S&P 500. Update June 2009

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

We have published a working paper on S&P 500 returns at the RePEc:

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 http://mpra.ub.uni-muenchen.de/6056/01/MPRA_paper_6056.pdf

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),

instead of that used in the paper: R_p=30dln(N9)-0.1.
In (1), R_p 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.

Figure 1 depicts the correct prediction of S&P 500 index using the number of 9-year-olds extrapolated from the number of 3-year-olds. A sudden drop in 2008 and 2009 to the level of 700 should be followed by an increase to 1800 in 2010. Notice that the start of the current growth in S&P 500 was first predicted in March 2009 in this blog, when the market was very low with the close ~735 in February. The last three points together with the turn to the growth were forecasted. This pattern should be presented instead of the wrong version displayed in the paper (see Figure 2).

The problem of the correct prediction was that the number of 9-year-olds in the end of any decade is prone to high bias. Only decennial censuses (next due in 2010) allow more accurate estimates. Because of the high uncertainty in N9, we have proposed to real GDP as a proxy to the N9.
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_p(t) = 15.0*dln(GDPpc(t)) - 0.32 (2)

where GDPpc(t)) is represented by the mean (annualized) growth rate during four previous quarters. Unfortunately, no monthly readings of real GDP are available.

The period after 2000 is well predicted including the sharp 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 [3] which proves the existence of a long-term equilibrium linear relation between these two variables since the early 1960s. As a result, one can use either 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.

We foresee the next post on S&P 500 in the beginning of July.

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

[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 http://mpra.ub.uni-muenchen.de/6056/01/MPRA_paper_6056.pdf

[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.