Approximately two years ago we introduced a concept linking share prices and CPI components (Kitov, 2009). To begin with, we modelled and predicted the evolution of share prices of ConocoPhillips (COP) and Exxon Mobil (XOM), which are classified in the S&P 500 list as related to energy. It was demonstrated that the time history of these prices could be accurately approximated by a linear function of the difference between core CPI and headline CPI in the United States. This difference is found to be the best to predict share prices in the energy subcategory of the S&P 500.

In this posts we are going to revisit those energy companies which shares were modelled in (Kitov, 2009) and (Kitov&Kitov, 2009) and check the predictive power of the underlying model. These companies are as follows: ConocoPhillips (COP), Chevron (CVX), Devon Energy Corporation (DVN), Halliburton (HAL), and Exxon Mobil (XOM).

The pricing model is common for all companies. It is simple. We assume the presence of a linear link between a share price and the difference between the core (or headline) CPI and some other subset of goods and services comprising the headline CPI. The intuition behind the model is simple; a higher pricing power for a given subcategory of goods and services, and thus related companies, is expressed in a faster increase in corresponding stock prices. In the first approximation, the deviation between relevant price indices is proportional to the ratio of the pricing powers. The presence of sustainable (linear or nonlinear) trends in the differences, as found in (Kitov&Kitov, 2008) allows predicting the evolution of the differences, and thus the deviation between prices for corresponding goods and services. The share prices have to follow up.

So, there exist sustainable trends in the differences between various subcategories of consumer (and producer) price indices. We consider the sustainability as an equivalent to the possibility to describe such trends by simple functions of time. Figure 1 shows that the difference between the core CPI, cCPI, and the headline CPI, CPI, can be approximated by a simple time function:

dCPI(t) = a + bt (1)

where dCPI(t) is the difference, a and b are empirical constants, and t is the elapsed time. Between 1981 and 1999, the linear trend has a slope +0.67, and from 2002 to 2008 the slope is (-1.65). Hence, the “distance” between the core CPI and the headline CPI is a linear function of time, with a positive or negative slope b. It might be of fundamental importance that absolute value of the ratio of the slopes is inversely proportional to the ratio of durations: │0.67/(-1.65)│≈7/19. If such a trade-off actually exists, one can predict the duration of the next trend from its slope.

Figure 1. The difference between the core CPI and the headline CPI between 1980 and 2008. There are two distinct periods from 1981 to 1999 and from 2002 to 2008, where the growth in the difference can be accurately approximated by linear functions of time with slopes +0.67 and -1.65, respectively. Notice that absolute value of the ratio of slopes is inversely proportional to the ratio of durations: │0.67/(-1.65)│≈7/19. The lower panel shows the beginning of the new trend in the difference.

Then, the pricing model states that a share price, for example, that of ConocoPhillips, COP(t), can be approximated by a linear function of the difference between the core and headline CPI (Kitov, 2009):

COP(t) = A + BdCPI(t + t1) (2)

where A and B are empirical constants (for COP, A=72 and B=-5.5) for the period between 1998 and 2009); t is the elapsed time; and t1=1/6 year is the time delay between the share and the CPI changes, i.e. the CPI has a lag behind the share price.

Empirical constants in (2) have to be determined for all distinct periods with different trends. This implies the possibility of structural breaks in the link between share price and CPI as caused by the turns to new trends. For example, the set of long-term economic bounds between goods and services, comprising the CPI and defining the linear trend in the dCPI between 1981 and 1999, underwent a three-year-long transition to a new set. In turn, the new set defined the trend observed from 2002 to 2008. So, it is reasonable to assume that the sign of slope in (2) should change to an opposite one after the end of the current transition period.

Figures 2 and 3 compare the original and updated predictions for COP and XOM. Coeffcients in (2) are given in the Figure captions.

Figure 2. The observed and predicted COP price. A2=72, B2=-5.5 (1999-2009). Upper panel - original model of 2009. Lower panel - updated for 2009 and 2010.

Figure 3. Same as in Figure 2 for XOM. A2=90, B2=-6 (1999-2009).

Figures 4 through 6 compare the original and updated predictions for Chevron, Devon Energy, and Halliburton. As for other energy-related companies, the difference driving relevant share prices is likely that between the core and headline CPI. The models for CVX, DVN, and HAL share price are the same in both cases:

CVX = -5.5*(cCPI - CPI) +85; 1999-2009

DVN = -7.7*(cCPI - CPI) +97; 1999-2009

HAL = -3.5*(cCPI - CPI) + 43; 1999-2009

The next move in all three shares will be up in line with the increasing oil price (Kitov, 2009). In the long run, the dCPI will likely be growing. The increasing difference will have the same effect on the prices in the future as always before – share price grows at a rate proportional to the slope in the dCPI.

Three companies in Figures 4 through 6 are characterized by different coefficients B between 2000 and 2010: from -3.5 (HAL) to -7.7 (DVN). Previously, we determined the slopes for COP (-5.5) and XOM (-6.0). Now one can conclude that these five energy-related companies demonstrate different levels of effectiveness in converting of the dCPI into share price.

Figure 4. The original and updated share price prediction for CVX

Figure 5. The original and updated share price prediction for DVN

Figure 6. The original and updated share price prediction for HAL

All in all, our concept gave a good prediction two years ago. All models are sound. Despite its striking dissimilarity to the mainstream concepts, our pricing model is deeply rooted in economics as expressed in terms of common sense: a higher pricing power achieved by a given company should be converted into a faster growth in corresponding consumer price index. So, the link between these two measured variables is, effectively, a causal one. If the evolution of the difference between various components of the CPI would have been a random walk, the mainstream stock pricing models would be correct. However, the existence of sustainable trends in the differences makes these models obsolete, at least for some companies from the S&P 500 list.

**References**

Kitov, I., (2009). ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finance, v. 2, pp. 129-134.

Kitov, I., Kitov, O., (2008). Long-Term Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101-112.

Kitov, I., Kitov, O. (2009). Modelling of selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany.

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