In August 2011, we routinely revisited our model of the S&P 500 returns where the driving force of the stock market is real GDP. Our quantitative model predicted a negative correction of the S&P 500 level in August-October 2011, as shown in Figure 1 borrowed from the post in August. Figure 2 shows that our prediction was accurate and the annual S&P 500 returns dropped to the level of 0.005 and even below. Hence, the model does predict major turns in the evolution of S&P 500. From Figure 2, we expect the index to grow in the beginning of 2012. This prediction is supported by the rate of unemployment reported for January 2012. According to the link between real GDP per capita and the rate of unemployment in the US (8.3%) we expect real GDP to grow at a rate above 3% (SAAR) in the first and second quarters.

Here, we update our model with the revised GDP estimates and include the advance GDP estimate for the fourth quarter of 2011. The monthly closing prices through January 2012 are used. As discussed in our working paper on the S&P 500 index, there exists a trade-off between the growth rate of real GDP,

*G(t),*and the S&P 500 return,*R(t).*The predicted returns,*R*can be obtained from the following relationship:_{p}(t),*R*(1)

_{p}(t) = 0.0054dlnG(t) - 0.03where

*G(t)*is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA.Figure 2 displays the observed S&P 500 returns and those obtained using real GDP. As before, the observed returns are MA(12) of the monthly returns. For the predicted curve, we use the same GDP value for all three months in a given quarter.

The period after 2003 is relatively well predicted. The updated GDP estimates highlighted two strong deviations from the observed trajectory started in February 2010 and February 2011. During the first excursion, the predicted curve returned to the observed one in May 2010. One might speculate that these excursions were caused by quantitative easing. In any case it was a transitory deviation.

One of the sources of controversial information is the BEA. It routinely revises all historical estimates of real GDP and introduces significant changes affecting any model referring to GDP data. Figure 3 depicts the prediction of S&P 500 returns carried out in March 2011 in this blog. The predicted curve fits the measured returns with a high accuracy for the period between 2007 and 2011. After the comprehensive GDP revision published in July 2011, the fit disappeared due to much smoother time series. This is not the final revision, however, and some of the fit in Figure 3 can be still recovered in the future.

Figure 4 illustrates the increasing volatility in the monthly closing S&P 500 returns since 2009. This is a clear sign that the economy and financial market are far from the stability observed in the mid-1990s and between 2004 and 2007.

Figure 1. The prediction given in August 2011. The predicted curve is smoothed by MA(4). The annual S&P return was predicted to drop to 0.005 and below by October 2011 as shown by red diamonds.

Figure 2. The observed S&P 500 returns and that predicted from real GDP through January 2012. The predicted fall did happen and the current expectation is that the S&P return will grow into 2012. This prediction is supported by the fall in unemployment reported for January 2012.

Figure 3. The S&P returns predcited from real GDP in March 2011. The peak in 2010 was well described by contemporary GDP estimates. The peak disappeared (was ironed out) after the comprehensive GDP revision in July 2011.

Figure 4. The S&P monthly (closing price) returns since 1990. It should be noted that the overal volatility has been increasing since 2009.

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