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Reader David Zaitzeff, a futures broker at Peregrine Financial Group, Inc., suggests:
"How about the T-bond yield minus T-bill yield as a stock market indicator? The wider the spread between these yields, the more likely we are to have significant economic and earnings growth. A narrow spread, or a negative spread, means increased possibility of slowdown or recession."
Since David's hypothesis involves changes in the economy, we consider the implications of this yield spread over periods of months rather than days or weeks. Specifically, is the spread between the yield on the 10-year Treasury note (T-note) and the yield on the 90-day Treasury bill (T-bill) predictive of future S&P 500 index returns over the next 63, 126 and 252 trading days (three, six and 12 months)? Using data over the period 1/1/90-11/20/06, we find that:
The following chart depicts the general behavior of the S&P 500 index and the T-note/T-bill yield spread during the period examined. Visual inspection suggests that stocks and the yield spread may tend to move in opposite directions. When stocks rise (fall), the yield spread tends to contract (expand). The Pearson correlation for these two series is -0.45, supporting that observation. The spread is currently inverted, with the T-bill yield higher than the T-note yield, as it last was in late 2000.
To examine the potential value of the T-note/T-bill yield spread as a stock market indicator (whether it relates to changes in the S&P 500 index), we start with daily yield data to capture fine variations in the yield spread. However, daily data can mislead in terms of sample size and reliability of results because the stock return intervals overlap considerably from day to day and therefore are not independent observations. Also, the T-note/T-bill yield spread generally varies slowly, suggesting substantial serial correlation from day to day.
The following scatter plot depicts the relationship between the return on the S&P 500 index over the next 63 trading days (three months) and the difference in the daily closing yields for the T-note and the T-bill. The Pearson correlation for these two series is a slightly negative -0.08, suggesting very weakly that three-month stock returns might tend to decline slightly as the T-note/T-bill yield spread increases. However, the number of independent data points is only moderate.
The next scatter plot depicts the relationship between the return on the S&P 500 index over the next 126 trading days (six months) and the difference in the daily closing yields for the T-note and the T-bill. The Pearson correlation for these two series is a slightly negative -0.08, again suggesting very weakly that six-month stock returns might tend to decline slightly as the T-note/T-bill yield spread increases. However, the number of independent data points is small.
The next scatter plot depicts the relationship between the return on the S&P 500 index over the next 252 trading days (12 months) and the difference in the daily closing yields for the T-note and the T-bill. The Pearson correlation for these two series is -0.03, suggesting that 12-month stock returns are unrelated to the T-note/T-bill yield spread. The number of independent data points in this case is very small.
After reviewing the above charts, David further asks:
"It seems that when the T-bill yield is higher than the T-note yield, the S&P 500 index has no instances of a positive return after either six months or one year. Also, when the yields are inverted, negative three-month returns on the S&P 500 index appear to outnumber positive returns by about 5:1. Don't these charts indicate that yield curve inversion is useful for predicting stock market returns?"
Note that all of the inversion points on the longer-term charts come from a six-month period spanning 7/00-1/01. These points arguably represent in aggregate one independent data point for both these longer return intervals. Inference from one data point is, of course, unreasonable. For the 3-month return chart, all of the inversion data points with negative returns come from this same period. One might argue that these points represent in aggregate two independent observations for this shorter return interval. Note also for the 3-month return chart that there are a few inversion data points with positive returns. All of these points come from August 2006, the beginning of the current inversion period. This positive cluster represents one additional clearly independent observation. If we continue tracking this data over the coming weeks, with the market at or near current levels, more and more positive-return daily data points would appear. Again, however, inference from two or three independent observations is unreasonable.
To amplify the preceding discussion, we construct alternative scatter plots using quarterly, semiannual and annual sample intervals for the yield variables, as follows:
The following scatter plot depicts the relationship between the return on the S&P 500 index over the next three months (63 trading days) and the difference in the closing yields for the T-note and the T-bill on the first trading day of each calendar quarter (sample size 67). The Pearson correlation for these two series is a slightly negative -0.06, indicating very weakly that three-month stock returns might tend to decline slightly as the T-note/T-bill yield spread increases.
The next scatter plot depicts the relationship between the return on the S&P 500 index over the next six months (126 trading days) and the difference in the closing yields for the T-note and the T-bill on the first trading day of each calendar half-year (sample size only 33). The Pearson correlation for these two series is a slightly negative -0.1, indicating very weakly that six-month stock returns might tend to decline slightly as the T-note/T-bill yield spread increases.
The last scatter plot depicts the relationship between the return on the S&P 500 index over the next 12 months (252 trading days) and the difference in the closing yields for the T-note and the T-bill on the first trading day of each calendar year (sample size only 16). The Pearson correlation for these two series is -0.07, suggesting very weakly the possibility that 12-month stock might decline slightly as the T-note/T-bill yield spread increases. However, sample size is so small that inference is problematic.
In summary, the T-note/T-bill yield spread does not appear to be a useful indicator of future stock returns.
Given the frequency of yield inversions in this data (two in 17 years), a sample of a few hundred years of similar data would be needed to generate reasonably reliable statistics on stock market performance following periods of T-note/T-bill yield inversion. However, the comparability of data across generations is questionable due to evolution of the investing environment (laws, regulations, investing vehicles, wealth, technology).
For research on other potential economic indicators of stock market behavior, see Blog Synthesis: The Economy and the Stock Market.
