I received the following chart from a broker earlier this week. It plots the trailing 12-month price return on the US stock market versus a survey of activity in the US manufacturing sector, where a score above 50 indicates expansion and vice versa.

The broker’s conclusion was straight-forward, “if you get the business cycle right…you get the stock market right”. Simple.

Simple, but hugely problematic. For two main reasons:

**Forecasting the past**

First, the chart plots backward-looking 12 month returns versus a level of current activity. Surely it is future returns we are interested in? The stock market is both a predictor and determinant of future economic activity. It moves in anticipation of future booms or recessions, while large market moves influence saving and investment decisions taken by companies and households.

So, in the relationship plotted here, past stock market returns are predicting future economic activity, the reverse of the causality inferred by the broker. A positive relationship as depicted in the chart should come as no surprise. *Causality between the stock market and economic conditions runs both ways*.

**Choosing the right time**

Second, the chart is constructed starting in 2000. Why so, when data exists going back to 1948? Perhaps it is because of the tighter series fit in the more recent period. But this supposes some reason for assuming a structural break in the data. Should we?

If we include all the data going back to the start of the series, the correlation is weaker. Sample selection is of fundamental importance to any statistical analysis and its relevance.

If we try to look at the relationship between *today’s* level of the US ISM Manufacturing index and *future* returns on the S&P 500 using the entire sample of data available, the relationship between them appears, to all intents and purposes, to be non-existent (R^{2} of 0.08).

With the caveat that there have been only a few such instances, the one apparent relationship is that very low ISM manufacturing readings (sub 40, i.e. deep recession) have been associated with better-than-average *future* stock market gains.

The discussion so far should probably satisfy us that we can dismiss the notion that Figure 1 is helpful in predicting future stock market returns. But what if you are still not convinced!

**What if we could predict the cycle?**

For the chart to be relevant, it supposes that we are able to predict future economic outcomes, a very heroic assumption. But let’s suppose we can, what does the data tell us about what to expect from the stock market?

I used the entire post-1948 dataset to run a linear regression of US stock market price returns against deviations in the ISM manufacturing index from 50 (the expansion/contraction threshold). The coefficient on the ISM is statistically significant, as is the intercept, and suggests an expected price return of 6.3% plus/minus 0.9% for every 1 point deviation in the ISM index above/below 50 for the individual month, 12 months hence.

Notwithstanding the significant problem of overlapping data points and the validity of the distribution I have imposed on the data, how tight is the correlation and how much faith can we have in the estimate? The answer is very little. Assuming we can predict the level of the ISM 12 months hence (good luck!), the predictive power of the regression is very limited because the standard errors are large. For example, take a given level of the ISM of 50. For all the months the 50 level is observed on the ISM, we should expect half of the trailing price return outcomes to have been in the range of -3% to +16% and half the observations to have been outside of this range.

Hardly a very helpful conclusion from a statistical perspective. And for the reasons already outlined above, clearly a misguided analysis from a theoretical and economic perspective. So next time you are presented with an alluring chart, beware!