Use Fed projections to deduct the forward premium?

I received the article “Views from the ground – getting tighter and tighter” from the Man Institute published last month. He discusses using the FOMC’s long-term projections to derive the term premium from the 10-year Treasury yield.

The methodology is simple (I have a busy week, so I haven’t collected the data to reproduce it myself). They describe it like this:

A better approach is to incorporate the FOMC’s projections for the federal funds rate into the expected path of short-term rates. This will make term premium estimates more consistent with growth below 2%. Figure 1 shows this model applied, with the assumption that the short rate matches the federal funds rate over the next year, then converges linearly to the long-term projection over the next three years, and then remains constant.

This matches my preferred structure for valuation models, which are based on the 10-year fair value generated by calculating the projected movement in short-term rates over the next 10 years. The fair value trajectory should start near the current level, then evolve towards a stable value in the “medium term” (2 to 5 years). This is necessary to avoid the stupidity of the old-fashioned “bond value” models that economists used to generate, in which the current level of short-term rates has no effect on fair value.

(Note that if you forecast a short-term rate path that is very different from that built into such a model, you do not need a model to know how to position yourself over time. For example, if the model involves a smooth path of rate hikes while you expect a recession to lead to rate cuts, you don’t need a stinky model to know how to go long.)

The problem is to determine the equilibrium level; in the article they use the FOMC’s long-term projections. The “term premium” is the difference between observed market returns and fair value.

The general methodology is sound, my concern is whether it is a good idea to throw information into the market and simply assume that the FOMC is right about the long term path of interest rates. In other words, if you have confidence in a long-term trajectory of the policy rate, deviations from this trajectory effectively correspond to a (term) risk premium. However, no sane market participant is willing to make public what they consider to be the evolution of their policy rate forecast, so we cannot determine what “market forecast” is. Can we have economist forecasts, but these economists as a group have no contribution to the positioning of market participants. FOMC forecasts seem reasonable to use if one takes DSGE models’ use of expectations seriously, but that requires believing that market participants believe the FOMC forecasts (and I see no evidence that they do it). Rate formation does not work as expected from DSGE models.

Term premium: what is it?

In chapter 3 of my book Breakeven inflation analysis, I examine the distinction between “forecasts” and “expectations” and how “risk premiums” fit into the topic. (I had a brief discussion on the subject in chapter 4 of Interest Rate Cycles: An Introduction, but it’s missing some of the concepts covered in the other book.)

If we look at academia, they think that risk premia are the result of affine term structure models, which you need to know stochastic calculus to understand. Since these models involve a lot of complex mathematics and can vary in many ways, there are an infinite number of papers to publish on the subject. As such, this is a “sophisticated” approach to the term premium, because my preferred way of thinking about the term premium implies that there isn’t much room to publish new articles academics.

If you trade bonds, the break-even point of your positions is relative to raw forward rates, i.e. your gains do not incorporate any risk premium (“risk-neutral expectations”). As such, you cannot ignore raw forecasts, no matter how much Ivy League-educated economists think you are in favor of it. That said, you should be aware that there is a risk premium: bonds have historically outperformed cash (although you have to use long enough histories to rule out the recent debacle).

I don’t want to repeat what I’ve already written, but I’ll just explain how to start thinking about the problem. Rather than tackling the thorny problem of the 10-year, why not ask: what is the term premium for 6-month Treasury bonds compared to 3-month ones? (You don’t want to compare day to day since Fed Funds or repo are not the same instruments, the “instrument spread” may be larger than plausible estimates of term premiums.)

If you can get good data, you should find that the 6 month appears to have a yield (term) premium built into it that generally leads it to outperform over time – except when it doesn’t. Large gaps in relative performance occur when the market is wrong about the movement of the key rate.

To the extent that there is a “steady state” risk premium, we should probably leave aside episodes where the market was badly wrong and then look at relative performance as rates moved. roughly as expected. For a six-month instrument, our databases allow us to judge performance over a large number of non-overlapping periods during these “unmissed” periods.

And the 10 years? These large deviations in forecasts are typically 10 years or less apart, and we do not have a long history of non-overlapping 10-year periods where bond yields were unregulated and there was a freely floating currency. Although we can test theories about a six-month premium, we have no data to confirm or refute any theory about the 10-year yield. (This could change around 2150 or so.)