A share price model for Forest Laboratories between 2009 and 2011

Forest Laboratories (FRX), like Abercrombie & Fitch, also was one of the first companies with a stable and deterministic share price model estimated in September 2009 (back into November 2008).  This is a company from Healthcare subcategory of the S&P 500 list specialized in drugs manufacturing. We revisited this model in September and December 2010 and always found the same defining variables with almost the same time lags.

Our approach to deterministic share pricing (we have been tracking approximately 70 companies from S&P 500) is based on the decomposition of a share price into a weighed sum of two selected consumer price indices. For FRX, all models between 2009 and 2011 are defined by the (not seasonally adjusted) index of dairy and related products (DAIRY) and the price index of other household equipment and furnishing (OHEF), as reported by the US BLS. The former CPI component leads the share price by 3 month and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011.

In this post, we compare the 2009 and 2011 share price models for FRX. For the 2009 model we use the most recent defining CPIs, as available in April 2011, and the measured monthly closing prices through March 2011. This allows validating the initial model and demonstrating its reliability.  These models are as follows:

FRX(t) =  -0.53DAIRY(t-3) – 4.18OHEF(t-5)  - 13.41(t-1990) + 706.57 (September 2009)   

FRX(t) =  -0.61DAIRY(t-3) – 3.89OHEF(t-4)  - 11.65(t-1990) + 668.75 (March 2011)   

where t is calendar time. All coefficients are close with just minor variations related to the updated share prices. Therefore, the model is effectively the same between November 2008 and March 2011. In other words, we obtained a deterministic (leading by three months) model which was valid during 30(!) months.   Figure 2 illustrates the difference between the original and current models.  

The residual error is $4.40 for the period between June 2003 and March 2011. From the most recent model in Figure 2, we expect a fall to the level of $20 per share in 2011 Q2.

 

Figure 1. Evolution of the price of DAIRY and OHEF.

Figure 2. Observed FRX share prices and that predicted in 2009 and 2011. The early model has a larger time lag for the OHEF index which results in a slight underestimation of the share price in 2010 and 2011.  

Alcoa share price

Alcoa (AA) is a company from Materials subcategory of the S&P 500 list specialized in aluminum. According to our general approach to share price modeling we decompose the observed time history of the monthly closing AA stock price (adjusted for splits and dividends) into a weighted sum of two CPI components, time trend and free term.  Two defining CPI components are selected to minimize the model (RMS) error and may lead or lag behind the share.  

The AA model is defined by the (not seasonally adjusted) index of food away from home (SEFV) and the price index of rent of primary residence (RPR), as reported by the US BLS. The former CPI component leads the share price by 2 months and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011. It seems these indices have been evolving in sync since 2002 with the only step-like change in the SEFV in 2008.  The final empirical pricing model for AA is as follows:

AA(t) =  -6.71SEFV(t-2) + 3.34RPR(t-4)  + 19.23(t-1990) + 298.87

where AA(t)  is a share price in US dollars, t is calendar time. Figure 2 illustrates the observed and predicted models.  The residual error is $3.12 for the period between July 2003 and March 2011. One can expect the share price to hover at the level of $15 in the near future.  

Figure 1. Evolution of the price of SEVF and RPR.

Figure 2. Observed and predicted AA share prices.

Krugman's misinterpretation of long-term inflation

Paul Krugman has shown the evolution of headline CPI (level) since 2000 in order to demonstrate that the current trend manifests upcoming inflation. His conclusion is likely wrong due to couple mistakes in the presentation and interpretation.

1. He narrowed the period to ten years and thus implied that the headline CPI trend was the same before 2000 and will be extended into the 2010s. Both assumptions are not true.

Figure 1 definitely shows that the trend before 2000 was different from the current one. Between 1980 and 1998, the headline CPI grew at a lower rate than the core CPI and they diverged. In 2000, the indices started to converge and the CPI curve intercepted the core CPI one in 2009. Very likely that the future trend will repeat that observed between 1980 and 2000, not continue the trend observed in the 2000s.

Therefore, the core CPI will be growing at a higher rate again and the headline CPI will sink below the core CPI level. Then the CPI inflation rate will be smaller than that defined by the core CPI. 

Figure 1.  Upper panel: The headline and core CPI levels between 1980 and 2011. Lower panel: the difference between the core and headline CPI demonstrates linear trends. One may expect the next trend to be positive and the headline inflation rate will be lower that the core inflation rate.  Krugman's assumption on the long-term trend in the headline CPI was not correct.

2. The core inflation rate has been on decline since 2007, as Figure 2 shows. Despite very high volatility, the headline CPI always returned to the core CPI level. Our inflation model [1] shows that the current trend in the core CPI will be retained in the next decade below the zero line. Hence, the overall inflation rate will be also negative. An extended deflationary period will be observed.

Figure 2. The rate of price inflation as defined by the headline and core CPI.

1. Kitov, I. (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

FOMC on inflation

Several days ago we presented a graph (see Figure 1) with headline and core (CPI) inflation which showed a downward trend in the core price inflation. Yesterday the Federal Open Market Committee (FOMC) issued a press release also addressing inflation among other topics. Specifically, the FOMC said:

…. Inflation has picked up in recent months, but longer-term inflation expectations have remained stable and measures of underlying inflation are still subdued…

The Committee will … continues to anticipate that economic conditions, …, subdued inflation trends, and stable inflation expectations, are likely to warrant exceptionally low levels for the federal funds rate for an extended period.

