The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. To obtain a prediction we use the number of three-year-olds, N3, as a proxy to N9 at a six-year horizon:
Rp(t+6) = 100dlnN3(t) - 0.23
where Rp(t+6)is the S&P 500 return at a six-year horizon. Because of the properties of the N3 distribution one can replace it with linear trends for the period between 2008 and 2011, as Figure 1 shows. The model shown in Figure 1 predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. (Correction from the previous post where 46 points per months was used by mistake.) In June, actual closing level was 1030 (-60 relative to May 2010). This level is about 90 points below that predicted in Figure 1. This is the continuation of the May’s panic. Such dynamic "overshoot" in the beginning of a new trend is a common feature.
Figure 1. 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 deviation from the new trend is a big one and one can expect the end of panic in July/August 2010. This is a nice feature of the trend. Any deviation, whatever amplitude it has, must return to the trend. So, by the past experience we may judge that 90 points should be compensated quickly. This means that the level of S&P 500 should not change much in July and August 2010. We would expect the close level between 1020 and 1050 in July 2010.
Then, the index will continue gradual decrease into 2011. Figure 2 demonstrates that the S&P 500 annual return will sink below zero in the third-fourth quarter of 2010.
Figure 2. Observed and predicted S&P 500 returns.