Good news from August 2010 is that the S&P 500 market index is back on the track predicted couple years ago. Figures 1 and 2 update the previous versions published on Seeking Alpha in August with the closing level of ~1050 reported on August 31. Both predicted curves are very close to the observed ones over the whole period between March 2009 and August 2010. This prediction would have been a convincing one for everybody except market players who do believe that stock prices are unpredictable.
So, we will continue tracking the level of S&P 500 and its returns. The next move is likely below the trend to compensate for a short positive excursion in July 2010. This might be a drop by 40 to 80 points, likely to the level below 1000. It might be accompanied by a small panic. However, a positive jerk associated with local positive news is not excluded but it should not be high in amplitude.
Our concern about possible repetition of the 1987 fall, if the index would continue its deviation from the predicted trend into October 2010, has been resolved by the drop of around 50 points from the July’s level of 1101. So, there is no danger of a severe panic on the stock market.
Below we repeat a mandatory part with a bit of mathematics for the readers interested in details of our excellent (in terms of predictive power) model. The model is also presented in our working paper  and monograph .
The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. In order to extend the prediction in time we use the number of three-year-olds, N3, as a proxy to N9 and obtain a forecast at a six-year horizon:
Rp(t+6) = 100dlnN3(t) - 0.23 (1)
where Rp(t+6) is the S&P 500 return six years ahead (in 2010 one can foresee the returns in 2016). Figure 1 depicts germane S&P 500 returns, both actual one and that predicted by relationship (1). Both curves are coinciding in practical terms.
Because of the observed linear growth in N3 one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.
Figure 1. Observed and predicted S&P 500 returns. The last point for the observed series is August 2010.
Figure 2. Observed S&P 500 monthly close level and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010. The last point in the observed series is August 2010. All in all, the S&P 500 is back on the predicted trend.