In this article we model the evolution of Peabody Energy (BTU) share price since 2003 and evaluate its current level relative to that predicted by the model. The main finding can be formulated as follows: the current price is much lower than that predicted by the model. At the same time, the same model has accurately predicted the rally between 2003 and 2007, the sharp fall in 2008 and the following recovery up to the third quarter of 2011. The same effect is observed for many energy companies, as we have already reported on Seeking Alpha. For example, Newfield Exploration (NFX) and GeoResources (NASDAQ:GEOI) demonstrate high-amplitude deviations from their relevant predicted prices but with opposite signs. Thus, we have been measuring strikingly abnormal deviations in share prices of many energy related companies since the middle of 2011. This observation needs careful analysis and investors' attention.

Our pricing concept is very simple and we explain it here step by step. First, we put forward a working hypothesis that a share price of an energy company can be driven by the change in the overall energy price or its components. Obviously, energy prices do not exist in vacuum: they affect and are affected by other goods and services. Therefore, we actually assume that the share price is driven by the difference between the energy price and some energy independent price, both can be presented as indices.

In its simplest form, the model is based on the difference between the headline CPI, *C*, and the core CPI, *CC*, without any time lag between these indices and the share price. The headline CPI includes all kinds of energy and thus provides the broadest proxy to the energy price index. The core CPI excludes energy (and food) and thus represents the energy independent and dynamic reference. Historically, these two indices were used in our original models for ConocoPhillips (COP) and Exxon Mobil (XOM) and are retained as a benchmark since then.

The best ever model was obtained for COP. Figure 1 depicts the observed and modeled COP prices in order to demonstrate the predictive power of the pricing concept. The agreement between curves is excellent. One can see that all deviations of the actual price from the predicted one are only short-term and the predicted curve might be considered as a "fundamental" one. In other words, the actual price gravitates to the predicted one. Quantitatively, we have estimated the following relationships to minimize the model error between 1998 and 2012:

COP(t) = 72.3 - 5.35(CC(t) - C(t)) (1)

where COP(t) is the share price in U.S. dollars at time t. In any case, both curves are close to each other throughout the whole period and there is deviation growing since 2011.

Figure 1. Historic (monthly closing) prices for COP (black line) and the scaled difference between the core CPI and the headline CPI (red line).

In Figure 2 we present a similar model for BTU. The best fit relationship is as follows:

BTU(t) = 59.5 - 5.55(CC(t) - C(t)) (2)

The overall agreement is also excellent with the predicted and observed prices very close near the 2008 peak and the 2009 bottom. The recovery since 2009 has been also described accurately to the peak value in April 2011. And then the prices started to deviate, which the predicted price falling at a much slower pace. In this situation one may consider the currently observed price as an highly **undervalued** one (between $20 and $25).

Figure 2. Historic (monthly closing) prices for BTU (black line) and the scaled difference between the core CPI and the headline CPI (red line).

The original model is very crude. Both CPIs depend on many other goods and services, what introduces high measurement noise in the model. Also, both CPIs have the same weight (1.0) and cannot lead or lag behind the modeled price or each other. Apparently, it can be some non-zero lag between the change in energy price and in prices of energy companies. Therefore, we extended the model and described the evolution of a share price as a weighted sum of two individual consumer price indices (or PPIs) selected from a large set of CPIs borrowed from the Bureau of Labor Statistics. We allow both defining CPIs (PPIs) lead the modeled share price. Additionally, we introduced a linear time trend on top of the intercept.

So, we continue presenting Peabody Energy Corporation which is engaged in the mining of coal. This is not an oil&gas company and we do not expect it directly depend on oil price. As for many already presented companies, we have tested two principal pairs of CPIs: C and CC; CC and the index of energy, E, as well as the pair the PPI and the producer price index of crude oil, OIL. The best fit (as defined by standard error) model is obtained with the pair CC and E:

*BTU(t)= 5.21C(t) - 5.09CC(t-0) - 0.45(t-2000) + 40.84; sterr=$7.85 (3)*

*BTU(t)= 1.34CC(t-9) + 0.52E(t) - 6.57(t-2000) - 228.58; sterr**=$7.02**(4)*

*BTU(t)= 1.46PPI(t-0) - 0.0346OIL(t-6) - 4.77(t-2000) - 123.01; sterr=$7.86 (5)*

where BTU(t) is the share price in U.S. dollars; the core CPI leads the price by 9 months. We allowed both time leads in (3) through (5) to vary between 0 and 12 months. As one can expect, the index of energy drives the price up. Surprisingly, the core CPI also affects the price positively and the long term time trend in both defining CPIs is compensated by the negative time trend. Figures 3 through 5 depict the observed and predicted monthly prices.

The best model shows even a better overall agreement than the original model with the standard error of $7.02 between July 2003 and February 2012. As we discussed above, the model residual has been growing since the second half of 2011. Currently, the error is -$23. This is an extremely high residual relative to the "fundamental" price. We believe that the current excursion is just a short-term deviation. Therefore, the BTU price is highly **undervalued**.

The reader may also suggest that the model has failed on BTU. We cannot exclude this explanation but then why the concept works for the biggest energy companies and has also been working relatively well before August 2011?

Figure 3. The observed and predicted monthly closing prices for BTU between July 2003 and |March 2012. The model is based on C and CC.

Figure 4. The observed and predicted monthly closing prices for BTU between July 2003 and |March 2012. The model is based on CC and E.

Figure 5. The observed and predicted monthly closing prices for BTU between July 2003 and March 2012. The model is based on PPI and OIL.

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