Historical Treasury Term Premia: Huge!

This post is an illustration of the concepts discussed in my primer on the term premium. Although we do not really know what the term premium is at any particular time, historical excess returns over a long period of time should average out near the average term premium. However, those excess returns have been implausibly high. Why this matters: if we do not know what the term premium is, we cannot know what the Treasury bond curve is pricing for the Fed outlook.

In the chart below, I show the behaviour of the realised (historical) excess returns for the 5-year Treasury.

To explain the chart, in the top panel we see the 5-year Treasury yield versus the 5-year average of the effective Fed Funds rate for the following 5 years. Since FRED does not yet have a time machine option, the data for the average ends in 2008 (i.e., 5 years ago).

In the bottom panel, the “Realised Excess Return” is the 5-year bond yield minus the average fed funds rate depicted above. This is a fairly good approximation of the excess return of a buy-and-hold position in a 5-year bond entered into a particular date versus a cash investment.

For example, in October 2008 (the end point of my sample), the 5-year yield was 2.73%, while the realised average effective fed funds rate since then was 0.16%, generating an excess return of  2.57%.

The table below shows the average realised excess returns for various periods, for the 2-, 5-, and 10-year points on the Treasury Curve. (Charts for the 2-year and 10-year are at the bottom of this post.)

Maturity	Start Date of Data	Mean Excess Return
		Entire Dataset	Since 1980-01-01	Since 1990-01-01
2-year	1976	0.51%	0.80%	0.81%
5-year	1962	0.77%	1.95%	1.74%
10-year	1962	1.01%	3.02%	2.56%

The experience for the 5-year maturity is particularly interesting. The negative premia pre-1980 could be explained by the various regulations that led to “financial repression”: yields held below what market forces would suggest. Once the deregulation of interest rates was completed, the premium has not been significantly been negative. Although the disinflation post-1980 was a surprise, the disinflation was largely finished by 1990. The market did not catch on to this, and the 5-year yield was on average 1.74% above the realised fed funds rate since 1990. In my opinion, the historical premium appears outsized for the amount of price risk associated with a 5-year bond; for example it is about double 5-year investment grade spreads right now (using the CDX index). Such a persistent miss by the market is hard to explain if it is in fact efficient.

This makes it hard to calibrate a model for calculating the “true” expected path of interest rates after adjusting for a term premium. If we blindly applied the post-1990 premium to the current curve, the implied expected average fed funds rate over the next 5 years is around -0.25%. This does not appear very plausible.

This also messes up any models for the fair value of bond yields which are based on historical data. In the post-1990s sample, the whole bond curve exhibited a very large term premium (or else market forecasts were consistently terrible). Therefore you end up basing your model target upon a too-high yield. I believe that this was a common analysis error made for the past 30 years, which explains the persistence of the bull market (whereas excess returns should theoretically be a random walk).

In an upcoming post, I will turn to model-based approaches to calculating the term premium – affine curve models.

(c) Brian Romanchuk 2013