Hence, the FOMC is currently expecting that the surge in oil price will calm down and the CPI will fall back below the core CPI in the next few quarters. In Economic Projection, the expected central tendency of price inflation (PCE) in 2012 is between 1.2 and 2.0 per cent per year with the range 1.0 and 2.8 % per year. 

We still expect that the core CPI inflation will fall below the zero line in 2012 and the headline CPI will rebound from its current higher level below the core CPI manifesting a deflationary period in the US [1].

Figure 1. The rate of price inflation as defined by the headline and core CPI.

Kitov, I. (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

Abercrombie & Fitch between 2009 and 2011

Abercrombie and Fitch (ANF) was one of the first companies with a stable and deterministic share price model estimated in September 2009.  This is a company from Services subcategory of the S&P 500 list specialized in apparel stores. We have revisited this model several times since 2009 and always found the same defining variables. The model is based on the decomposition of a share price into a sum of two selected consumer price indices. All models are defined by the (not seasonally adjusted) index of pets, pet products and services (PETS) and the price index of transportation services (TS), as reported by the US BLS. The former CPI component leads the share price by 1 month and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through March 2011.

In this post, we compare the 2009 and 2011 share price models for ANF. For the 2009 model we use the most recent defining CPIs as available in April 2011 and the measured monthly closing prices through March 2011. This allows validating the initial model and demonstrating its reliability.  These models are  as follows:

ANF(t) =  -4.56PETS(t-1) – 2.96TS(t-4)  + 47.09(t-1990) + 544.90 (September 2009)   (1)

ANF(t) =  -4.74PETS(t-1) – 2.45TS(t-4)  + 44.47(t-1990) + 494.79 (March 2011)   (2)

where t is calendar time. All coefficients are very close with just minor variations related to the updated share prices. Therefore, the model is effectively the same between January 2009 and March 2011. In other word, we obtained a deterministic (leading by one month) model which was valid during 27(!) months.   Figure 2 illustrates the difference between the original and current models.  

The residual error is $5.88 for the period between June 2003 and March 2011. One can expect a fall in the share price. Otherwise, the model will fail in the near future after 2 successful years.  

 

Figure 1. Evolution of the price of PETS and TS.

Figure 2. Observed ANF share prices and that predicted in 2009 and 2011.

Chesapeake Energy stock price model

Another successful example of an energy company with a stable pricing model is Chesapeake Energy Corporation (CHK). Here we present a new price model for CHK using an extended set of 92 CPIs. It is an example with a share price leading defining components of the CPI.  As always, the model is seeking for two CPI components which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and March 2011.

The two-component (2-C) model also includes free term (constant) and linear time term which compensates well known linear (time) trends between various CPI components. The best-fit 2-C 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:

CHKN(t)= 0.52TUIT(t-0) + 0.43E(t+2) – 16.771(t-1990) – 21.48; stdev=$2.64    

where (t-1990)  is the elapsed time. Therefore, the predicted curve should lag the observed price by 2 months. In other words, the price of a CHK share defines the behaviour of the index of energy. Figure 1 depicts the observed and predicted price; the latter is shifted three months ahead for synchronization. The model residual error, i.e. standard deviation, is of $5.54for the period between July 2003 and January 2010.

Figure 1. Observed and predicted CHK share prices.

Wal-Mart share in 2011 (update)

We  estimated a price model for Wal-Mart Stores(WMT) three months ago. The model is based on the decomposition of a share price into a sum of two selected consumer price indices. This is a new model defined by the index of hospital and related services (HOSP) and the price index of miscellaneous personal services (MISS), as reported by the US BLS. The former CPI component leads the share price by 10 months and the latter one evolves in sync with the price. Figure 1 depicts the overall evolution of both involved indices through March 2011. A very specific feature of both indices is their linearity over time: they are close to straight lines.

In this post, we re-estimate the WMT share price using new data for the first quarter of 2011. This allows validating the initial model and demonstrating its reliability. The previously obtained defining components are the same and provide the best fit model between June 2010 and March 2010 with only one month change in the lag for the HOST index.  All coefficients in (1) are only slightly different for the new model (see below).  The slope of the time trend is negative. The best-fit 2-C model for WMT(t) is as follows:

WMT(t) =  0.50HOSP(t-10) + 1.42MISS(t)  - 28.39(t-1990) – 158.12 (January 2011)   (1)

WMT(t) =  0.46HOSP(t-9) + 1.49MISS(t)  - 28.03(t-1990) – 165.50 (March 2011)

where t is calendar time. The predicted curve in Figure 2 evolves in sync with the observed price. The residual error is $2.15 for the period between June 2003 and March 2011. One can expect just slight variations around the $50 level since linear growth in HOSP and MISS is effectively compensated by the negative time  trend in (1).

Figure 1. Evolution of the price of HOSP and MISS.

Figure 2. Observed and predicted WMT share prices.

Figure 3. Residual error of the model.