Time to buy SPY

A month ago, we predicted a 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 deflation by 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.

Black Tuesday?

I assume that the closing S&P 500 level of 1183 in October 2010 and its following growth to 1225 in November 2010 is not good news for the US stock market. Figures 1 and 2 update the previous versions published in this blog in September. Both Figures demonstrate that the difference between the predicted and observed curves has been increasing since September.

This observation raises a question on the following events. Our concern about possible repetition of the 1987 fall, if the index would continue its deviation from the predicted trend into October 2010 is on again. So, I see a danger of a severe panic on the stock market. Because Tuesday is a common day for such events, I cannot exclude that one of Tuesdays in the nearest future will end in a return of the observed curves to the predicted one.

There is also a chance that the population estimates underlying the prediction become wrong since September 2010. The methods of population projection and updates used by the Census Bureau are also not well predicted.

Below we repeat a mandatory part with a bit of mathematics for the readers interested in details of our model. The model is also presented in our working paper [1] and monograph [2].

The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. In order to extend the prediction in time we use the number of three-year-olds, N3, as a proxy to N9 and obtain a forecast at a six-year horizon:

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

where Rp(t+6)is the S&P 500 return six years ahead (in 2010 one can foresee the returns in 2016). Figure 1 depicts germane S&P 500 returns, both actual one and that predicted by relationship (1). Both curves are coinciding in practical terms.

Because of the observed linear growth in N3 one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.

Figure 1. Observed and predicted S&P 500 returns. The last point for the observed series is October 31, 2010.

Figure 2. The observed monthly closing level of the S&P 500 stock market index and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010. The last point in the observed series is October 31, 2010. The deviation between the predicted and observed curves has been increasing since September 2010.

1987, 2001, 2008 … 2011

The essence of any quantitative model consists in the accuracy of prediction or predictive power. The higher is signal/noise ratio in a given data set the better can be the estimate of model parameters or the uncertainty of corresponding prediction. For the S&P 500 stock market index, the most prominent signals were measured during the periods of the fastest change: 1987, 2001 and 2008.

We have developed a model [1] linking the S&P 500 and its returns to the population of some characteristic age. The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9:

Rp(t) = AdlnN9(t) + B (1)

where Rp(t) is the S&P 500 yearly return, A and B are empirical coefficients to be determined by some fitting procedure. They may change depending on the approximation used to represent N9. In the previous post on the S&P 500 returns we have approximated N9 by the number of three-year-olds, N3, six years before. Accordingly, we have obtained a prediction of the S&P return at a six year horizon, i.e. in 2010 one can foresee the returns in 2016. Relevant empirical relationship is as follows”

Rp(t+6) = 100dlnN3(t) - 0.23 (2)

Figure 1 depicts the S&P 500 returns, both actual one and that predicted by relationship (2). Both curves are coinciding in practical terms between 2008 and the middle of 2010.

In 1987 and 2001 abrupt falls in the returns were also observed. In this respect, the model also demonstrates an excellent predictive power, as Figures 2 and 3 depict. There are obvious differences between the measured S&P 500 returns. In 1987, the fall was very fast but not deep, from +0.3 to -0.1. In 2001, the returns declined gradually from +0.3 to -0.3 in 2002. In 2008, the observed curve fell from 0 to -0.5, i.e. approximately same as in 1987.

In all cases the model gives a good prediction of the timing and amplitude of the observed returns. So, the model has a good predictive power, considering that the prediction can be obtained at a nine year horizon with the birth rate used as a proxy to N9.

Therefore, one might treat our prediction of the 2011 fall as a reliable one.

During the last two weeks, the S&P 500 has been growing at a healthy pace. Currently, it exceeds the predicted level by approximately 50 to 100 points. This is a good reason to suggest that a significant force, which must eventually return the index to the trend line, has been developing in September 2010. If the growth continues into the second half of September one might expect a dramatic drop in October 2010. However, this will be just a part of the overall decrease to the level of -0.5 expected in July-August 2011.

Figure 1. The prediction of the S&P 500 annual return for the period between 2008 and 2012. We tentatively put the September's closing level at 1030.

Figure 2. The prediction of the S&P 500 annual return for the period between 1985 and 1989.

Figure 3. The prediction of the S&P 500 annual return for the period between 1998 and 2003.

References

1. Kitov, I., Kitov, O. (2010). S&P 500 returns revisited, http://ideas.repec.org/p/pra/mprapa/21733.html.

S&P 500 in September 2010

Good news from August 2010 is that the S&P 500 market index is back on the track predicted couple years ago. Figures 1 and 2 update the previous versions published on Seeking Alpha in August with the closing level of ~1050 reported on August 31. Both predicted curves are very close to the observed ones over the whole period between March 2009 and August 2010. This prediction would have been a convincing one for everybody except market players who do believe that stock prices are unpredictable.

