# Should the “Anxious Index” Make Investors Anxious?

May 2, 2013 • **Posted in** Economic Indicators, Investing Expertise

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 U.S. economic recession during each of the next four quarters. The “Anxious Index” is the probability of recession during 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 first quarter of 2013 (179 surveys), *we find that:*

The following chart compares the behaviors of the S&P 500 Index (logarithmic scale) and the Anxious Index (forecasted probability of recession during the next quarter) over the available sample period. The average value of the Anxious Index is 20%. Visual inspection suggests that peaks in the Anxious Index correspond to troughs in the S&P 500 Index, but does not clearly indicate which series leads.

For greater precision, we relate the Anxious Index to stock market returns.

The following scatter plot relates the forecasted probability of recession for the next quarter to the S&P 500 Index return over that same quarter since survey inception. The Pearson correlation for the relationship is -0.01 and the R-squared statistic is 0.000, 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 late 1990), the correlation is 0.01. For the second half of the sample, the correlation is -0.03.

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 ranked fifth (quintile) of forecasted probability of recession for the same quarter over the entire sample period, with one standard deviation variability ranges. Quintile size is 35-36 observations. Lack of systematic progression in average returns across quintiles confirms the low correlation above and undermines belief in any exploitable relationship. Results do suggest that stock market volatility increases with forecasted probability of recession.

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 beyond the next quarter are mostly a little positive, indicating that predicted probabilities of recession for these quarters are slightly (probably not exploitably) contrarian for future stock market returns.

In summary, *evidence from simple tests suggest that the “Anxious Index” from the Survey of Professional Forecasters is probably not a useful 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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