We continue tracking the evolution of the S&P 500 and our prediction made in the beginning of 2009 for the next six years. Since March 2009, the prediction fits the observed S&P 500 with minor deviations likely related to the emotion component of the stock market. However, the trend and its turn in May 2010 were forecasted precisely. All in all, fifteen months in a raw we are right and do not see any source which may disturb our prediction for the period between June 2010 and 2014. The prediction was documented in a working paper (S&P 500 returns revisited) and several posts.
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 (1)
where Rp(t+6)is the S&P 500 return at a six-year horizon. Figure 1 depicts relevant S&P 500 returns, both actual one and that predicted by relationship (1). The former curve has been approaching the latter one since May 2010.
Because of the linearity in the N3 growth 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.
In July, actual closing level was ~1100 (+50 relative to June 2010). As predicted in the post devoted to the July’s level of S&P 500, the panic behavior observed in May and June 2010 ended in July (the quiet period continues into August 2010). However, we expected the close level between 1020 and 1050 in July 2010. Actual level was 50 points above the expected one, which is the effect of dynamic overshoot.
Figure 2 shows that the level of S&P 500 was above the trend line in July 2010. In the first decade of August 2010, the level of S&P 500 has been hovering around 1100. It may stay at this level by the end of August. In this case the difference between the actual and trend levels will be growing. If this tendency will stretch into September 2010, the difference will increase above 100 points. This will create a potential, which may express itself in a force returning the S&P 500 to the trend level with likely overshoot well below the trend. Same effect was observed in 1987. The cumulated potential may release in a market crash, if the level of S&P 500 will not be decreasing in August and September 2010. So, it will be interesting to follow up the future S&P 500 trajectory.
Figure 1. Observed and predicted S&P 500 returns.
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.