Here we model the evolution of Apache (NYSE: APA) share price and evaluate its current level relative to that predicted by our pricing model. We also compare the APA model and the ConocoPhillips (COP) model in order to evaluate their relative performance. In other words, we estimate quantitatively which of these two companies provides a better return. Two main findings can be formulated as follows: 1) the current price is slightly lower than that predicted by the model; 2) both companies show the same level of return.

The first finding is not surprising. We have already reported that for many energy related companies (e.g. Newfield Exploration (NFX) and Peabody Energy (BTU)) our empirical models show that their current prices are highly undervalued. In this group, APA is not the worst. However, it is still slightly undervalued despite our 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 second finding is might be an expected one since the stock market seeks for the best return. Therefore, investments are redistributed in a way to provide some constant return. At least this approach should work for all successful companies in the same industry.

We assume that a share price of an energy company is likely to be driven by the change in the overall energy price or some of its components. Considering the secular increase (change) in the overall price level it is not the absolute change in energy prices what affects the stock price but the difference between the energy price and some energy independent price. The simplest model can be 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. Four years ago, these two indices were used in our original models for ConocoPhillips and Exxon Mobil (XOM) and are retained as a benchmark since then.

During these four years, the best model was that for COP. We use it as a benchmark showing the quality of the concept and its predictive power. Figure 1 depicts the observed and modeled COP prices. Taking into account the character of the defining CPIs (they include many irrelevant components which are measurement noise for the model) the agreement between curves is outstanding. One can consider the predicted price as a fundamental one. These are two broadest consumer price indices which define the fundamental price. 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. dollar at time t.

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

Accordingly, we depict in Figure 2 a similar model for APA. The best fit relationship is as follows:

APA(t) = 110 - 8.1(CC(t) - C(t)) (2)

The overall agreement is also good with the predicted and observed prices very close near the 2008 peak and the 2009 bottom. The recovery since 2009 has been described with a slight underestimation of the measured price, i.e. the actually observed growth was slightly stronger than the predicted one. This undervaluation was quickly compensated by the 2011 fall. Currently, the actual price is undervalued one by a few dollars.

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

Comparing the slopes in (1) and (2) one can estimate relative performance of APA and COP. These slopes define the price reaction to a given change in the CPI difference. For a one unit change in CC-C, the COP price changes by $5.35 and the APA price by $8.1. Since the price levels are approximately $67 and $100, respectively, the ratio of the slopes (0.66) completely corresponds to the ratio of price levels (0.67). This means that the returns provided by COP and APA are equal if their prices are driven by the difference between CPIs.

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. 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 PPI and OIL:

APA(t)= 5.83C(t) - 5.81CC(t-0) + 3.81(t-2000) + 28.53; sterr=$9.13 (3)

APA(t)= 2.69CC(t-9) + 0.57E(t) - 8.25(t-2000) - 447.41; sterr=$8.81 (4)

APA(t)= 1.66PPI(t-0) - 0.059OIL(t-9) - 1.25(t-2000) - 175.90; sterr=$7.68 (5)

where APA(t) is the (monthly closing) share price in U.S. dollar. We allowed both time leads in (3) through (5) to vary between 0 and 12 months. Figures 3 through 5 depict the observed and predicted monthly prices from (3) through (5). For an oil company, it is not excluded that oil controls its price. Interestingly, however, that the index of oil drives the price down, i.e. increasing oil price suppresses the return. From Figure 5, we expect the price to rise to $115 in the near future. Oil price may fall in this case. Thus, we suggest that APA is currently a more attractive company since it is slightly undervalued and provides the same return in the long run as COP.

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

Figure 4. The observed and predicted monthly closing prices for APA between July 2003 and

March 2012. The model is based on CC and E.

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

**Disclosure: **I have no positions in any stocks mentioned, but may initiate a long position in COP, XOM over the next 72 hours.