, in turn, “is the simple difference between the nominal and the real term premium”, according to the NY Fed economists’ paper on breakevens.

The problem is that this would imply the “term premium” is driven almost entirely by changes in the uncertainty surrounding inflation forecasts.

Remember, changes in the forward “term premium” are almost identical to changes in the forward breakeven inflation rate times two. So either the real interest rate risk premium doesn’t move at all, or it moves almost in lockstep with the inflation risk premium, for unexplained reasons.

However!

The NY Fed team also had this to say in their paper on breakevens:

Variation in nominal term premia is primarily driven by variation in real term premia.

That’s literally the opposite of the only explanation Alphaville could come up with for the chart at the top of this post! Or maybe changes in the inflation risk premium are really driven by changes in real interest rate uncertainty?

We contacted Tobias Adrian to get his insight in all this, but unfortunately he was unavailable. We’ll be sure to update you if he gets back.

Related links:
What’s up with the “term premium”? — FT Alphaville
The maddening task of measuring the “term premium” — FT Alphaville
Why isn’t the Fed worried about collapsing breakevens? — FT Alphaville