The methodology is straightforward (I have a busy week, so I have not gathered the data to replicate it myself). They describe it as follows:
A better approach is to incorporate the FOMC’s projections of the Fed Funds Rate into the expected path of short rates. This will make term premia estimates more consistent with sub-2% growth. Figure 1 shows that model applied, with an expectation that the short rate matches the Fed Funds Rate over the next year, then it linearly converges to the long-run projection over the next three years, and then remains constant.
This matches my preferred structure for valuation models, which are based on the fair value for the 10-year being generated by calculating a projected path of short rates over the next 10 years. The fair value path needs to start near the current level, then move towards some steady state value over the “medium term” (2-5 years). This is needed to avoid the silliness of old school “bond value” models that economists used to generate where the current level of short rates has no effect on the fair value.
(Note that if you forecast a wildly different short rate path than what is embedded in such a model, you do not need a model to know how to position for duration. For example, if the model implies a gentle path of rate hikes while you expect a recession to prompt rate cuts, you do not need no stinkin’ model to know to go long duration.)
The issue is determining the steady state level; in the article, they use the FOMC long-term projections. The “term premium” is the deviation of observed market yields from fair value.
The general methodology is sound, my concern is whether it is a good idea to throw out market information and just assume that the FOMC is correct about the long-term path of interest rates. That is, if you have a long-term path for the policy rate that you have confidence in, deviations from that path do correspond to a risk (term) premium. However, no sensible market participant is willing to make public what they view as their forecast path for the policy rate, so we cannot determine what the “market forecast” is. We can get economist forecasts, but those economists as a group have zero input to market participants’ positioning. The FOMC forecast looks reasonable to use if one takes DSGE models’ use of expectations seriously, but doing so requires us to believe that market participants believe the FOMC’s forecasts (and I see no evidence that they do). Rate formation does not work as suggested by expectations in DSGE models.
Term Premium — What is It?
In Chapter 3 of my book Breakeven Inflation Analysis, I discuss the distinction between “forecasts” and “expectations” and how “risk premia” fit into the topic. (I had a brief discussion of the topic in Chapter 4 of Interest Rate Cycles: An Introduction, but it misses some of the concepts discussed in the other book.)
If we look at academia, they went the idea that risk premia are the output of affine term structure models, which you need to know stochastic calculus to understand. Since these models imply a lot of complicated mathematics and can be varied any number of ways, there is an infinite number of papers to publish on the topic. As such, this is the “sophisticated” approach to the term premium, as my preferred way of looking at the term premium implies that there is not much room to publish new academic papers.
If you are trading bonds, your breakeven on positions is versus the raw forward rates — that is, your pay offs embed no risk premium (“risk neutral expectations”). As such, you cannot ignore the raw forwards, no matter how unsophisticated Ivy League-educated economists think you are for doing so. That said, you need to know that there is a risk premium: bonds have historically outperformed cash (although you need to use sufficiently long histories to throw out the recent debacle).
I do not want to repeat what I already wrote, but I will just throw out how to start thinking about the problem. Rather than dealing with the thorny problem of the 10-year, why not ask: what is the term premium of the 6-month Treasury Bill versus the 3-month? (You don’t want to compare to the overnight since Fed Funds or repo are not the same instruments, the “instrument spread” can be larger than plausible term premia estimates.)
If you can get good data, you should see that the 6-month seems to embed a yield (term) premium that leads to it generally outperforming over time — except when it does not. The big deviations in relative performance occur when the market was wrong about the path of the policy rate.
To the extent that there is a “steady state” risk premium, we probably need to throw out those episodes of the market being severely wrong, and then looking at relative performance when rates evolved roughly as expected. For a six-month instrument, our databases allow us a large number of non-overlapping periods to judge performance during those “non-miss” periods.
What about the 10-year? Those big forecast misses are typically 10 or less years apart, and we do not have a long history of non-overlapping 10-year periods when bond yields were not regulated along with having a free-floating currency. Although we could test theories about a six-month term premium, we do not have data to confirm or deny any theory about the 10-year yield. (This might change around 2150 or so.)