On its global economic forum for April 17, Morgan Stanley is gushing about “green shoots” and improvement in the second derivative of GDP (we added the emphasis):

“Our latest global economic forecasts and our bull/base/bear scenarios for output, inflation and policy rates have left our main thesis intact, but show quite clearly where the risks to the main macroeconomic indicators lie going forward. In a nutshell, we continue to expect global growth to resume in 2H09 but warn our readers that any recovery will likely be anaemic. We see some ‘green shoots’ in the survey measures, with improvements in the Ifo and the ISM for the last three months along with a significant improvement in the second derivative of GDP. Further, we expect that the drop in global inflation and deflation in most of the G10 and much of Asia will likely be temporary and mild inflation will make a return to both these regions in 2010.”

The idea that the SECOND derivative of GDP is important stems from the “advance knowledge” it gives us about where the FIRST derivative – that is, growth in GDP will fall in the next quarter or two.   Indeed there are beau coup recent references across the net to the improving second derivative as a “supposed” justification for bidding stocks up from their low levels.  However, it should be obvious that the same “green shoots” that lead one forecaster to raise his economic forecast for 3rd quarter 2009 from (say) -.05 to -.04 (like Roubini) could lead another forecaster to raise his (like the FED) from +.01 to +.02 for the same quarter.  Clearly the future level of GDP growth is much more important … and difficult to forecast than examining a few “green shoots”.

It is often said that stock prices forecast GDP about 2 quarters in advance. There is empirical evidence to support this.  In fact, our own research indicates the best fitting statistical relation between stock returns and real GDP growth is for GDP growth 2quarters ahead (rather than coincident or only one quarter ahead).  Our raw data was quarterly seasonally adjusted real GDP from the BEA and the monthly average level of the S&P for the last month of each quarter as provided by Robert Shiller, going back to II1947 from IV2008.  Here is a scatter plot of the gross return each quarter of the S&P versus two quarter ahead quarterly growth in real GDP:


The regression had an R squared = .0961 and the slope had a standard error = .4240.  The resulting regression equation was:

S&P gross return for current quarter = (forecast real GDP growth 2 quarters forward) x 2.1555  – 1.152

The practical implications of this result is that, if one can correctly forecast what the growth rate in GDP will be two periods from now, then we can determine whether the current return in the S&P is warranted by the model. Below is a table for a few values for forecast real GDP growth in third quarter 2009 (note the growth rates are gross, e.g. a forecast for -2% growth for a quarter is input as .98):

Real GDP growth
S&P gross
forecast III2009
return now
0.94 0.8737
0.96 0.9168
0.98 0.9599
1.00 1.003
1.02 1.0461
1.04 1.0892
1.06 1.1323

We think a -.04 forecast (.96) for third quarter 2009 is viable, and the model would indicate in that case that the stock market should end this quarter about 8.4% lower than when it began. And for what it’s worth, the model indicates that stock prices being 25% higher at the end of this quarter are not justified even with the most optimistic forecasts for real GDP growth, 2 quarters ahead.   However, wouldn’t it be nice if real GDP growth two quarters forward was the only variable investors needed to try to forecast to determine what to expect for a return on stocks?

The reality is that this relation “explains” less than 10% of the variation in the S&P.  So…even if we had PERFECT foresight -that is, even if we new EXACTLY how the “green shoots and second derivatives”  would affect what GDP growth will be 2 quarters from now, we could “predict” stock returns correctly only 10% of the time by referring to real GDP.  What’s the bottom line?  Examining those “green shoots and second derivatives” may make interesting fodder for CNBC but it won’t do much good in predicting stock returns.