Forward Interest Rates

Forward interest rates have emerged as a bone of contention in the analysis of the proposed TransAlta preferred share exchange offer, so as part of the preparation for my promised weekend post, I’ll post a few links to some papers that illustrate why the Expectations Hypothesis cannot be used as a predictor.

Joseph R. Dziwura and Eric M. Green wrote a paper in 1996 for the New York Fed titled Interest Rate Expectations and the Shape of the Yield Curve:

According to the rational expectations hypothesis of the term structure (REHTS) long term rates should reflect market expectations for the average level of future short-term rates. The purpose of this paper is to examine whether REHTS assumptions conform to the term structure of outstanding U. S. Treasury securities from 1973 to 1995, and to examine the behavior of term premiums and to what extent they influence the shape of the forward curve. REHTS assumptions are re-examined using familiar regression tests to determine the forecast power of forward rates for subsequent spot rates, and we use excess holding period returns, the extra return earned on a security sold prior to maturity, as the ex poste measurement of the term premium. We find that forward rates explain only some of the variance in future spot rates, the forecast power of forward rates varies with maturity, and the term premia is time-varying. We decompose the forward rate into the current spot rate, a term premium, and an expected interest rate change, where the term premium is the sum of a risk premium and a convexity premium. We find that on average term premiums have contributed more to the shape of the forward curve than have expected rate changes, and find that expected and past interest rate volatility, as well as the slope of the yield curve, may provide information on the size of expected term premiums.

Another paper was by Massimo Guidolin and Daniel L. Thornton of the St. Louis Fed, titled Predictions of Short-Term Rates and the Expectations

Despite its role in monetary policy and finance, the expectations hypothesis (EH) of the term structure of interest rates has received virtually no empirical support. The empirical failure of the EH has been attributed to a variety of econometric biases associated with the single-equation models most often used to test it; however, none of these explanations appears to account for the massives [sic] failure reported in the literature. We note that traditional tests of the EH are based on two assumptions—the EH per se and an assumption about the expectations generating process (EGP) for the short-term rate. Arguing that convential [sic] tests of the EH could reject it because the EGP embedded in these tests is significantly at odds with the true EGP, we investigate this possibility by analyzing the out-of-sample predictive prefromance [sic] of several models for predicting interest rates and a model that assumes the EH holds. Using standard methods that take into account parameter uncertainty, the null hypothesis of equal predictive accuracy of each models relative to the random walk alternative is never rejected.

One may hope their work is more reliable than their proof-reading!

Intuitive Analytics is a financial software firm which has published a blog-post by Peter Orr titled 50 Years of UST Yields – How Well do Forwards Predict? that was exactly what I was looking for:

As we’ve written on these pages before, forecasting is a necessary evil in finance. It’s uncertain by nature and of course the longer the horizon, the more difficult the job. The theory that forward rates are good predictors of future realized rates is called the expectations hypothesis and as one MIT professor put it, “If the attractiveness of an economic hypothesis is measured by the number of papers which statistically reject it, the expectations theory of the term structure is a knockout.”

For fun (and to dust off my fast fading coding skills) I went back and looked at how US Treasury implied forward 10Y rates have done in forecasting realized 10Y UST yields from July, 1959 to the present. We used first of month data for 3, 6 and 12 month Tbills as zero rates (making the appropriate daycount adjustments of course) and then 2, 3, 5, 7, 10, 20, and 30-year UST coupon instruments for our implied 10Y forward calculations. And this is what we get…

Click for Big

The red line is the actual 10Y yield over the period and the “hair” is the implied 10Y par yield 1, 2, 3, and 5 years forward. The way to read this then is to look at how often the hair tracks with the actual realization of the 10Y yields as shown by the red line. In general, during this single big rate cycle we’ve seen over the last 50 years, forward rates have badly underpredicted when rates were going up (note the implied decreasing 10Y forwards during the 70s) and then overpredicted over the last 30 or so years as rates have fallen. How badly do forwards do? Well over this 50 year span, and this holds over most subperiods as well, you’d be better off as a forecaster just assuming today’s yield curve stays constant i.e. a perfectly random walk.

Update, 2024-1-18: See also Predictions of Short-Term Rates and the Expectations Hypothesis of the Term Structure of Interest Rates, Massimo Guidolin & Daniel L. Thornton:

Despite its important role in monetary policy and finance, the expectations hypothesis (EH) of the term structure of interest rates has received virtually no empirical support. The empirical failure of the EH was attributed to a variety of econometric biases associated with the single-equation models used to test it; however, none account for it. Moreover, Sarno, Valente, and Thornton (2006) find that the EH is readily rejected using more powerful multi-equation Lagrange Multiplier test developed by Bekaert and Hodrick (2001). The ubiquitous rejection of the EH raise the possibility that its failure is fundamental rather than econometric. This paper analyzes the EH by focusing on its fundamental tenet—the predictability of the short-term rate. This is done by comparing h-month ahead forecasts for the 1-month Treasury yield implied by the EH with the forecasts from random-walk, Diebold and Lei (2003), and Duffee (2002) models. The evidence suggests that the failure of the EH is likely a consequence of market participants’ inability to predict the short-term rate.

The evidence suggests that the theoretical forecasts implied by the EH do not differ appreciably from the random walk or term structure forecasts. Moreover, it is shown that, just as the EH implies, long-term rates reflect significant information about the markets’ expectation for the short-term rate. That is, to the extent that the market is able to forecast the future short-term rate, long-term rates reflect that information. The difficultly arises from the fact that the observed short-term rates are dominated by new information that appears to be difficult to forecast. For this reason, the spread between the long-term and short-term rate is a relatively poor predictor of the future short-term rate.

Hence, while the EH is fundamentally correct—longer-term rates incorporate the markets’ expectation for the future short-term rate—its usefulness for financial market analysts and policymakers is doubtful. Of course, policymakers targeting short-term interest rates might increase the predictability of the rate spread by making short-term rates more predictable. Indeed, some recent evidence (e.g., Lange, et al., 2003; Poole, et al., 2002; and Watson, 2002) indicates that the predictability of the federal funds rate has increased since the Fed began announcing its funds rate target in 1994.

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