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.

Can we derive energy price in 2011 Q2 from Devon Energy share price?

We have already presented about 30 deterministic models for share prices from the S&P 500 list. The existence of these deterministic models might be perceived as if the stock market does not drive real economy, i.e. the stock market lags behind the economy and does not use all currently available information. It was not our intention to mislead the reader. On the contrary, we have tried to help investors. To recover our belief in real economic forces as expressed in stock pricing we have presented rough models of oil-related companies: XOM, COP, DVN, HAL, and CVX. Their share prices lead defining CPI components by several months. In other words, the defining consumer price indices (CPI and core CPI in these rough models) lag behind oil price.

In this post we refine the price model for Devon Energy Corporation (DVN) using an extended set of 92 CPIs. Even in this case, Devon Energy provides an example of a company whose share price has been 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 know linear (time) trends between various CPI components. The best-fit 2-C model for DVN(t) is as follows:

DVN(t)= 2.70CF(t-2) + 0.49E(t+3) – 12.21(t-1990) – 370.88     

where CF in the headline CPI less food leading  the stock price by 2 months, E is the index of energy lagging behind by 3 months, (t-1990)  is the elapsed time. Therefore, the predicted curve should lag the observed price by 3 months. In other words, the price of a DVN share defines the behaviour of the index of energy. Figure 1 depicts the observed and predicted prices, the latter shifted three months ahead for synchronization. The model residual error, i.e. standard deviation, is of $5.54for the period between July 2003 and December 2010.

The DVN  model does not predict the share price. However, the share price in the first quarter of 2011 demands both indices to grow in 2001 Q2. It is most likely that the index of energy will grow much faster than the CF.

Figure 1. Observed and predicted DVN share prices.

Figure 2. The index of energy, E, and the CPI less food, CF.

Avery Dennison in 2011 Q2

We presented a tentative model for Avery Dennison Corporation (AVY) in January 2011 and predicted a period of no growth in Q1. This prediction was right. Hence, it is instructive to revisit the previous model and forecast the share behaviour in Q2.

According to [1], the share price model for AVY is still defined by the index of food (F) and that of new and used motor vehicle (NUMV). The former CPI component leads the share price by 4 months and the latter one leads by 2 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between July 2010 and March 2011.  Relevant coefficients are both negative. The slope of time trend is positive.  The best-fit 2-C model for AVY(t) is as follows:

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

where AVY(t) is a share price in US dolalrs, t is calendar time.

The predicted curve in Figure 2 leads the observed price by 2 months with the residual error of $2.68 for the period between July 2003 and March 2011. The model residual for the same period is shown in Figure 3. The model does predict the share price in the past and foresees a fall in 2011 Q2.

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

Figure 2. Observed and predicted AVY share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.68. Currently, the price is slightly overestimated.

References

1. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

Paychex Inc. in 2011 Q2

Paychex (PAYX) is a services company specialized in staffing & outsourcing. Here we present a share pricing model for PAYX as based on decomposition into a weighed sum of two CPI components, time trend and free term. The final model includes the price index of food less beverages (FB) leading the share price by 3 months and the index of tenants’ and household insurance  (THI).  The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between October 2010 and March 2011.  The model is as follows:

PAYX (t) = -1.12(t-3) - 1.20THI(t-0) + 8.17(t-1990) + 255.59

where PAYX(t) is a share price in US dollars, t is calendar time. The observed and predicted models are depicted in Figure 2. The residual error is of $2.01 for the period between July 2003 and March 2011. Since the last three months in 2011 were characterized by a quick growth in the FB index one can expect a slight decrease in the share price in 2011 Q2.

Figure 1. Evolution of the price indices THI and FB.

Figure 2. Observed and predicted PAYX share prices.

Novellus Systems share predicted

An investor is usually interested to know the future evolution of stock prices. The current stock pricing paradigm does not allow to see far enough and not much helpful for a small/middle size investors. (Very big investors can always play nasty games in their favour.) Therefore, only deterministic pricing model can equalize chances. We propose such a concept which  is very simple and is based on deterministic links between share prices and prices of goods and services included in the consumer price index, CPI.

Literally, we decompose a share price (monthly closing price adjusted for splits and dividends) into a weighted sum of two individual CPI components, linear time trend component and constant free term. We allow positive and negative time lags between all variables in the relationship and seek to minimize the RMS model error by varying the involved coefficients. The set of CPI components consists of 92 independent price indices of different level: from major (overall and core CPI) to very small (e.g. photo and related materials). When the modeled share lags behind both defining CPI components we have a deterministic model predicting at a horizon of the smallest time lag. This concept gives excellent results in terms of the model error and very stable pricing models which are valid during several years. In 2008, the model successfully predicted bankruptcy of some major banks, including Lehman Brothers. Fannie May and Freddie Mac. We were able to forecast negative share prices several months ahead [1].  One can also find in [1] a formal model description. 

In this blog, we present and track successful models from the S&P 500 list. They are numerous. For other companies from the S&P 500 list, we also have accurate quantitative models, but they are not deterministic since at least one of defining CPI components lags behind the modeled price. We revisit (recalculate) all models every quarter using new data and report on successful models. In some cases, a model should hold for a year before we publish it.

In this post, we present a share pricing model for Novellus Systems (NVLS). It belongs to Technology sector and is specialized in semiconductor equipment and material.  A preliminary model was obtained in September 2009 (18 months ago) and covered the period from January 2009 (25 months!). This old model included the same indices as the current one: the price index of food less beverages (FB) and the index of motor vehicle parts (MVP).  Both indices seem to be not related to the major product of this company, but define a very reliable stock price model.

The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. Both indices lead by 4 months the NVLS share price.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between January 2009 and March 2011.  The model is as follows:

NVLS (t) = -2.62FB(t-4) + 2.34MVP(t-4) + 4.21(t-1990) + 196.8

where NVLS(t) is a share price in US dollars, t is calendar time.

It is interesting that food related indices have negative coefficients in our models. This means that increasing food price suppresses the growth in all shares on the market. This effect has perfect sense because the food demand is likely not very flexible and is considered as a major threat to the growth of real U.S. economy and stock market.

The observed and predicted models are depicted in Figure 2. The residual error is of $2.52 for the period between July 2003 and March 2011. From Figure 2, one can expect the share will drop to the level of $30 by the end of 2011 Q2, and then even lower.

Figure 1. Evolution of the price indices MVP and FB.

Figure 2. Observed and predicted NVLS share prices.

 

1. Kitov, I. (2010). Modelling share prices of banks and bankrupts, Theoretical and Practical Research in Economic Fields, ASERS, vol. I(1(1)_Summer) pp. 59-85