Analysis: Chesapeake Energy Corporation's share price

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 + B₁CPI₁(t + t₁) + B₂CPI₂(t + t₂) + C(t-t₀)                                       

where A, Bi, and C are empirical constants for the studied period; t is the elapsed time; t₁ and t₂ 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.

PPI of metals

We have been following the evolution of several price indices of metals since 2008. Our general approach is based on the presence of long-term sustainable (linear and nonlinear) trends in the evolution of the CPI and PPI in the United States. The difference between various components of these indices is not a random one but rather a predetermined process. Using these trends, one can predict consumer and producer price indices for select goods, services and commodities. 

In this post, we revisit the trends in the PPI of three commodities related to metals: steel iron, nonferrous metals, and metal containers. Originally, we reported on these items in 2008 and then revisited in 2010.  

1.               Figure 1 compares the difference between the PPI and the index for iron and steel (101). The difference is characterized by the presence of a sharp decline between 2001 and 2008. Between 1985 and 2000, the curve fluctuates around the zero line, i.e. there was no linear trend in the absolute difference. A year ago we expected the negative trend to start transforming into a positive one as the green line in Figure 2 shows. Our previous predictions were correct. For example, two years ago we wrote:

“Between March and June 2009, the difference continued to increase, and likely reached its peak in June (Figure 2). In July or August 2009, the difference will stall around its peak value and then will start to decrease. As a result, the index for iron and steel will be growing faster than the PPI. In the short run, one can expect a fast recovery of iron and steel prices to the level observed in January-March 2008, i.e. the index will reach the level 210 to 220. However, this recovery will not stretch into 2011, and the index of iron and steel will be declining in the long run to the level of 2001, as depicted in Figure 2.  In other words, the period between 2008 and 2010 is characterized by very high volatility, which will fade away after 2011. “  

2.     The index for non-ferrous metals (102) shows an example of the absence of sustainable trends in the normalized difference. The curve is rather a comb with teeth of varying width. Although varying, the distance between consecutive troughs is several years at least. Therefore, we expect this index to decrease relative to the PPI and the difference in Figure 3 to rise to the level of -10. Non-ferrous metals will be getting cheaper.   

3.             The index for metal containers (103) provides an excellent example of linear trends in the normalized difference (see Figure 4). There are two distinct periods between 1960 and 2008 with a turning point in 1987. As we predicted in 2009, the sudden drop in the difference in the end of 2008 manifested the start of transition to a new period with a negative trend. The price index for metal containers will be increasing relative to the PPI, i.e. the index will get back its price setting power.   

Figure 1. The difference updated for the period between June 2010 and January 2012. As expected, the difference has been decreasing during the reported period and sank below the new trend (green). The trajectory has to turn up in the near future and reach the new trend.  This means that the price index for iron and steel will be growing at a lower rate than the overall PPI.   

Figure 2. The evolution of the difference between the PPI and the price index of iron and steel between January 2005 and January 2012. Green line predicts the evolution of the difference after 2008. Red circles represent the difference between April 2009 and January 2012.

 Figure 3.  The evolution of the difference between the PPI and the index of nonferrous metals from 1985 and January 2012. There are no linear trends in the difference, but its behavior demonstrates a clear periodic structure with relatively deep but short troughs, which reflect the fast growth in the PPI for nonferrous metals. 

Figure 4. The evolution of the difference between the PPI and the index of metal containers from 1985 to January 2012. There are distinct linear trends in the difference. The difference has started its transition to a negative trend.

The rate of unemployment in the UK will likely rise to 9%

We estimated a version of Okun’s law for the UK in July 2011. We developed an integral version of Okun’s law and applied the LSQ method to estimate coefficient in :

u(t) = u(t₀) + bln[G/G₀] + a(t-t₀)  (1)

where u(t) is the predicted rate of unemployment at time t, G is the level of real GDP per capita, a and b are empirical (LSQ) coefficients.   The best-fit (Okun’s) model minimizing the RMS error of the cumulative model (1) is as follows:

du = -0.39dlnG + 0.63 (2)

The most recent estimate on the unemployment rate in the UK is 8.4% for the fourth quarter of 2011 as reported by the NSO for the economically active population between 16 and 64 years of age. The Conference Board has also published an estimate of real GDP per capita for 2011. Figure 1 depicts the observed and predicted curves of the unemployment rate, including the rates for 2011. The overall agreement is very good but the current rate of unemployment is lower than the predicted one by 0.6%.  Figure 1 suggests that the rate of unemployment has been driven by real economic growth and one can expect the rate to grow to the level of 9.0%. The will be no decease in the rate of unemployment if the growth rate of real GDP per growth does not exceed (0.63/0.39=) 1.63% per year.  In 2011, this rate was only 0.09%.

Figure 1.  The observed and predicted rate of unemployment in the UK between 1971 and 2011. 

How CPI drives the federal funds rate

The interest rate defined by the Federal Reserve is an instrument to control inflation. Ignoring the heaps of quasi-economic lie around the effect of the monetary policy we just present some observations.  Figure 1 depicts the effective rate, R, and the consumer price inflation. The former has to control the latter. One can see that the rate lags behind the CPI since 1980, i.e. inflation grows at its own rate and R has to follow up. The idea of R is that a higher rate should suppress inflation due to the effect expensive money. The reaction of inflation is also expected not momentarily but with some time lag.

