Blog - Investing Notes

May 19, 2009 - The Probability of Recession and Future Stock Returns

A reader suggested:

"Political Calculations has a tool to 'reckon the odds of U.S. recession in the next 12 months' based on a formula developed by the Econobrowser from a paper entitled 'The Yield Curve and Predicting Recessions' by the Federal Reserve Board's Jonathan Wright. What about looking at it the other way in trying to gauge the odds of recovery using the tool? There is the obvious question of how do you define recovery, but it may be a useful exercise."

Focusing on the usefulness of this yield curve model for predicting a recovery in the stock market, we relate its outputs to future stock market returns. Using monthly values for the 10-year Treasury note yield, the 13-week Treasury bill (T-bill) yield, the Federal Funds Rate (FFR) and the S&P 500 index over the period January 1990 through April 2009 (232 months), we find that:

The following chart compares the behavior of the S&P 500 index and the Wright Model Probability of Recession (as calculated by the tool described above) over the entire sample period. The modeled probability of U.S. recession appears to peak roughly with the U.S. stock market, but the peaks are of different heights. The troughs in probability are extended, and they appear to start well before stock market bottoms.

Does the modeled probability of recession have stock market timing value?

To check the value of the Wright Model Probability of Recession for stock market timing, we use two tests.

First, we calculate correlations between the probability of recession and future stock returns at horizons of 1, 3, 6, 9 and 12 months. A reasonable hypothesis is that the modeled probability of recession should relate negatively to future returns. In other words, a high (low) modeled probability of recession should relate to relatively low (high) future stock market returns.

In fact, however, using monthly data, the correlation between probability of recession and 1-month future S&P 500 index returns is an insignificant 0.03. For horizons of 3 / 6 / 9 / 12 months, the correlations based on monthly data are 0.02 / -0.01 / -0.06 / -0.10. For these longer horizons, there is considerable overlap in stock return calculation intervals, and overlap can distort correlations. Using modeled probability of recession at an annual frequency (each January) the correlation between probability of recession and 12-month future S&P 500 index returns is 0.02. These correlations do not support a belief in any relationship between modeled probability of recession and future stock returns. In other words, scaling allocation of assets to stocks based on the modeled probability of recession is probably not worthwhile.

Second, we test whether trading at specific extreme values of the modeled probability of recession would beat a buy-and-hold strategy. The next chart compares the cumulative return over the entire sample period of timed and passive $10,000 initial investments in the S&P 500 index made at the end of January 1990. The timed strategy exits stocks when the modeled probability of recession rises over 50% and re-enters stocks when the probability of recession returns to 0%. When out of stocks, the timed strategy earns the T-bill yield.

Since the series begins with the probability of recession over 50%, the timed strategy does not enter stocks until the end of January 1992. It subsequently exits stocks at the end of July 2000, re-enters stocks at the end of November 2001, exits at the end of February 2007 and re-enters at the end of April 2008. The cumulative values of the timed and buy-and-hold strategies are $34,237 and $26,523, respectively. Buy-and-hold leads for the first half of the sample, and the timed strategy leads for the second half. Other entry and exit thresholds produce different results.

This threshold test offers some evidence in support of timing based on the Wright Model Probability of Recession, but the number of trades (five) is so small that the test is not convincing. Extending the test period backward across additional recessions may generate more confident results (but older FFR targets can be squishy).

In summary, very limited evidence suggests that the Wright Model Probability of Recession may have some value for timing the U.S. stock market based on recession probability thresholds but no value based on systematic variation of the modeled probability of recession.

For related research, see Blog Synthesis: The Economy and the Stock Market.