Time to buy SPY

A month ago, we predicteda drop in the S&P 500 to the level of 1300 by the end of May. We also suggested buying the index when it is 1300.  Both are done by now. We are waiting the level 1500 in October 2013 to sell and fix profit. The explanation from April is fully repeated below. The red segment in Figure 2 is now black since the prediction is realized.

We also expect oil price to drop further and force deflationby the end of 2012.

This repeats our previous postSeveral days ago we predicted the current fall in the S&P 500 index. For this reason, we did not enter the stock market and instead invested in a defensive portfolio. We are waiting the level of 1350.  The reason is explained below.

Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007.  There are two deep troughs in 2002 and 2009 which are marked by red and green lines, respectively.  For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious – in the long run the market depends on the overall economic growth.

Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line).  When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360).  The black curve returned to the blue one in August/September 2011. A month ago, we observed a middle-size deviation of about 100 units and predicted that the index will have a negative correction down to the level of 1300 any time soon.  If the index will repeat the path of the previous rally one-to-one, one may expect the peak level of 1500 in the end of 2013.  In two to four weeks it might be a good time to invest for a 15% return cumulated to October 2013 (but not more than two months), when the negative correction is over. 

With the S&P 500 falling down to 1350, the prediction does not seem inappropriate. The next several weeks should decide on the new level. In Figure 2, we have drawn the fall we expect by the end of May 2012. We would wait by the end of April to decide on the following move in the S&P 500. If the current fall will reach 1300, it’s likely a good time to buy. Otherwise, the end of May is the horizon to wait the bottom.

Figure 1. The evolution of the S&P 500 market index between 1980 and 2012. 

Figure 2. The curve in Figure 1 peak is shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in Mach to 1300 in May.

Time to buy stocks

Two months ago we revisited our model of the S&P 500 returns where the driving force of the stock market is real GDP.  This quantitative model predicted a negative correction of the S&P 500 level in 2011. As an alternative, we suggested that the Bureau of Economic Analysis could revise its real GDP estimates up. However, the BEA revised the GDP estimates significantly down for the years after 2005. As a consequence of this revision, all empirical coefficients in our model have to be re-estimated. Accordingly, the difference between the predicted and observed level of S&P 500 has to change.

Here, we update our model with the revised GDP estimates and include the advance GDP estimate for the second quarter of 2011.  The monthly closing prices through July 2011 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_p(t), can be obtained from the following relationship:

R_p(t) = 0.0054dlnG(t) - 0.03   (1) 

where G(t) is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA.  In our previous model the slope was slightly larger (0.0064) and the intercept did not change.  

Figure 1 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 give quarter.  Figure 2 displays the predicted curve smoothed by MA(4). This smoothed line stresses the mid-term deviation between the curves. 

The period after 2003 is relatively well predicted. The updated GDP estimates highlighted two strong deviations from the observed trajectory started in November 2009 and October 2010. During the first excursion, the predicted curve returned to the observed one in May 2010. One might speculate that this excursion was caused by the first quantitative easing. In any case it was a transitory deviation. 

The current deviation may have the same transitory nature but it is not over yet. In June, we expected this deviation to disappear in 2011. For the current estimates of real GDP, the level of S&P 500 has to be around 1250 in October 2011 in order to intercept the predicted line (see red diamond in Figure 2). Currently, the S&P 500 is below 1200 (the fall we forecasted in June) and thus one could buy stocks. However, the long-term growth does not exclude short-term falls due to the extremely high volatility of the stock market and one can wait for a deeper local trough. 

Figure 1. The observed S&P 500 returns and that predicted from real GDP. For a given quarter, all monthly values of the GDP growth rate are equal.

Figure 2. The predicted curve is smoothed by MA(4). The S&P return prediction for the next three months is shown by red diamonds.

