First, we report on the performance of our pricing model linking share prices of energy companies with the difference between the headline and core CPI. In essence, we are trying to use the core CPI as an energy independent (dynamic) reference to the headline CPI index which includes energy. Then the difference might be related to the energy pricing power relative to other goods and services. This idea has proven to be fruitful for oil (energy) companies and other categories of companies in the S&P 500 index and other consumer price indices.

Our original pricing model states that a share price, for example, that of Chesapeake Energy Corporation, *CHK(t)*, can be approximated by a linear function of the difference between the core CPI, CC, and headline CPI, C:

CHK(t) = A + B (CC(t) - C(t)) (1)

where *A *and *B *are empirical constants; *t* is the elapsed time. It should be noted that both indices are fixed to be contemporary to the modeled price. Also, both linear coefficients (slopes) are equal, which might be an oversimplification. This model has proven its predictive power for many companies and we have been reporting on its performance since 2009.

In January 2011, we extended the set of defining indices by the consumer price index of energy, E, and the producer price index of crude petroleum, OIL, together with the overall PPI. We also introduced time shifts between the price and defining CPIs and varying coeffcients.

Here we estimate three new models for the period between July 2003 and January 2012. The relevant estimates of CPI and PPI through January 2012 have been retrieved from the BLS website. Figures 1 through 3 display the observed and predicted models. The best model are defined by standard error. For CHK, the best fit models are as follows:

CHK(t) = 3.73C(t+1)–2.05CC(t)–8.64(t-1990)-162.57 (2)

CHK(t) = 1.76CC(t+3) + 0.35E(t+1)-9.42(t-1990) – 248.05 (3)

CHK(t) = 0.91PPI(t+1) +0.032OIL(t+1) -5.30(t-1990) – 42.47 (4)

In all models, some future estimates of the defining indices are needed to describe the current price. This means that the CHK price is likely to drive the CPI and PPI components.

The model defined by CC and E is the best among these three models. It provides the smallest model error of $3.27. In any case, all models have predicted the sharp fall in the price in 2008 and the following recovery in 2009. The price has been falling since July 2011. The defining indices lag behind the CHK price and one could expect these indices not to grow fast in the first quarter of 2012. A slight fall in OIL and E is not excluded.

Figure 1. The observed CHK price and that predicted from the core and headline CPI; stdev=$3.69.

Figure 2. The observed COP price and that predicted from the core CPI and the consumer price index of energy; stdev=$3.27.

Figure 3. The observed CHK price and that predicted from the overall PPI and the producer price index of crude petroleum (domestic production); stdev=$4.13.

In its most general form, our pricing model states that a share price, *SP(t),* can be approximated by a linear function of the difference between two CPI components with different lags behind the price:

*SP(t) = A + B*_{1}CPI_{1}(t + t_{1}) + B_{2}*CPI*_{2}(t + t_{2}) + *C(t-t*_{0})

where *A,* *Bi, *and* C *are empirical constants for the studied period; *t* is the elapsed time; *t*_{1} and *t*_{2} are the time delays between the share and the CPIs, both to be determined. We seek to minimize the standard model error, RMSE, by the LSQ method in ordre to find all 6 coefficients (*A,Bi,C,t*_{i}) for two CPI components among the set of 92.

This approach was also successful for Chesapeake Energy Corporation. In January 2011, we estimated a preliminary model for CHK with a smaller set of major CPI categories and found the following model:

CHK(t)= -1.47ED(t-7) + 0.41E(t+1) +11.4(t-1990) – 12.1; RMSE=$2.68.

where ED(t-7) is the consumer price index of education which leads the price by 7 months.

In April 2011, we revisited the CHK model with 92 defining CPIs and found that the best-fit 2 model for *CHK(t)* is based on the index of tuition, other school fees, and child care (TUIT) contemporaneous with the share, and the index of energy (E) lagging by 2 months:

*CHK(t)= 0.52TUIT(t-0) + 0.43E(t+2) – 16.77(t-1990) – 21.48; *stdev=$2.64, March 2011* *

In other words, the price of a CHK share defines the behaviour of the index of energy and the model with TUIT explains the overall behaviour of the CHK price much better than models (1) through (3). Figure 4 depicts the observed and predicted price. The current version of the model is as follows:* *

*CHK(t)= 0.52TUIT(t-0) + 0.43E(t+2) – 16.99(t-1990) – 16.06; *stdev=$2.81, January 2012* *

The model error has increased since April 2011 to $2.81. This model is also depicted in Figure 4 and shows that the current price is slightly below the predicted one. We expect a correction to both predicted and observed prices in the near future. Figure 5 presents the evolution of the TUIT and E indices.

Figure 4. Observed and predicted CHK share prices. Upper panel: March 2011. Lower panel: January 2012.

Figure 5. The index of tuition, TUIT, and the index of energy, E.