The cumulative influence of the interest rate should produce a desired effect in the long run and inflation should go in the direction towards bearable values. Figure 2 displays the cumulative effect, i.e. the cumulative values of the monthly estimates of R and CPI multiplied by 1.4. This is an intriguing plot. In the long run, the R curve fluctuates around the CPI one and returns to it every 15 to 20 years. It seems that the sign of deviation of R from the 1.4CPI curve does not affect the behavior of the CPI. Therefore, the influence of monetary policy is under strong doubt. The Feds have tried all means to return the CPI to R without any success and have to return R to the CPI.  

Figure 1. The federal funds rate, R, and the rate of consumer price inflation, CPI, between 1956 and 2012.

Figure 2. Cumulative values of the monthly estimates of R and CPI multiplied by a factor of 1.4.

A paradox of income inequality among young people

We have already presented the evolution of Gini coefficient in the USA since 1994 as measured by the Census Bureau. Figure 1 depicts time series in all age groups including the youngest ones. The difference between the age group between 15 and 24 and 25 to 34 is astonishing. In the youngest age group, the level of income inequality is the highest. Gini coefficient fluctuates around 0.51. In the second youngest group, Gini is rock solid at the level of 0.42. And both coefficients are calculated only for people with income, i.e. the portion without income does not influence the Gini estimates.
Figure 2 shows the Gini as a function of age for some selected years. The lowermost Gini belongs to the group between 24 and 34 and then starts to grow to the level of the youngest group. There should be two competitive mechanisms to produce this minimum.

Figure 1. The evolution of Gini coefficient in various age groups between 1994 and 2009.

Figure 2. Gini coefficient as a function of age

Modeling Avery Dennison's share price

This is a regular revision of our stock pricing model as applied to Avery Dennison Corporation (AVY). We decompose the time series of a given share price into a weighted sum of two individual consumer price indices plus linear time trend and free term over an extended period of time. The best fit model has to provide the lowermost RMS residual and also do not change with time.

In April 2011, we presented an original model for Avery Dennison Corporation based on the consumer price index of food (F) and that of new and used motor vehicle (NUMV). In the original model, the former CPI component led the share price by 4 months and the latter one led by 2 months. Figure 1 depicts the evolution of both (NSA) CPIs through January 2012. The upper panel of Figure 2 displays the predicted and observed monthly closing prices (adjusted for splits and dividends) as of March 2011.

In September 2011, we revisited the model using the prices and CPIs for the period through September 2011. (The CPIs were available only for August 2011.) The principal result was that the underlying model is practically the same as six months before with the same time lags but slightly different coefficients. In March 2011, we predicted a fall in the price which actually happened. In September, we expected that AVY stocks would be falling by the end of 2011 down to $16 per share from the September closing level $25.08 (see the middle panel in Figure 2). This was not a good prediction.

Here we revisit the model using data through January 2012 (see the lower panel in Figure 2). The three best-fit models for AVY(t) are as follows

AVY(t) = -4.24F(t-4) – 3.23NUMV(t-2) + 23.29(t-1990) + 799.24 , March 2011

AVY(t) = -3.92F(t-4) – 2.70NUMV(t-2) + 21.60(t-1990) + 710.60 , September 2011

AVY(t) = -3.61(t-5) – 2.10NUMV(t-3) + 19.86(t-1990) + 622.01 , January 2012

where AVY(t) is a share price in US dolalrs, t is calendar time. Relevant coefficients are both negative. The slope of time trend is positive. There is some drift in all coefficients caused by the uncertainty in measurements of both the stock prices and CPIs and by a slight collinearity between the CPI difference and linear time trend. Nevertheless, all models provide a prediction at a two- to three-month horizon.

The currently predicted curve in Figure 2 leads the observed price by 3 months with the residual error of $2.81 ($2.57 in September) for the period between July 2003 and January 2012. The model residual for the same period is shown in Figure 3. We expect the actual price to have a slight negative correction in the near future and the predicted curve to grow up in order to close the gap between the predicted and observed prices. The residual in Figure 3 has to return to 0. This might be accompanied by a slight fall in food prices.

Figure 1. Evolution of the price of F and NUMV.

Figure 2. Observed and predicted AVY share prices. Upper panel – March 2011; middle panel – September 2011; lower panel – January 2012.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.81. Currently, the price is slightly overestimated.

Modeling Exxon Mobil's share price

In this post, we describe the pricing model for Exxon Mobil’s (XOM) share as based on our concept of stock dependence on consumer price index. Unlike in the simplified model for ConocoPhillips’ share, which included only the core and headline CPI, here we use a set of 92 individual consumer price indices to select the best two.  

Exxon Mobil provides an example of a company with share price leading defining components of the CPI.  Our model is seeking two CPI components from a large number of pre-selected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and January 2012. A two-component (2-C) model also includes free term (constant) and linear time term, which compensates well know linear (time) trends between various CPI components. The best-fit 2-C model for XOM(t) is as follows: 

XOM(t)= -1.70OFH(t-3) – 2.98RRM(t-10) + 22.73(t-2000)  + 581.17 

where OFH in the index other food at home lagging  the stock price by 3 months, RRM is the index of recreation reading materials leading by 10 months, (t-2000) is the elapsed time. Figure 1 depicts the evolution of both CPIs.  

Figure 2 depicts the observed and predicted prices, the latter shifted three months ahead for synchronization, i.e. the predicted curve leads the observed price by 3 months. The model residual error shown in Figure 3 has standard deviation of $4.41 for the period between July 2003 and January 2012.   

The estimated model shows that Exxon Mobil’s share will be growing in 2012Q1.

Figure 1. The evolution of CPIs.

Figure 2. Observed and predicted XOM share prices.

Figure 3. The model error.