**Stock market behavior has always been a source of surpizes for researchers, traders, and investors. The long term aggregate price trends have been explained as related to fundamental factors. Here we present a model, which makes the difference. Only one factor drive the long-term trends. Hence, the market volatility will be suppressed when everybody understands the market driving force, which is well predictable at a several year time horizon. **

**It is worth noting here that share prices of some companies in the S&P list can be also predicted at a five- to ten-year horizon. See our previous post:**

Comparative modelling of selected SP 500 share prices: IBM, DOV, PG, DD, APD, CVX, DVN, and HAL

**Now, June Update**

We have been carefully tracking the evolution of S&P 500 since 2007, when predicted a sudden fall in 2008 [1]. The 2008 crisis revealed one major mistake in our prediction for 2008 and 2009 – we were afraid to recognize the possibility a dramatic drop in the S&P 500 returns, when the relationship describing the years between 1985 and 2003 was applied. The right relationship is:

*R*,

_{p}(t) = 165dln[N3(t+6)] - 0.17 (1)*R*.

_{p}=30dln(N9)-0.1In (1),

*R*is the 12-month cumulative return;N3 is the number of three-year-olds; N9 is the number of 9-year-olds; t+6 – time shifted six years ahead to extrapolated the number of 3-year-olds in the number of 9-year-olds. Correct coefficient is 5.5 times larger than that used in the paper for the prediction after 2007.

_{p}^{ }Originally, the link between real GDP growth rate and the change rate of the number of 9-year-olds was found by Kitov [2]. Corresponding relationship should work in both directions, i.e. one can estimate the growth rate of real GDP from population measurements, and the number of 9-year-olds from real GDP measurements.

So, in relationship (1), 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 3 displays the observed SP500 returns and those obtained using real GDP, as presented by the US Bureau of Economic Analysis (www.bea.gov). As before, the observed returns are 12-month cumulative values. The predicted returns are obtained from the relationship

*R*(2)

_{p}(t) = 15.0*dln(GDPpc(t)) - 0.32*GDPpc(t))*is represented by the mean (annualized) growth rate during four previous quarters. Unfortunately, no monthly readings of real GDP are available.

*N9(t)*or

*GDPpc(t)*for the modeling of the S&P 500 returns, where one of them is more appropriate. Obviously, the

*GDPpc(t)*is consistent with the S&P 500 returns after 2007. The years between 2007 and 2010 should confirm or reject this statement.

Currently, relationship (2) is in a good shape. The 2008-2009 deep fall is well described. It also predicts that real GDP will start to increase in the nearest future following the observed increase in S&P 500. It would be very strong evidence in favor of (2) is valid. Red circle is the prediction for 2009Q2. The rate of growth should be +5% relative to previous quarter. We also expect a positive revision to real GDP estimates during the last four years. The May 2009 revision actually shifted many readings up, including the last three.

Finally, as predicted S&P 500 rose in May by +47 (not +80) units from 872 to 919, however. In June, we expect another rise by approximately 70 to 90 units. Figure 4 shows the past and future predictions using the number of 3-year-olds. The number of 9-year-olds should be measured precisely in the future to stabilize the stock market.

*Figure 1. Evolution of S&P 500. Red line – observations; black line – prediction from the number of 9-year-olds. The prediction is obtained using a transformed form of (1).*

*Figure 2. Incorrect prediction of S&P 500 return given in [1]. Actual returns fell much below the predicted ones*.

*Figure 3. The link between S&P 500 and real GDP between 2000 and 2009. Red circle is the prediction for 2009Q2. The rate of growth should be +5% relative to previous quarter. *

*Figure 4. Observed and predicted S&P 500 returns. The next (June) level of S&P 500 index is around 985, or ~70 from May close level of 914. Last three months we well predicted.*

**References**

[2] Kitov, I., (2006). GDP growth rate and population, Working Papers 42, ECINEQ, Society for the Study of Economic Inequality, http://ideas.repec.org/p/inq/inqwps/ecineq2006-42.html, www.ecineq.org/milano/WP/ECINEQ2006-42.pdf

[3] 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), pp. 80-96.

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