We have already presented our pricing model for Halliburton (NYSE: HAL). Also we have been routinely reporting on similar models for ConocoPhillips (COP) and ExxonMobil (XOM). All these models were based on our general concept that the evolution of any share price can be (quantitatively) represented as a weighted sum (or difference) of two CPI/PPI components. This pricing concept was developed four years ago by predicting share prices for a few energy companies. Essentially, we were trying to use the core CPI as an energy independent (dynamic) reference to the headline CPI which includes energy and, in turn, is related to oil price and thus the prices of energy companies. Therefore, we assumed that the difference between these two CPIs might be manifested in the energy pricing power relative to all other goods and services. At the later stages, the set of companies was extended to the S&P 500 list as a whole, and the model obtained new CPIs, time lags and a linear trend term.

ConocoPhillips and Exxon Mobil are the biggest energy companies and they have demonstrated almost the same sensitivity to the difference between the core,

*CC*, and headline CPI,*C*, i.e. their pricing models were almost identical. Halliburton’s share price was also modeled and showed a different sensitivity to the change in the defining CPIs. We made a tentative conclusion that COP and XOM might have a larger return to the investor considering energy stocks.Originally, we have demonstrated that the time history of a share price, p(t), (for example, HAL) could be accurately approximated by a linear function of the difference between the core CPI and the headline CPI in the United States. At the initial stage of our research, this difference was found to be the best to predict share prices of energy related companies. Mathematically, a share price,

*HAL**(t),*(we use a monthly closing price adjusted for dividends and splits) can be approximated by a linear function of the lagged difference between the core and headline CPI:*HAL(t) = 42 - 3.5dCPI(t+t*(1)

_{1})where

*dCPI(t+t*=CC(_{1})*t+t*)–C(_{1}*t+t*),_{1}*t*is the elapsed time, and*t*=0 year is the time delay between the share and the CPI change. In the original model, the CPI difference had no time lag behind the share price,_{1}*t*=0, and we covered the period between 1999 and 2009. The upper panel of Figure 1 shows the original model performance between July 2003 and February 2012, with the standard model error of $4.51._{1}Since 2009, the original model has been routinely validated by new data. Overall, it has demonstrated a good predictive power but we have also revealed some short-term deviations from observed prices. It was instructive to improve its performance and, using the experience with non-energy companies, to extend the set of defining CPIs. We have tested several pricing models for Halliburton with the same CPI and PPI components which were tested for ConocoPhillips and ExxonMobil. The extended set of defining indices includes: the core and headline CPI, the consumer price index of energy, E, and the producer price index of crude petroleum, OIL, together with the overall PPI. Thus, we tested models similar to (1) using two more differences for the period between 2001 and 2011. For this article, we have modeled the period between July 2003 and February 2012 with the same coefficients, which were obtained and reported in 2011:

HAL(t) = 30 - 0.30(CC - E);

*sterr =$4.85*(2)HAL(t) = 25 - 0.13(OIL - PPI);

*sterr =$9.34*(3)In other words, all coefficients in (1)-(3) were estimated by the least squares for the period between January 2001 and July 2011 and then used to describe the period through February 2012. The zero time lag was retained in the model similar to that in the ConocoPhillips and ExxonMobil models, where we found no time delay between the share price and defining differences. Unlike for COP, both standard model errors are larger than for the original model, i.e. the original model based on the headline and core CPI is the best among the three studied models. The upper panels in Figures 1 through 3 compare these three HAL models with zero time lags and no time trend. The modeling period is extended by seven months and the most important difference from the July 2011 is that the large excursion in the observed price has been well described by the dCPI. According to the best model, the current price is slightly undervalued.

At the same time, model (3) based on the producer price indices is the worst (

*sterr*=$9.34). This may mean that Halliburton does not depend much on the producer prices. Interestingly, the change in oil price does accurately describe the period of the financial crisis. However, the model fails to predict slow changes in the share price. Model (3) has failed to predict the recent price peak but this deviation was only a transient one – the observed price is back to the predicted level.Another possibility to improve the overall agreement between the observed and predicted prices is to allow for different coefficients for the defining CPIs, time lags and linear trend. The latter is an obvious component since we expect all share prices to rise with real economic growth. There models below have been estimated using these new features which have brought visible improvements as expressed by the standard model errors for the same period:

*HAL(t)= 3.48C(t) – 4.97CC(t-1) + 5.81(t-2000) + 249.24; sterr=$4.16 (4)*

*HAL(t)= -2.08CC(t-2) + 0.34E(t) + 7.61(t-2000) + 261.93; sterr=$3.55 (5)*

*HAL(t)= 0.96PPI(t) – 0.028OIL(t-7) – 3.33(t-2000) – 73.21; sterr=$4.13 (6)*

Model (5) provides the best explanation of the variability in the HAL share price since July 2003 using a time lead of only two months for the core CPI. The CPI of energy evolves in sync with the share. The CC slope is negative while the E slope is positive and thus we have the difference between the CPIs. The overall agreement between the observed and predicted prices is very good for the past nine years. The PPI model (6) is much better (

Finally, Figures 1 through 3 clearly indicate that the closing price in February 2012 was slightly undervalued and one can expect that the current deviation from the predicted price will disappear in the near future. The observed price may rise to $40-$42 per share in March/May 2012. The previous burst in price, observed between February and September 2011, has proved that the price quickly returns to the predicted level.

*sterr*=$4.13 instead of $9.35) with time leads (OIL leads the share price by seven months) than model (3) without lags. Instructively, that the OIL slope is very small - the HAL share price does not depend on oil directly, but rather through the consumer price of energy as model (5) suggests. The dCPI model (4) is also better than (1) but has lost its position.Finally, Figures 1 through 3 clearly indicate that the closing price in February 2012 was slightly undervalued and one can expect that the current deviation from the predicted price will disappear in the near future. The observed price may rise to $40-$42 per share in March/May 2012. The previous burst in price, observed between February and September 2011, has proved that the price quickly returns to the predicted level.

In the long-run, the expected fall in oil price at a five-year horizon down to $30 per barrel will likely (judging by model (5)) result in a proportional increase in HAL’s shares.

Figure 2. The observed HAL price and that predicted from the energy index, E, and the headline CPI. Upper panel: model (2); lower panel: model (5) with time delays and individual weights.

Figure 3. The observed HAL price and that predicted from the PPI of oil, OIL, and the overall PPI. Upper panel: model (3); lower panel: model (6) with time delays and individual weights.

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