December 7, 2006 - T-bill/T-note Yield Flattenings and Bear Markets
After reading our blog entry of 11/24/06 on the usefulness of the spread between the yield on the 10-year Treasury note (T-note) and the yield on the 90-day Treasury bill (T-bill) as a signal for future S&P 500 index returns, reader and newsletter editor Jack Schannep sent a longer-term analysis of the relationships between yield curve flattenings and recessions/bear markets. He concludes that a flattening or inverted yield curve points to a bear market and recession. To take a closer look, we examine here the relationships between onsets of yield curve flattenings/inversions, as indicated by the relationship between the T-bill yield and the T-note yield, and: (1) onsets of bear markets; and, (2) stock returns over the next 3, 6 and 12 months. We find that:
To tackle this question, we use monthly data as follows:
Monthly yields since April 1953 for T-notes and T-bills come from the Federal Reserve Bank of St. Louis. The T-note yield data, available only since April 1953, is limiting for sample duration. Other measures of yield inversion are feasible but not strictly comparable. Inversion means that the T-bill yield exceeds the T-note yield. Flattening, as a potential early warning of inversion suggested by Jack, means that the T-bill yield is at least 95% (rounded) of the T-note yield.
Bear market onsets for 1900-2005 come from the "GFD Guide to Bull and Bear Markets (Worksheet)" for the S&P 500 index. Definitions of bull and bear markets vary somewhat by source. This source is readily available for review by readers.
Business cycle reference dates (onsets of recessions) for 1953-2005 come from the National Bureau of Economic Research. We omit the recession starting in July 1953 because potentially matching data for yield curve behavior is unavailable before April 1953.
Monthly S&P 500 index data to calculate stock returns since April 1953 comes from Yahoo! Finance.
One problem in determining relationship among these economic variables is that they have different numbers of occurrences in the sample. Omitting the July 1953 recession, there are: 9 recessions, 11 bear markets, 7 yield curve inversions (including the current one) and 11 yield curve flattenings (including the current one). We judgmentally align the onsets of various occurences, based on the number of months from the start of the sample, leaving gaps for some variables. What do we do with the gaps?
The number of occurences represent statistically very small samples for all the variables. Good theory can mitigate small sample size. The theory in this case might be that very wise Treasuries traders flatten/invert the yield curve when they foresee a recession, which means declining corporate earnings and a bear market. This theory is not good, in that some recessions occur without preceding inversions, some flattenings do not lead to recessions and some bear market occur without recessions. We ought therefore to be skeptical of the small samples, and we ought to penalize variables with gaps. We elect to penalize the gaps by filling them with the value of the nearest actual occurence. This approach is equivalent, for example, to viewing one yield curve inversion as related to more than one bear market.
We also generate three sets of 11 random numbers from 1 to 575 (the beginning of the sample to the start of the most recent recession in months). We order these random sets from lowest to highest for use in a crude confidence test of the real data.
The following table shows the data resulting from the above sources and assumptions, expressed in number of months since April 1953. The pink-shaded cells are gaps created by aligning variables with different numbers of occurrences. We fill these gaps with adjacent data as described above. Note that, while the Pearson correlations between yield curve flattening onsets and both bear market onsets and recession onsets are very high, so are the analogous correlations for the three random datasets.
The following scatter plot depicts the relationships between onsets of inverted and flattened yield curves and onsets of bear markets as listed in the above table. The relationship for flattening looks promising; that for inversion suffers from gap "penalties" as described above.
The next scatter plot depicts the relationships between the three ordered random number sets and onsets of bear markets as listed in the above table. The promising appearance of these three relationships emphasizes that the approach and data do not generate actionable information.