So, we will continue tracking the level of S&P 500 and its returns. The next move is likely below the trend to compensate for a short positive excursion in July 2010. This might be a drop by 40 to 80 points, likely to the level below 1000. It might be accompanied by a small panic. However, a positive jerk associated with local positive news is not excluded but it should not be high in amplitude.

Our concern about possible repetition of the 1987 fall, if the index would continue its deviation from the predicted trend into October 2010, has been resolved by the drop of around 50 points from the July’s level of 1101. So, there is no danger of a severe panic on the stock market.

Below we repeat a mandatory part with a bit of mathematics for the readers interested in details of our excellent (in terms of predictive power) model. The model is also presented in our working paper [1] and monograph [2].

The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. In order to extend the prediction in time we use the number of three-year-olds, N3, as a proxy to N9 and obtain a forecast at a six-year horizon:

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

where Rp(t+6) is the S&P 500 return six years ahead (in 2010 one can foresee the returns in 2016). Figure 1 depicts germane S&P 500 returns, both actual one and that predicted by relationship (1). Both curves are coinciding in practical terms.

Because of the observed linear growth in N3 one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.

Figure 1. Observed and predicted S&P 500 returns. The last point for the observed series is August 2010.

Figure 2. Observed S&P 500 monthly close level and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010. The last point in the observed series is August 2010. All in all, the S&P 500 is back on the predicted trend.

S&P 500 in August 2010

We continue tracking the evolution of the S&P 500 and our prediction made in the beginning of 2009 for the next six years. Since March 2009, the prediction fits the observed S&P 500 with minor deviations likely related to the emotion component of the stock market. However, the trend and its turn in May 2010 were forecasted precisely. All in all, fifteen months in a raw we are right and do not see any source which may disturb our prediction for the period between June 2010 and 2014. The prediction was documented in a working paper (S&P 500 returns revisited) and several posts.

The original model 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 former curve has been approaching the latter one since May 2010.

Because of the linearity in the N3 growth one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.

In July, actual closing level was ~1100 (+50 relative to June 2010). As predicted in the post devoted to the July’s level of S&P 500, the panic behavior observed in May and June 2010 ended in July (the quiet period continues into August 2010). However, we expected the close level between 1020 and 1050 in July 2010. Actual level was 50 points above the expected one, which is the effect of dynamic overshoot.

Figure 2 shows that the level of S&P 500 was above the trend line in July 2010. In the first decade of August 2010, the level of S&P 500 has been hovering around 1100. It may stay at this level by the end of August. In this case the difference between the actual and trend levels will be growing. If this tendency will stretch into September 2010, the difference will increase above 100 points. This will create a potential, which may express itself in a force returning the S&P 500 to the trend level with likely overshoot well below the trend. Same effect was observed in 1987. The cumulated potential may release in a market crash, if the level of S&P 500 will not be decreasing in August and September 2010. So, it will be interesting to follow up the future S&P 500 trajectory.

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

Figure 2. Observed S&P 500 monthly close level and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010.

Procter and Gamble on rise?

According to [1], the model for Procter and Gamble (PG) is defined by the index of food away from home (SEFV - CUUS0000SEFV) and that of rent of primary residency (RPR). The former CPI component leads the share price by 3 months and the latter one leads by 8 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and June 2010. Relevant coefficients are negative and positive, respectively. The slope of time trend is also positive.

So, the best-fit 2-C model for PG(t) is as follows:

PG(t) = -5.88SEFV(t-3) + 3.43RPR(t-8) + 17.60(t-2000) + 174.08

where t is calendar time.

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $2.08 for the period between July 2003 and June 2010. In other words, the price of a PG share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresees a period of modest growth in the near future. This contradicts the predicted overall fall in the S&P 500 in 2010. One might expect a slight growth in PG share price, but this deviation also can manifest the end of the period where the model is valid. This deviation may be induced by the change in the trend in both or one of the underlying CPIs: SEFVand RPR, as Figure 1 illustrates.

Figure 1. Evolution of the price of SEFV and RPR.

Figure 2. Observed and predicted PG share prices. The original prediction, i.e. the prediction three months before actual time, is shown by red line. Black diamonds present the original line shifted 3 months ahead to fit actual data.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.08. The largest errors were observed in 2007.

References

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

PepsiCo share price

According to [1], the model for PepsiCo (PEP) is defined by the index of food at home (FH) and that of information technology (IT). The former CPI component leads the share price by 4 months and the latter one leads by 8 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and June 2010. Both coefficients are negative and the slope of time trend is positive.