Angry Bear on the relation between S&P 500 and GDP

A month ago Mike Kimel had a post on Angry Bear dealing with the relationship between the S&P 500 market index and nominal GDP. His naive regression showed correlation of ~94%. One should not forget that Clive Granger introduced the idea of spurious regression 30 years ago. (A surrogate Nobel Prize for this finding in 2003.) This correlation is a good example; both variables are nonstationary, I(1), and are not cointegrated. Hence, the above correlation is spurious.

Actually, the S&P 500 returns are coitegrated with the change rate of real GDP per capita and this correlation is not spurious as shown in this blog and our paper on S&P 500.

Forecasting S&P 500 returns. Quarterly update

Three months ago we revisited our prediction of the S&P 500 return including the estimate of real GDP for the fourth quarter of 2010. Here, we update our model and include the GDP estimate for the first quarter of 2011 and the monthly closing prices through May 2011. As discussed in our working paper on S&P 500, there exists a trade-off between the growth rate of real GDP, G(t),  and the S&P 500 returns, R(t). The predicted returns, R_p(t), can be obtained from the following relationship: 

R_p(t) = 0.0064dlnG(t) - 0.03   (1) 

where 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. The period after 2003 is relatively well predicted. Therefore, it is reasonable to assume that G(t) can be used for modeling of the S&P 500 index and returns. Reciprocally, current S&P 500 may be used for the estimation of real GDP. The predicted return is lower than that observed in April and May 2011. We can assume that the level of S&P 500 should be corrected downwards or the preliminary estimate of GDP should be revised up.

Figure 1. Observed S&P 500 return and that predicted from real GDP. For a given quarter, all monthly values of the growth rate relative to the previous quarter are equal.  

Modeling S&P 500 returns. March 2011

We restart (or continue) reporting on the evolution of the S&P 500 and our prediction made in the beginning of 2009. Between March 2009 and September 2010, the prediction based on the number of nine-year-olds, N9, fitted the observed S&P 500 with minor deviations. All in all, sixteen months in a raw we were right and did not see any source which might disturb our prediction. However, there is one source of problem for many economic and econometric models we have built – population distributions provided by the US Census Bureau.

Here, we reintroduce the original model which links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. To obtain a prediction we use the number of three-year-olds, N3, as a proxy to N9 at a six-year horizon:

Rp(t+6) = 100dlnN3(t) - 0.23 (1)

where Rp(t+6)is the S&P 500 return at a six-year horizon. Figure 1 depicts relevant S&P 500 returns, both actual one and that predicted by relationship (1). The latter curve has been deviating the latter one since October 2010. Currently, this deviation is very big and put our model under strong doubt.

Figure 1. Observed and predicted S&P 500 returns.

This is not the end of the model, however. We continue using the link between real GDP and N9, as described in this paper. It was shown that one can exchange them when one of these two is not well estimated (usually N9). In that sense, one can use real GDP instead on N9.

As discussed in our working paper on S&P 500, there exists a trade-off between the growth rate of real GDP, G(t), and the S&P 500 returns, R(t). The predicted returns, Rp(t), can be obtained from the following relationship:

Rp(t) = 0.0062dlnG(t) - 0.01 (2)

where G(t) is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA.

With a small correction of the coefficients in (2), Figure 2 displays the observed S&P 500 returns and those obtained using real GDP, as presented by the US Bureau of Economic Analysis. As before, the observed returns are MA(12) of the monthly returns. The period after 2003 is relatively well predicted, including that not predicted by (1). Therefore, it is reasonable to assume that G(t) can be used for modeling of the S&P 500 index and returns. Reciprocally, current S&P 500 may be used for the estimation of real GDP.

Figure 2. Observed S&P 500 return and that predicted from real GDP. For a given quarter, all monthly values of the growth rate relative to the previous quarter are equal.

To understand the deviation associated with N9 we are waiting for the final results of the 2010 census. This is also crucial for many economic models we have developed for the U.S. Other developed countries do not demonstrate such big deviations.