Believe you or not, we predicted the fall in the S&P 500 returns in March 2009. In February 2009, there was no indication of the following linear growth in the returns. Below we present our model and predictions for 2010 and 2011. The model in best described in (Kitov, 2010).

**The returns will drop again to -0.5!**

**S&P 500 returns and real GDP**

As discussed in (Kitov, Kitov and Dolinskaya, 2009), there exists a trade-off between the growth rate of real GDP pre capita and the change rate of the number of 9-year-olds. Corresponding relationship should work in both directions and the number of 9-year-olds can be estimated from GDP measurements. So, one can replace N9(t) with GDPpc(t), taking into account that second term in the relationship between real GDP per capita and population is constant.

Figure 1 displays the observed S&P 500 returns and those obtained using real GDP, as presented by the US Bureau of Economic Analysis (www.bea.gov). The observed returns are presented by MA(12) of the monthly returns. The predicted returns, Rp(t), are obtained from the following relationship:

Rp(t) = 0.6*dln(GDPpc(t)) - 0.0092,

where GDPpc(t) is represented by MA(6) of the (annualized) growth rate during or six previous months or two quarters as only quarterly readings of real GDP are available.

The period after 1996 is relatively well predicted including the increase in 2003. Therefore, it is reasonable to assume that the 9-year-old population was not well estimated by the US Census Bureau after 2003. This conclusion is supported by the cointegration test conducted for real GDP per capita and the charge rate of the number of 9-year-olds, which proves the existence of a long-term equilibrium linear relation between these two variables since the early 1960s (Kitov, Kitov and Dolinskaya, 2009). As a result, one can use either N9(t) or GDPpc(t) for modeling of the S&P 500 returns, where appropriate. Obviously, the GDPpc(t) is consistent with the S&P 500 returns after 2003.

Figure 1. The observed and predicted S&P 500 returns. The latter are obtained using quarterly readings of the growth rate of real GDP. One may expect rapid economic growth in 2010.

There is a concern related to the accuracy of population and real GDP measurement in 2006. In Figure 1, the predicted curve fell to -0.075 in the third quarter of 2006. There was no significant decrease in the S&P 500 returns during the same period. A possible reason for the discrepancy is that the real GDP was underestimated. This issue should be resolved in the next comprehensive revision to the GDP.

A striking feature in Figure 1 is the agreement between the annual curves in 2008 and 2009. The GDP readings predict the S&P 500 returns in time and amplitude. Moreover, the S&P index leads the GDP curve and predicts a rapid real economic growth in 2010. This is a good prediction to validate the link. All in all, real GDP per capita is a good predictor of the S&P 500 returns, especially during periods of big changes.

Using the number of 3-year-olds and the model linking it to the S&P 500 returns we have predicted the evolution between 2008 and 2014. The graph shown in Figure 2 is borrowed from (Kitov, 2010) with the amendments related to 2010.

If the level of S&P 500 will not reach 1200 by the end of March 2010, it will manifest the start of the fall. In any case, April 2010 will be the last months with growth, if any. Since May 2010, the fall is inevitable. It will be fast and deep – down to -0.5 (cumulative over the previous 12 months) by August 2011. One should bear in mind, that all predictions for 2009 and the beginning of 2010 have been realized.

There is a concern related to the accuracy of population and real GDP measurement in 2006. In Figure 1, the predicted curve fell to -0.075 in the third quarter of 2006. There was no significant decrease in the S&P 500 returns during the same period. A possible reason for the discrepancy is that the real GDP was underestimated. This issue should be resolved in the next comprehensive revision to the GDP.

A striking feature in Figure 1 is the agreement between the annual curves in 2008 and 2009. The GDP readings predict the S&P 500 returns in time and amplitude. Moreover, the S&P index leads the GDP curve and predicts a rapid real economic growth in 2010. This is a good prediction to validate the link. All in all, real GDP per capita is a good predictor of the S&P 500 returns, especially during periods of big changes.

Using the number of 3-year-olds and the model linking it to the S&P 500 returns we have predicted the evolution between 2008 and 2014. The graph shown in Figure 2 is borrowed from (Kitov, 2010) with the amendments related to 2010.

If the level of S&P 500 will not reach 1200 by the end of March 2010, it will manifest the start of the fall. In any case, April 2010 will be the last months with growth, if any. Since May 2010, the fall is inevitable. It will be fast and deep – down to -0.5 (cumulative over the previous 12 months) by August 2011. One should bear in mind, that all predictions for 2009 and the beginning of 2010 have been realized.

Figure 2. Observed and predicted S&P 500 returns. By August 2011, the 12-month cumulative return will drop to -0.5. The period between March 2009 and March 2010 was predicted with high accuracy, taking into account the change in calibration.

Figure 3. The S&P 500 returns are currently reaching the peak with the following fall down to -0.04 (in average over the previous 12 months) by August 2011, as Figure 2 shows.

KITOV, I. KITOV, O., DOLINSKAYA, S. (2009). Modelling Real Gdp Per Capita In The Usa:Cointegration Tests, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 4(1(7)_ Spr)

Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

KITOV, I. KITOV, O., DOLINSKAYA, S. (2009). Modelling Real Gdp Per Capita In The Usa:Cointegration Tests, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 4(1(7)_ Spr)

Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

**Disclosure:**No positions

**Disclosure:**No positions