So, the best-fit 2-C model for PEP(t) is as follows:

PEP(t) = -1.41FH(t-12) – 8.54IT(t-4) +1.54(t-2000) + 416.80

where t is calendar time.

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $2.26 for the period between July 2003 and June 2010. In other words, the price of a PEP share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresee no change in the near future. This is one of rare shares that is not predicted to drop with the overall fall in the S&P 500 in 2010.

 

Figure 1. Evolution of the price of FH and IT.

Figure 2. Observed and predicted PEP share prices. The original prediction, i.e. the prediction four months before actual time, is shown by red line. Black diamonds present the original line shifted 4 months ahead to fit actual data.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.26. The largest errors were observed in 2008.

References

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

IBM share price on decline

According to [1], the model for IBM (IBM) is defined by the index of motor vehicle maintenance and repair (MVR - CUUR0000SETD) and that of transportation services (TS - CUUR0000SAS4). The former CPI component leads the share price by 12 months and the latter one leads by 4 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and June 2010. Both coefficients and the slope of time trend are negative. ]

So, the best-fit 2-C model for IBM(t) is as follows:

IBM(t) = 4.93MVR(t-12) – 3.51TS(t-4) - 10.39(t-2000) + 39.39

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $5.94 for the period between July 2003 and June 2010. In other words, the price of an IBM share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresee a fall in the near future. This drop will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Evolution of the price of MEAT and IT.

Figure 2. Observed and predicted IBM share prices. The original prediction, i.e. the prediction four months before actual time, is shown by red line. Black diamonds present the original line shifted 4 months ahead to fit actual data.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $5.94. The largest errors were observed in 2008.

References

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

Xilinx share price

This is a funny example. According to our approach discussed in [1], the model for Xilinx (XLNX) is defined by the index of communication (CO-CUUR0000SAE2) and that of information and information processing (INF-CUUR0000SAE21). The former CPI component leads the share price by 11 months and the latter one leads by 4 months. From our past experience, the larger is the lag the more unreliable is the model. These defining components provide the best fit model, i.e. the lowermost RMS residual error, between August 2009 and June 2010. Both coefficients in the XLNX model are positive. This means that the decreasing price of communication and information (see Figure 1) forces the share price down.

So, the best-fit 2-C model for XLNX(t) is as follows:

XLNX(t) = 4.05CO(t-11) + 3.54INF(t-4) +0 .17(t-2000) + 33.25

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $1.92 for the period between July 2003 and June 2010. In other words, the price of a XLNX share is completely defined by the behaviour of these two CPI components.

The model accurately predicts the share price in the past and foresees no significant change in the next quarter, in July through September 2010. Considering the overall fall in the S&P 500 in 2010, one should not expect any growth in this stock price at all.

Figure 1. Evolution of the price index of communication (CO) and information (INF).

Figure 2. Observed and predicted XLNX share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $1.92. The largest errors were observed in 2004 and 2005.

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

Ball Corporation share price

According to [1], the model for Ball Corporation (BLL) is defined by the index of motor vehicle maintenance and repair (MVR- CUUR0000SETD) and that of communication (CO- CUUR0000SAE2). The former CPI component leads the share price by 13 months and the latter one leads by 2 months. These defining components provide the best fit model between August 2009 and June 2010.

So, the best-fit 2-C model for BLL(t) is as follows:

BLLB(t) = 2.66MVR (t-13) – 5.84(t-2) - 20.44(t-2000) + 321.46

The predicted curve in Figure 1 leads the observed price by 2 months with the residual error of $2.42 for the period between July 2003 and June 2010. In other words, the price of a BLL share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresee a significant fall in the near future. This drop will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Observed and predicted BLL share prices. Black diamonds present the original forecast shifted 2 months ahead.

References

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

Schlumberger share price

According to [1], the model for Schlumberger Limited (SLB) is defined by the index of meat and meats, poultry, fish and eggs (MEAT- CUUR0000SAF112) and that of information technology (IT- CUUR0000SEEE). The former CPI component leads the share price by 2 months and the latter one leads by 6 months. Figure 1 depicts the overall evolution of both involved indices. However, both defining components provide the best fit model between August 2009 and June 2010. Both coefficients and the slope of time trend are negative.

So, the best-fit 2-C model for SLB(t) is as follows:

SLB(t) = -3.56MEAT(t-2) – 48.58IT(t-6) - 30.24(t-2000) + 1858.34

The predicted curve in Figure 2 leads the observed price by 2 months with the residual error of $6.30 for the period between July 2003 and June 2010. In other words, the price of a SLB share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresee a significant fall in the near future. This drop will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Evolution of the price of MEAT and IT.

