Michael T. Kiley published an interesting term premium paper “Why Have Long-term Treasury Yields Fallen Since the 1980s? Expected Short Rates and Term Premiums in (Quasi-) Real Time.” *(OK, it’s interesting for those of us who read term premium papers.)*

I am currently on a trip and am not in a position to dig too deeply into the paper, but it discusses the implications of some of the academic term premium modelling strategies.

## Term Premium

I have written fairly extensively about the term premium elsewhere, but I will give a minimal potted summary of the concept here. We can take U.S. Treasury prices and back out an implied risk-free yield curve. This curve can be expressed in a number of equivalent ways — either as a curve of zero coupon Treasury yields (or discount rates/factors) or an implied forward curve. This curve is what you are trading against when taking positions. In option pricing theory, the forward curve variant represents the risk-neutral expected path of the overnight rate.

Since this is what you are trading against, this forward rate path represents the hurdle rate for bets about the path of the overnight rate (which most duration bets represent). However, traders have picked up an empirical regularity that has been around since the dawn of money market trading — long-duration bonds tend to outperform short duration ones. This implies that there is a risk premium — the term premium — that results in the observed forward rates having an upwards bias versus the realised path “most of the time” (except in rather painful bond bear markets). Estimating the average term premium for bonds of 10+ year maturities is difficult due to the low number of non-overlapping intervals in the historical data set in the era of non-regulated interest rates. *(The excess return over cash of a 10-year issued in 1995 is highly correlated to the excess return over cash of a 10-year issued in 1996.)*

In a sensible world, that would be the end of the discussion. But academia is not sensible, and academics need to produce articles — whether or not the articles add any value for non-academics. Since it is possible to come up with a great many models for the term premium, that is exactly what academics have done.

## Kiley Paper

Returning to the Kiley paper, he points out an interesting defect in certain classes of term premium models. The models need to have an “average” overnight rate that the overnight rate is assumed to revert to in its stochastic model. What certain papers have done is to take the average of the overnight rate over the entire modelling period (e.g., 1980-present).

This has the entirely predictable outcome that the model is effectively aware of the secular decline of interest rates from 1980-present, and thus the expected path of the overnight rate resembles what actually happened — it was allegedly expected to fall. This is contradiction to the yield curve, which shows recency/normalcy bias — the short rate is generally priced to revert to the recent cycle average. *(If the central bank cuts rates in a recession, the market prices hikes, and it tends to price cuts once the cycle has advanced to a recessionary state, which historically happened near the peaks in the policy rate.) *The divergence between market pricing and the model “expectations” implies that the term premium had to be quite high back in the era of high yields.

Although the results might be plausible in retrospect — bonds greatly outperformed cash since the early 1980s — real world bond investors certainly did not expect the secular decline in yields based on expressed sentiments.

Kiley then looked at what happens if you do not allow future data to pollute your model estimation algorithms. As one would expect, there was much less of a secular decline in the term premium, since there is no downward bias to expectations created by the future data. That is, the fall in rate expectations explains most of the fall in yields.

## Comments

I am currently not in a position to dig into this topic. However, it does suggest that if one looks at other term premium estimation papers, one needs to look at the rate reversion dynamics, and whether there is a reversion to a long-term average that can pollute the historical fitting. (The few papers I spent some time were based off of economist surveys for determining expectations, which posed other issues.)

This issue also highlights the importance of never letting future data pollute model fitting. The only time where it is acceptable to use the full set of data within algorithms is when is doing a descriptive analysis of a fixed historical period that terminates long before the present. Otherwise, calculated time series should only use data that are available up until the calculated time point. It should surprise nobody that a time series that is calculated based on future values will have predictive properties.

Another idea that the paper highlights is that we need to evaluate claims based on term premium models based on large changes in yields. If someone says that a 50 basis point rise in the 10-year yields is due to the term premium rising by 25 basis points and expectations rising by 25 basis points, the claim contains almost no useful information that can be evaluated. The 10-year yield can jump 25 basis points on a bad day due to a data print, so how meaningful is a 25 basis point change in a hidden variable that economists steadfastly refuse to measure properly? *(The only way one might get a useful term premium estimate is to survey dealers and large investors as to what they believe the term premium is. Of course, this probably will not work as large investors are not going to cooperate, and they would just have some intern economist build them a term premium model and have them read off the model results when the survey arrives.) *We need to look at chunky changes in yields, and see what the model results look like.

Kiley’s results also indicate the importance of looking at the front end term premiums. These premiums would be less effected by the use of reversion to historical averages. Nobody really has strongly-held views on the expected path of short rates over the next 10 years. At best, one has a view as to what the long-term average rate would be, and it becomes a purely semantic issue as to whether deviations from that average is due to pressure on expectations as a result of structural economic/financial factors or a term premium. However, we can very easily calculate excess returns on risk-free bonds/bills with maturities under 2 years with many non-overlapping intervals. Although expectations can be obviously incorrect at cyclical turning points, excess returns are well-behaved most of the time (during the boring parts of the cycle). Does the term premium model plausibly align with that excess return experience? *(I ignore a lot of these models as this is not the case.) *If the front end term premium estimate is garbage, then longer premiums are in trouble based on construction.

## Concluding Remarks

I have launched a *jihad* against term premium models since they appear to me to be a classic bit of academic publishing papers for the sake of publishing papers. The concept has been unmoored from the reason the concept existed in the first place — what are the expected excess returns of long duration instruments over cash? *(Admittedly, the term premium estimates are very useful for central bankers — they use them to argue that the markets are not suggesting a policy error on their part, rather that term premiums are moving around. Since the models dump all the volatility onto the term premium, they can point to “anchored expectations” suggesting that central bankers are doing a great job.) *Assuming that the term premium is small and stable is the most useful perspective for fixed income valuation.

Nevertheless, the persistent inversion of the curve in the absence of a recession does raise questions. *(Although it is useful to deflating the yield curve maximalists’ claims about the usefulness of the yield curve in predicting recessions.)* Has there been a dumbing down of fixed income investors in recent years (coincidentally after I retired from markets)? Is there a recession waiting just around the corner? Or has there been a structural factor driving down long-term yields (like an increased interest in liability matching)? This recent behaviour is unusual enough that even I might be willing to expect a wackier term premium structure at present. That said, models that give a wacky term premium structure now are very likely to suggest that it has been wacky during eras when market pricing looked quite sensible based on available information at the time.

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