Should the “Anxious Index” Make Investors Anxious?

Since 1990, the Federal Reserve Bank of Philadelphia has conducted a quarterly Survey of Professional Forecasters. The American Statistical Association and the National Bureau of Economic Research conducted the survey from 1968-1989. Among other things, the survey solicits from experts on the economy the probabilities of recession for each of the next four quarters. The “Anxious Index” is the probability of recession in the next quarter. When professional forecasters are relatively pessimistic (optimistic) about the economy, does the stock market go down (up) over the coming quarters? Using survey results and quarterly S&P 500 Index data from the fourth quarter of 1968 through the second quarter of 2011 (171 surveys), we find that:

The following scatter plot relates the forecasted probability of recession for the next quarter to the change in the S&P 500 Index over that same quarter since survey inception. The Pearson correlation for the relationship is 0.03 and the R-squared statistic is 0.00, indicating that forecasted probability of recession for a quarter explains none of the stock market return for that quarter.

For the first half of the sample (late 1968 through early 1990), the correlation is 0.09. For the second half of the sample, the correlation is -0.05.

Might there be an exploitable non-linear relationship between forecasted probability of recession and future stock market return?

The next chart summarizes the average quarterly return for the S&P 500 Index by quintile of the forecasted probability of recession for the same quarter over the entire sample period. Quintile size is 34 observations. Results suggest that extremely high (above 30%) and low (below 7%) forecasted probabilities of recession may indicate a relatively weak stock market, with moderate probabilities (11%-17%) indicating a relatively strong stock market.

Are there any useful relationships between forecasted probabilities of recession and stock returns over different intervals?

The final chart summarizes relationships between forecasted probabilities of recession and S&P 500 index returns over the entire sample period for different forecast horizons and different lead-lag relationships. Specifically, it plots the correlations for different combinations of:

• Recession probability forecasts for 3, 6, 9 and 12 months into the future.
• S&P 500 Index returns for 3, 6, 9 and 12 months back into the past and 3, 6, 9 and 12 months forward into the future.

There are notable negative correlations between forecasted probabilities of recession for the next 3, 6 and 9 months and past S&P 500 index returns. If the stock market has been rising (falling), forecasts of the probability of recession for the next three quarters tend to be lower (higher). In other words, forecasters seem to regard the past behavior of stocks as predictive for the economy over the next few quarters.

Correlations between forecasted probabilities of recession and future S&P 500 index returns are all a little positive, indicating that predicted probabilities of recession for quarters during the coming year are mildly (probably not exploitably) contrarian for future stock market returns.

In summary, evidence from simple tests suggest the “Anxious Index” from the Survey of Professional Forecasters is a mildly (not materially) contrarian indicator of future U.S. stock market behavior.

Cautions regarding findings include:

• Analyses are in-sample. An investor operating in real time may have drawn different conclusions based purely on inception-to-date data.
• Quintile sample sizes are fairly small for reliable inference.
• Results may be different for stock market returns measured over quarters between forecast releases (about the middle of calendar quarters) instead of the subsequent calendar quarters.
• Simple stock market reversion may account for any relationship between forecasted probability of recession and future returns.

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