Share prices (sp) of energy companies showed an excellent relation to the difference between core CPI (cCPI) and headline CPI (CPI) in the USA (see our papers and posts). Wa have studied five companies of different size: XOM, COP, CVX, DVN, and HAL. The latter company is not pure energy one, but has a tight link to oil and gas extracting companies. The principal result of our share price modelling is that the price is represented by a linear function of the difference:

sp(t+t1) = A + B[cCPI(t) – CPI(t)] (1)

where A and B are empirical constants, t1 is the time lag of the CPI behind the change in share price. The slope B is of particular importance because its absolute value depends on the rate of growth of the difference.

Previously [1,2], we have estimated constants A and B for all five companies together with some companies in other subcategories of the S&P 500 list. In general, bigger companies reveal the same slope B between -5.5 and -6.0 for the period from 1999 to 2009. DVN showed a larger (in absolute terms) slope of -7.7, and HAL the smallest slope -3.5. This finding indicates that DVN is likely of higher efficiency in translation of oil price, i.e. cCPI-CPI, into share price. HAL was and is a less efficient company in sense of usage of the rally in oil price since 2002.

Relationship (1) implied a direct causality – share prices affect the CPI and its components with some time lag t1>0. This direction of causality is obvious. However, one can predict the evolution of share prices using (1). This prediction is based on the empirical observation that the difference between the core and headline CPI is characterized by the presence of long-term sustainable trends. In other words, when a new trend emerges one can link given share prices to the evolution of cCPI-CPI over the whole period where the trend exists. Two previously observed periods were between 1982 and 1999 and between 2001 and 2009, i.e. 19 years and 8 years. So, when the slope of the most recent trend became clear one could forecast several years ahead. Moreover, since the trend was negative, a working assumption on the next turning point could be related to the intersection with the zero line. We used this assumption predicting the turn in the middle of 2008 [2].

All above findings have been already reported. This post concerns another crucial issue – the current transition to the new trend in the difference between the core and headline CPI. There are several related questions:

Where does the old trend fade away?

When does the new trend emerge?

Is it possible to estimate the slope of the new trend when the old trend disappears?

or

Is the transition period characterized by a (nonlinear?) relation different from (1)?

sp(t+t1) = A + B[cCPI(t) – CPI(t)] (1)

where A and B are empirical constants, t1 is the time lag of the CPI behind the change in share price. The slope B is of particular importance because its absolute value depends on the rate of growth of the difference.

Previously [1,2], we have estimated constants A and B for all five companies together with some companies in other subcategories of the S&P 500 list. In general, bigger companies reveal the same slope B between -5.5 and -6.0 for the period from 1999 to 2009. DVN showed a larger (in absolute terms) slope of -7.7, and HAL the smallest slope -3.5. This finding indicates that DVN is likely of higher efficiency in translation of oil price, i.e. cCPI-CPI, into share price. HAL was and is a less efficient company in sense of usage of the rally in oil price since 2002.

Relationship (1) implied a direct causality – share prices affect the CPI and its components with some time lag t1>0. This direction of causality is obvious. However, one can predict the evolution of share prices using (1). This prediction is based on the empirical observation that the difference between the core and headline CPI is characterized by the presence of long-term sustainable trends. In other words, when a new trend emerges one can link given share prices to the evolution of cCPI-CPI over the whole period where the trend exists. Two previously observed periods were between 1982 and 1999 and between 2001 and 2009, i.e. 19 years and 8 years. So, when the slope of the most recent trend became clear one could forecast several years ahead. Moreover, since the trend was negative, a working assumption on the next turning point could be related to the intersection with the zero line. We used this assumption predicting the turn in the middle of 2008 [2].

All above findings have been already reported. This post concerns another crucial issue – the current transition to the new trend in the difference between the core and headline CPI. There are several related questions:

Where does the old trend fade away?

When does the new trend emerge?

Is it possible to estimate the slope of the new trend when the old trend disappears?

or

Is the transition period characterized by a (nonlinear?) relation different from (1)?

