Time to buy stocks

Two months ago we revisited our model of the S&P 500 returns where the driving force of the stock market is real GDP.  This quantitative model predicted a negative correction of the S&P 500 level in 2011. As an alternative, we suggested that the Bureau of Economic Analysis could revise its real GDP estimates up. However, the BEA revised the GDP estimates significantly down for the years after 2005. As a consequence of this revision, all empirical coefficients in our model have to be re-estimated. Accordingly, the difference between the predicted and observed level of S&P 500 has to change.
Here, we update our model with the revised GDP estimates and include the advance GDP estimate for the second quarter of 2011.  The monthly closing prices through July 2011 are used. As discussed in our working paper on the S&P 500 index, there exists a trade-off between the growth rate of real GDP, G(t),  and the S&P 500 return, R(t). The predicted returns, Rp(t), can be obtained from the following relationship:
Rp(t) = 0.0054dlnG(t) - 0.03   (1) 
where G(t) is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA.  In our previous model the slope was slightly larger (0.0064) and the intercept did not change.  
Figure 1 displays the observed S&P 500 returns and those obtained using real GDP. As before, the observed returns are MA(12) of the monthly returns. For the predicted curve, we use the same GDP value for all three months in a give quarter.  Figure 2 displays the predicted curve smoothed by MA(4). This smoothed line stresses the mid-term deviation between the curves. 
The period after 2003 is relatively well predicted. The updated GDP estimates highlighted two strong deviations from the observed trajectory started in November 2009 and October 2010. During the first excursion, the predicted curve returned to the observed one in May 2010. One might speculate that this excursion was caused by the first quantitative easing. In any case it was a transitory deviation. 
The current deviation may have the same transitory nature but it is not over yet. In June, we expected this deviation to disappear in 2011. For the current estimates of real GDP, the level of S&P 500 has to be around 1250 in October 2011 in order to intercept the predicted line (see red diamond in Figure 2). Currently, the S&P 500 is below 1200 (the fall we forecasted in June) and thus one could buy stocks. However, the long-term growth does not exclude short-term falls due to the extremely high volatility of the stock market and one can wait for a deeper local trough. 

Figure 1. The observed S&P 500 returns and that predicted from real GDP. For a given quarter, all monthly values of the GDP growth rate are equal.

Figure 2. The predicted curve is smoothed by MA(4). The S&P return prediction for the next three months is shown by red diamonds.

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