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Time To Buy SPY
A month ago, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. Figure 1 shows the predicted behavior in April and May 2012, with the predicted segment shown by red line. We expected that the path observed in the previous rally would be repeated with the bottom points coinciding. Now the prediction has realized and the expected level has been reached. (There is some room for a slight fall.)
We also suggested buying the index when it is 1300. It's done by now. We are waiting the level 1500 in October 2013 to sell.
We also expect oil price to drop further and to force deflation by the end of 2012.
(click to enlarge)
Figure 1. The original S&P 500 curve (black line) and that shifted forward to match the 2009 trough (blue line). Red line  expected fall in the S&P 500: from 1400 in March to 1300 in May. It's been realized by now.
Disclosure: I am long SPY.
Cameron International Share Price
Cameron International Corporation provides flow equipment products, systems, and services worldwide. Here we demonstrate that the time history of a CAM share price, CAM(t), can be accurately approximated by a linear function of the difference between the core CPI, CC, and the headline CPI, C, in the United States. We test two more pricing models with the consumer price index of energy, E, and the difference between two PPI components: the overall PPI and the PPI of oil, OIL. Our goal is to find the model which describes the observed prices the best according to the LSQ criterion.
Three models below have been estimated together with their standard model errors for the same period between July 2003 and February 2012:
CAM(t)= 2.72C(t)  3.03CC(t) + 3.75(t2000) + 38.40; sterr=$5.11 (1)
CAM(t)= 0.56CC(t9) + 2.5E(t)  0.25(t2000)  134.20; sterr=$4.95 (2)
CAM(t)= 0.12PPI(t9) +0.12OIL(t) + 3.27(t2000)  30.55; sterr=$4.12 (3)
Model (3) provides the best explanation of the variability in the CAM share price since July 2003. The PPI of oil evolves in sync with the share, which grows proportionally to oil price. The PPI slope is negative and thus the growth in producer prices suppresses the growth in CAM price. Figures 1 through 3 clearly indicate that the closing price in February 2012 was estimated accurately and we do not expect any correction beyond the natural evolution according to (3).
Figure 1. The observed CAM price and that predicted from the core and headline CPI.
Figure 2. The observed CAM price and that predicted from the energy index, E, and the headline CPI.
Figure 3. The observed CAM price and that predicted from the PPI of oil, OIL, and the overall PPI. The high and low monthly prices represent the uncertainty of the observed price.
Disclosure: I have no positions in any stocks mentioned, but may initiate a long position in CAM over the next 72 hours.
Analysis: Chesapeake Energy Corporation's Share Price
Our original pricing model states that a share price, for example, that of Chesapeake Energy Corporation, CHK(NYSE:T), can be approximated by a linear function of the difference between the core CPI, CC, and headline CPI, C:
CHK = A + B (CC  C) (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 coefficients.
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 models are defined by standard error. For CHK, the best fit models are as follows:
CHK = 3.73C(t+1)2.05CC8.64(t1990)162.57 (2)
CHK = 1.76CC(t+3) + 0.35E(t+1)9.42(t1990)  248.05 (3)
CHK = 0.91PPI(t+1) +0.032OIL(t+1) 5.30(t1990)  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, can be approximated by a linear function of the difference between two CPI components with different lags behind the price:
SP = A + B_{1}CPI_{1}(t + t_{1}) + B_{2}CPI_{2}(t + t_{2}) + C(tt_{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 order 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= 1.47ED(t7) + 0.41E(t+1) +11.4(t1990)  12.1; RMSE=$2.68.
where ED(t7) 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 bestfit 2 model for CHK is based on the index of tuition, other school fees, and child care (TUIT) contemporaneous with the share, and the index of energy (NYSE:E) lagging by 2 months:
CHK= 0.52TUIT(t0) + 0.43E(t+2)  16.77(t1990)  21.48; stdev=$2.64, March 2011
In other words, the price of a CHK share defines the behavior of the index of energy and the model with TUIT explains the overall behavior 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= 0.52TUIT(t0) + 0.43E(t+2)  16.99(t1990)  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.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.