We have been following the link between the S&P 500 and real GDP
since 2008, when the first
version of our S&P 500 quantitative model
was published. We revisit our prediction on a regular basis and calculate a new
forecast. Last time, we discussed the model on February
5, 2012 and reported a good prediction for the prior period. Here, we update
our model with the revised GDP estimates and include the advance GDP estimate
for the third quarter of 2012. The monthly
closing prices through September 2012 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,*R*can be obtained from the following relationship:_{p}(t),*R*(1)

_{p}(t) = 0.0054dlnG(t) - 0.03
where

*G(t)*is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA. Figure 1 compares the observed and predicted returns through September 2012. The third quarter of 2012 is characterized by a rapid rise in the level of the S&P 500 index and its returns over the previous 12 months. The real GDP estimate for the third quarter will be available in approximately two weeks, but one may estimate this value from the S&P 500 returns using (1). Three red diamonds in Figure 1 represent the predicted growth in the returns for the (annualized) GDP growth rate of 4%.
Therefore, the stock market index
indicates the growth rate of real GDP above the consensus estimate for the
third quarter. Our estimate is
also supported by the fall in the rate of unemployment to 7.8% in September
from 8.1% in August, which corresponds to the GDP growth rate above 3% per year.

Figure
1. The predicted and observed S&P 500 return. The predicted curve is smoothed by MA(4). The 12-month
S&P return observed during the third quarter of 2012 implies the real GDP
growth rate of 4%.

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