*By Stanislaw Zarzycki and Kenneth C Marshall*

**CORRELATION OF STOCKS TO GDP**

There has been a significant amount of research done on the lack of correlation between changes in GDP and forward looking changes in the stock market. A study published by Vontobel Asset Management on the relationship between GDP and stock market returns concluded that there is no relationship and in fact the relationship between GDP/Capital and equity returns was negative.

Just to confirm the results I conducted my own research over the period of 1950-2012. We calculated the correlation between quarterly GDP changes and subsequent equity (S&P 500 Index) quarterly returns. Not surprisingly the results were similar to previous studies - the correlation was 0.05 which is significantly no different from zero, concluding that GDP has no predictive power for future stock market returns.

Why is that, one might ask? There are many hypothetical explanations to this fact. They range from the fact the stock market does not reflect the full economy - the GDP represents companies' revenues but not corporate profits; corporate profits can be earned outside the company's listed country; and closing with the fact the government released GDP is only an estimate. I believe the best explanation is that the markets are efficient and that financial analysts' opinions and research already reflects the changes in GDP that occurred in the previous quarter.

**GDP CHANGES REFLECTED IN STOCK MARKET**

To test the last hypothesis we then proceeded to calculate the correlation between quarterly changes in GDP and quarterly changes in S&P 500 Index over the same time period. Interestingly enough the correlation coefficient turned out higher, 0.28. The correlation might seem low but in a sample of 250 observations it is statistically significant at the 99.95% level (p<0.005).

**GPD, STOCK MARKET AND THE ECONOMIC CYCLE**

Knowing that stocks already reflect the changes in the GDP, we wanted to find out if the stocks more or less closely follow the path of the GDP in any particular point in the cycle. In order to do so we split the GDP quarters based on the relative S&P 500 Index Shiller PE Ratio valuation metric. First we calculated the S&P 500 Index Shiller PE Ratio (price earnings ratio is based on average inflation-adjusted earnings from the previous 5 years, known as the Cyclically Adjusted PE Ratio (CAPE Ratio)). Secondly we ranked the PE ratio for each quarter based on relative valuation compared to the previous 10 years on a scale from 0-100, where 0 corresponds to lowest PE (most undervalued - market bottoms) and 100 corresponds to highest PE (most overvalued - market tops). Lastly we divided the S&P 500 Index PE valuation data points into quarters (0-25, 25-50, 50-75 and 75-100) in order to distinguish between the parts of the market cycle based on valuations. What we found was that while the overall correlation of GDP changes to S&P 500 Index changes over the same quarter is 0.28, the correlation varies significantly based on where we are in the market cycle:

When the market is bottoming out (PE Ratio rank 0-25), the correlation of GDP to stocks increases as investors look for signs of market improvement via changes in GDP numbers which is what one could reasonable expect. The interesting observation is that the correlation during market tops goes slightly negative. One explanation for that might be that at market tops corporate revenues are high causing the GDP numbers to be inflated. However, the corporate profits are on the decline due to increased competition in the markets causing a disconnect between the stock market returns and GDP changes.

**CONCLUSION**

Based on the above observations it could be deducted that the changes in correlation between the stock market and GDP used in conjunction with market valuations (S&P 500 Index Schiller PE ratio) can be used to confirm market tops and bottoms. Not only does the analysis has statistical validity but also possesses fundamental explanation.

**CURRENT OUTLOOK**

Knowing that changes in correlation between GDP and stock market around the market tops and bottoms can be used as confirmation signs for the regular valuation metric, one should look at the current state of affairs. As of April 1st, 2013, the S&P 500 Index Schiller PE ratio was 23.51 which relative to the last five years correspond to a rank of 100 (overvalued). Knowing that, one should closely track of the correlation of GDP changes in 2013 to the changes in the S&P 500 Index. If one sees the stock market decline while the GDP increases it could be a warning sign of a market reversal.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.