This is a semi-annual report on the evolution of S&P 500 index. It compares the actually observed monthly closing levels to those predicted by our model, as originally presented in [1]. The major conclusion is that the prediction of a monotonic growth in S&P level made in March 2009 is correct. There is no indication that the growth will end before May 2010, where we foreseen the turn to a negative slope. Accordingly, the S&P 500 annual return will soon reach positive figures and will be growing at an accelerated rate till May 2010.

The model links S&P 500 annual returns to the number of 9-year-olds and has passed econometric tests for cointegration, with goodness-of-fit reaching 0.9. Since the number of 9-year-olds can be accurately predicted using younger cohorts, one can predict S&P returns at a several-year horizon. (Standard demographic projections may be used to predict over a decade ahead.)

The model links S&P 500 annual returns to the number of 9-year-olds and has passed econometric tests for cointegration, with goodness-of-fit reaching 0.9. Since the number of 9-year-olds can be accurately predicted using younger cohorts, one can predict S&P returns at a several-year horizon. (Standard demographic projections may be used to predict over a decade ahead.)

We revealed the link between S&P 500 and the number of 9-year-olds in December 2007 using historical data since 1985. Since the very beginning of 2008, we have been carefully tracking the evolution of S&P 500. The original model actually predicted a sharp fall in 2008 [1]. (As in many scientific studies, the attempt to improve the original model, in order to fit data between 2003 and 2007, had failed, as we reported in this blog at several occasions.) The re-calibrated version of the original model developed in March 2009 is as follows:

*Rp(t) = 165dln[N3(t+6)] - 0.17 (1),*

In (1),

*Rp*is the 12-month cumulative return;

*N3*is the number of three-year-olds;

*t+6*– time shifted by six years ahead to extrapolate the number of 3-year-olds into the number of 9-year-olds; dln is the rate of growth, i.e. the monthly increment in N3 normalized to the contemporary level. The time step is one month or 1/12 of a year.

Figure 1 compares the initial prediction of the S&P 500 evolution, the observed trajectory for the period since February 2009, and a new prediction till 2011. Relationship (1) is used with the number of 9-year-olds extrapolated from the number of 3-year-olds. In March 2009, we used a preliminary calibration of the original model and assumed the monthly increment in S&P 500 would be 80 points. This assumption was too optimistic and the growth was weaker. The original prediction is shown by blue lin with solid circles in Figure 1, and the observed values are shown by red diamonds. The black line represents an updated prediction since September 2009. It reproduces the old prediction but with a 46-point monthly increment since October 2009, as discussed below.

All in all, Figure 1 presents strong evidence in favour of our original model. Six months of almost monotonic growth were not expected by many market players in March 2009. The next nine months should bring additional validation to the model. The most important event will be the turn in May 2010. But the growth before this date is of crucial importance as well.

All in all, Figure 1 presents strong evidence in favour of our original model. Six months of almost monotonic growth were not expected by many market players in March 2009. The next nine months should bring additional validation to the model. The most important event will be the turn in May 2010. But the growth before this date is of crucial importance as well.

Figure 1. The evolution of S&P 500. Blue line - the original prediction using (1) with 80 unit per month increment. Red line – observations. Black line – the updated prediction since October 2009 with a 46-point monthly increment.

In any case, the model predicts a sudden drop in 2008 and 2009 to the level of 700, which has been followed by constant growth to the level 1050 in September 20009. Initially, we estimated the peak value in 2010 as 1800. But the last six months demonstrated the necessity to re-calibrate the model using new data. (In physics, even fundamental constants are under permanent re-estimation, and empirical and even fundamental models are constantly recalibrated.) Therefore, we also re-estimated coefficients in (1) to fit the last six S&P 500 (monthly) readings. The new model is as follows:

In any case, the model predicts a sudden drop in 2008 and 2009 to the level of 700, which has been followed by constant growth to the level 1050 in September 20009. Initially, we estimated the peak value in 2010 as 1800. But the last six months demonstrated the necessity to re-calibrate the model using new data. (In physics, even fundamental constants are under permanent re-estimation, and empirical and even fundamental models are constantly recalibrated.) Therefore, we also re-estimated coefficients in (1) to fit the last six S&P 500 (monthly) readings. The new model is as follows:

*Rp(t) = 135dln[N3(t+6)] - 0.17 (2),*Actually, we needed to reduce the coefficient of linear term from 165 to 135 with free term unchanged. Figure 2 depicts the updated prediction of the S&P 500 annual returns. The peak S&P 500 value in May 2010 should be 1425 (not 1800) if the future increment will be 46 points per month, as observed between March and September 2009.

Figure 2. Observed and predicted S&P 500 returns. The September level of S&P 500 index is 1057. The past six months are relatively well predicted.

**Conclusion**

Between 1985 and 2009, the S&P 500 returns can be accurately described by population estimates. The model based on the number of 9-year-olds produces a time series which is cointegrated with the S&P 500 returns, i.e. reveals a weak causality, as proved by the cointegration tests.

The re-calibrated model predicts the continuation of S&P 500 growth into 2010 with the peak level of ~1400 in May. The annual returns will reach positive zone soon and also peak in May 2010 at the level of 50% to 70%.

**References**

[1] Kitov, I., Kitov, O., (2007). Exact prediction of S&P 500 returns, MPRA Paper 6056, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/6056.html

## No comments:

## Post a Comment