Figure 2. Observed and predicted SLB share prices. Original prediction is shown by red line. Black diamonds present the original line shifted 2 months ahead.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $6.30. The largest errors were observed in 2008.

References

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

HPQ share price

According to [1], the model for Hewlett-Packard (HPQ) is defined by the index of food less beverages (FB) and that of rent of primary residency (RPR). The former CPI component leads the share price by 4 months and the latter one leads by 5 months. Figure 1 depicts the overall evolution of both involved indices. However, these two defining components provide the best fit model between August 2009 and June 2010. One coefficients is negative and one is positive together with time trend, with slope of 3.64.

So, the best-fit 2-C model for HPQ(t) is as follows:

HPG(t) = -3.20FB(t-4) +2.91RPR(t-5) + 3.64(t-2000) - 50.82

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $2.13 for the period between July 2003 and June 2010. In other words, the price of a HPQ share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresees a fall in 2010. It will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Evolution of the price of DAIRY and TPU.

Figure 2. Observed and predicted HPQ share prices. Original prediction is shown by red line. Black diamonds present the original line shifted 4 months ahead, i.e. the model.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.13. The largest errors were observed in 2007.

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

MMM share price

According to [1], the model for 3M Company (MMM) is defined by the index of dairy products (DAIRY- CUUS0000SEFJ) and that of public transportation (TPU- CUUS0000SETG). The former CPI component leads the share price by 10 months and the latter one leads by 6 months. Figure 1 depicts the overall evolution of both involved indices. However, both defining components provide the best fit model between August 2009 and June 2010. Both coefficients are negative and only positive time trend with slope of 8.7 has been compensating the negative input of both CPIs .

So, the best-fit 2-C model for MMM(t) is as follows:

MMM(t) = -0.74DAIRY(t-10) – 0.54TPUP(t-6) + 8.70(t-2000) + 180.88

The predicted curve in Figure 2 leads the observed price by 6 (!) months with the residual error of $3.79 for the period between July 2003 and June 2010. In other words, the price of a MMM share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresee a significant fall in the last quarter of 2010, i.e. through December 2010. It will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Evolution of the price of DAIRY and TPU.

Figure 2. Observed and predicted MMM share prices. Original prediction is shown by red line. Black diamonds present the original line shifted 6 months ahead.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $3.79. The largest errors were observed in 2005 and 2006.


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

Predicting DeVry's share price

According to [1], the model for DeVry (DV) is defined by the index for the rent of primary residency (RPR-CUUS0000SEHA) and that of pets, pet products and services (PETS-CUUR0000SERB). The former CPI component leads the share price by 11 months and the latter one leads by 4 months. Figure 1 depicts the overall evolution of both involved indices. From our past experience, the larger is the lag the more unreliable is the model. However, both defining components provide the best fit model between August 2009 and June 2010. The positive influence of RPR (+7.90) is compensated by the negative input of all other terms . So, the best-fit 2-C model for DV(t) is as follows:

DV(t) =7 .90RPR(t-11) – 2.76PETS(t-4) - 35.73(t-2000) - 757.63

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $3.24 for the period between July 2003 and June 2010. In other words, the price of a DV share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresees A significant fall in the next quarter, i.e. through September 2010. It will be in line with the overall fall in the S&P 500 in 2010.

Figure 1. Evolution of the price of RPR and PETS.

Figure 2. Observed and predicted DV share prices . Original predcition is shown by red line. Black diamonds present the original prediction shifted by 4 months ahead.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $3.24. The largest errors were observed in 2007 and 2008.

References

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

Prediction of Legg Mason share price

According to [1], the model for Legg Mason (LM) is defined by the index of food (F-CUUS0000SAF ) and that of appliances (APL-CUUR0000SEHK). The former CPI component leads the share price by 4 months and the latter one leads by 13 months. From our past experience, the larger is the lag the more unreliable is the model. However, both defining components provide the best fit model between August 2009 and June 2010. Both coefficients in the LM model are positive. This means that increasing food price forces the share price up. The fall in the index of appliances has been compensating *see Figure 1) both the increase in F and positive linear time trend in the share price, as defined by the slope of +33.024. So, the best-fit 2-C model for LM(t) is as follows:

LM(t) = 5.88F(t-4) + 8.29APL(t-13) + 33.024(t-2000) + 1425.45

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $6.89 for the period between July 2003 and June 2010. In other words, the price of a LM share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresees no significant increase in the next quarter, in July through September 2010. Considering the overall fall in the S&P 500 in 2010, one should not expect any growth in stock prices at all.

Figure 1. Evolution of the price index of food (F) and appliances (APL).The latter has been falling since July 2009.

Figure 2. Observed and predicted LM share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $6.89. the largest errors were observed in 2005 and 2006.

References

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