We begin with the illustration of the previous change in the trend. Figure 1 displays observed COP (monthly close adjusted for splits and dividends) share price and that predicted according to (1) with empirical coefficients A=80 and B=-6.0 estimated for the period between April 1998 and May 2009. The observed and predicted share prices diverge from March 1998. However, when the coefficients A=+2.5 and B=-8 obtained for the earlier period are applied the predicted curve does not deviate much from that with the coefficients for the later period before 2000. Thus, one can not distinguish between two sets of coefficients and the transition period has a dualistic properties.

Figure 2 depicts the difference between the core CPI and headline CPI between 1985 and 2005, with the vertical red line corresponding to March 1998. There was no dramatic change in the difference around 1998 except a slight increase in slope in the late 1997. Therefore, it is possible that the transition period started in the late 1997 and lasted till 2000. Arbitrary, we have chosen relationship (1) with A=80 and B=-6.0 to reign since March 1998. All in all, one can conclude that the transition was not associated with any visible change in the behavior of the cCPI-CPI except the segment with a higher volatility between 1999 and 2001. Same behavior in expected during the current transition period – one can not distinguish between the old and new sets of coefficients in (1).

We are interested to know the performance of (1) during the most recent period and find any signs of the new trend. Figures 3 though 7 compare observed share prices of the five companies and those predicted by visual fit by relationship (1). All predicted curves are shifted by 2.5 months ahead in order to synchronize them with the observed curves. This implies that share prices are converted into consumer prices with a delay of 2.5 months. Figure 8 compares all prices for the period after 2007 with the difference cCPI-CPI not shifted.

Results of the modelling will be scrutinized later on, but at first glance, one can formulate some preliminary findings:

- All share prices still obey (with varying accuracy) the empirical relationships obtained for the previous period.
- DVN has been demonstrating the higher effectiveness of the conversion of oil price into share price. Currently, this effectiveness has a slight negative effect – the deepest fall in share price. Among all studied companies, the observed DVN price in the best modelled.

XOM is the most conservative company. It has the smallest rise in price during the 2007-2008 rally and the smallest fall in 2009. - The change in HAL share price leads that for other companies by 0.5 months. It might be of usage for short-term investors. However, HAL share price has been falling with a slight overshoot in 2008-2009, i.e. below the level predicted from cCPI-CPI. It might be an indication of the transition to the new relationship as well.
- CVX is also a reliable company with the price fell less than predicted.

The predicted price of COP share fits the observed one over the entire period. Potentially one might be interested in finding a better pair of CPI components instead of the core and headline CPI. At first stage, we focus on the effect itself and do not optimize the prediction. - Last but not least. Since the difference cCPI-CPI will be decreasing in the near future, all share prices will be growing according to the old coefficients in (1).

*Figure 1. The transition between two periods with different constants A and B in relationship (1) in March 1998 .*

*Figure 2. The difference between the core CPI and headline CPI. Vertical line corresponds to March 1998. There was no dramatic change in the difference around 1998 except a slight increase in slope in the late 1997.*

*Figure 3. Observed and predicted COP share price. The predicted curve is shifted 2.5 months ahead in order to synchronize it with the observed one.*

*Figure 4. Observed and predicted CVX share price. The predicted curve is shifted 2.5 months ahead in order to synchronize it with the observed one.*

*Figure 5. Observed and predicted DVN share price. The predicted curve is shifted 2.5 months ahead in order to synchronize it with the observed one.*

*Figure 6. Observed and predicted HAL share price. The predicted curve is shifted 2.5 months ahead in order to synchronize it with the observed one.*

*Figure 7. Observed and predicted XOM share price. The predicted curve is shifted 2.5 months ahead in order to synchronize it with the observed one.*

*Figure 8. Comparison of share prices of five energy-related companies between January 2007 and May 2009. The cCPI-CPI is shown by red line and lags behind other curves by 2.5 months.*

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