To dig deeper, we calculate the intervals in months between sequential occurences for all variables. Comparing intervals rather than raw sequences may reveal subtleties in relationships. Pink-shaded cells indicate intervals (or lack thereof) derived from the gap "penalties" described above. There are no compelling correlations among these sets of intervals. The wide range of correlations between the random data intervals and the bear market and recession intervals emphasizes the unreliability of these small samples
As a final test of the meaning of yield curve inversions/flattenings for stocks, we calculate the returns on the S&P 500 index 3, 6 and 12 months after onsets of both. The following table presents the average return, the number of advances (A) and declines (D) and the standard deviation of returns for both flattening and inversion onsets since April 1953. Results suggest that an inversion might be a bad sign for the stock market. However, confidence in this conclusion is very low because: (1) standard deviations are large compared to averages (noise swamps signal); and, (2) sample sizes are so small that just two or three future counter-instances might significantly change results
In summary, there may be some relationship between yield curve inversions/flattenings and future stock market behavior, but weak theory and small sample sizes drastically undermine confidence in predictability.
Other approaches to measuring the predictive value of yield curve inversions/flattenings are possible. However, the more one tweaks assumptions to produce a more convincing fit between yield curve behavior and the behavior of the economy or the stock market, the greater the risk that one has just stumbled upon a "lucky" dataset. With very small samples as in this analysis, such data dredging is unlikely to discover valuable predictive relationships.
For some related discussions, see the following:
In an entry in his blog, Mark Thoma (University of Oregon) speculates that yield curve inversion had a different meaning prior to World War II because of substantially lower inflation expectations. [In the 1930s, expectations may, in fact, have been for deflation, and an inverted yield curve would have been "normal."] He concludes that: "given the Fed's strong commitment to price stability, the possibility of an inverted yield curve does not seem as ominous."
In early 2006 Jonathan Wright of the Federal Reserve Board of Governors published "The Yield Curve and Predicting Recessions," in which he tests different ways of extracting information from yield spreads. He concludes that: "...[T]here is more information in the shape of the yield curve about the likely odds of a recession than that provided by the term spread alone. Probit models forecasting recessions that use both the level of the federal funds rate and the term spread give better in-sample fit, and better out-of-sample predictive performance, than models with the term spread alone. ...The shape of the yield curve that has historically been the strongest predictor of recessions involves an inverted yield curve with a high level of the nominal funds rate. Currently, the yield curve is flat, not owing to a historically high level of the federal funds rate, but rather, to a low level of distant-horizon forward rates due in turn to some combination of low inflation expectations, low expected equilibrium real rates, and/or low term premiums. ...While a probit model using the term spread alone predicts high odds of a recession in the next four quarters, the other probit models that I estimate, which all control for the level of the funds rate, do not. This gives formal empirical support to a view that has been widely expressed by commentators that the present flatness of the yield curve is a reflection of low term premiums rather than especially tight monetary policy, and this flatness accordingly does not seem to herald a sharp slowdown." He points out that the UK and Australia have done just fine economically with yield curves inverted for some time.
In an October 2006 article entitled "Looking at the Yield Curve: Time to Reconsider Stock Market Exposure?," Erik Dellith calculates stock returns nine months after onsets of yield curve inversion determined by 1-year and 10-year Treasury instrument yields.
In a November 24, 2006 "Letter" entitled "Is a Recession Imminent?," John Fernald and Bharat Trehan of the Federal Reserve Bank of San Francisco comment on the yield curve: "There is reason to be skeptical about the current high estimate of the probability of recession, because the unusually low rates at the long end of the yield curve are not well understood... [T]he recent behavior of long-term rates...argues for reducing the weight one places upon the term spread and relying upon other variables when making forecasts. ...[O]ur review of the available surveys, indicators, and model forecasts leads to estimates of the probability of recession that are all lower than the one based on the term spread and the yield curve. Furthermore, financial markets exhibit little evidence of distress: the Dow has hit record highs recently, and various risk spreads (such as the rate on corporate bonds relative to Treasuries) remain at low levels. Taken together with our inability to explain the unusually low level of long-term rates, this suggests to us that while the probability of recession might have gone up somewhat in recent months, it is not yet at worrisome levels."
Unfortunately for investors, there are many economic variables that offer only small samples of unusual, potentially predictive, levels. Better theories would mitigate the statistical weakness of small sample sizes. Pushing further and further back into historical data to extend sample size would also build confidence in results, but this mode of sample extension risks comparability of data. Relationships that hold under one set of financial/regulatory/technological conditions may not hold for another very different set.