## 4/30/11

### Why the level of unemployment does not matter for real economic growth II

In the previous post we demonstrated that the level of unemployment could hardly influence real economic growth because the portion of people out of labor force changes in a much wider range (by  a factor of 5) and still does not affect the real growth. Here we present a quantitative model explaining the long-term change in the labor force participation rate, LFP, which, obviously, defines the portion of people not in labor force. In this blog, we presented similar models for Canada and Italy but without appropriate math.

We first try to model dLFP/LFP as a nonlinear function of real GDP per capita, G, and tested a simple relationship:

dLFP(t)/LFP(t) =  D1[dG(t-T)/G(t-T) - A2/G(t-T)] +D2                                       (1)

where D1 and D2 are empirical constants, and A2 is also an empirical. The time interval is dt=1 year, and thus, omitted in the equation. The intuition behind this model is that it is real economic that drives the change in LFP. The evolution of LFP depends on the difference between the observed rate of growth and the potential rate of growth defined by a reciprocal function of G, A2/G.

Figure 1 depicts the measured LFP and that predicted from real GDP per capita using equations (2) and (3). Both variables are borrowed from the Total Economy Database provided by the Conference Board. All in all, the model describes the evolution of LFP in the US since 1964 with an extremely high accuracy. In the mainstream economics, there is no other model of LFP predicting its evolution with a compatible accuracy. Moreover, the predicted curve leads by 2 years (T=2) that allows forecasting at a 2 year horizon. (See our post in January 2011 on the short term LFP prediction.)

Al in all, the rate of participation in  labor force depends only on the evolution of real GDP per capita two years ago. Therefore, the level and rate of unemployment, as a part of labor force, plays no role in real economic growth. At least empirical facts say so.

Figure 1. Measured and predicted LFP in the US, where A2= \$360 (1990 US dollars) is empirical constant. T=2 years.

### Why the level of unemployment matters nothing for real economic growth

Unemployment is a painful economic phenomenon which drives many social and political processes. For example, the Federal Reserve System has a dual mandate aimed at balancing of inflation and unemployment.  (In macroeconomic, there is no empirically derived link between these variables, however.) By definition, unemployment is treated as a crucial parameter which theoretically responsible for the level of real economic performance. When unemployment is high, real economic growth is considered as a suppressed one, and thus, below its potential value with some “natural” rate of unemployment.  In reality, economic recessions are usually accompanied by tangible increase in the rate of unemployment.  Economic logic is often faulty and says “in sync means interlinked”.   This is not the case for the relation between unemployment and real growth. Fluctuations in real growth are caused by external forces and result in the change of unemployment. This does not mean that one can decrease unemployment and thus drive economic growth.

The reason of the independence of real economic growth on unemployment is simple. The portion of unemployed, in the total working age population, UE/POP, is too small compared to the portion of people out of labor force, NLF/POP. Figure 1 displays both ratios. The portion of unemployed fluctuates near 4%  (mean value 3.8%) of the total population with amplitude of 2%. Currently, the portion of unemployed is around 6%. At the same time, the portion of people out of labor force has dropped from 42% in 1983 to 33% in 1999. Effectively, the economy included 10% more population in 2000 than in 1963. This is a much bigger change than the observed variation in the portion of unemployed. All unemployed in 2000 would be out of labor force in 1963, i.e. irrelevant to real economic growth according to the mainstream macroeconomic paradigm.

Figure 1. Comparison of the portion of unemployed, UE/POP, and the portion of people out of labor force, NLF/POP, in the total working age population, POP.
Now, it is instructive to evaluate the influence of the increasing portion of employed people, E/POP, on the rate of real economic growth. Figure 2 compares E/POP (reduced by 0.55) and the rate of GDP per capita growth, dGDP/GDP, where the overall real GDP is divided by the working age population, POP. One can see that the rate of growth has a negative trend since 1960. During this period the E/POP has increased from 55% to 63% and then dropped to59%.  From Figure 2, it is possible to conclude that the increasing proportion of employed population suppresses the rate of economic growth.

Figure 2. The portion of employed in the working age population, E/POP, compared to the rate of GDP per capita growth, dGDP/GDP.

Finally, we can answer the question why the level of unemployment means nothing for real economic growth. The fluctuations in UE are too small and their effect is opposite to the growth in the level of employment, which reduces the rate of real economic growth. In this regard, an increasing rate of unemployment is a positive phenomenon in the long run.

## 4/29/11

### 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.

1. 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  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

## 4/28/11

### 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 .
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.

## 4/27/11

### 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 , 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.

## 4/26/11

### 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 .  One can also find in  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

### A preliminary model for Cephalon share

After the model for Altero Corporation, we present a share pricing model for Cephalon (CEPH). The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. The tenants' and household insurance index (THI) leads by 2 months and the index of prescription drugs (PDRUG) leads by 9 months the CEPH share price.  The latter index might be directly related to Cephalon product. Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between November 2010 and March 2011.  The model is as follows:
CEPH(t) = -3.94THI(t-2) + 1.61PDRUG(t-9) – 10.04(t-1990) + 120.83
where CEPH(t) is a share price in US dollars, t is calendar time.
Both models are depicted in Figure 2. The residual error is of \$5.00 for the period between July 2003 and March 2011.  2009. Notice that the PDRUG index has been growing at a high rate since the beginning and any fluctuation in this index has been directly mapped into the price, which is characterized by high volatility. The THI index has been rising steadily but slowly.
Figure 1. Evolution of the price indices THI and PDRUG.
Figure 2. Observed and predicted CEPH share prices.

### Altera Corporation share in 2012

Our stock pricing concept 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 .  One can also find in  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 Altera Corporation (ALTR). It belongs to Technology sector and is specialized in semiconductors.  A preliminary model was obtained in September 2010 and covered the period from January 2010. This old model included the same indices as the current one: the price index of food away from home (SEFV) and the index of communication (CO).  The latter index makes some sense as using semiconductors.
The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. The SEFV index leads by 6 months and the CO index leads by 10 months the ALTR 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 2010 and March 2011.  The model is as follows:
ALTR(t) = -2.84SEFV(t-6) + 2.88CO(t-10) +22.54(t-1990) – 40.23
where ALTR(t) is a share price in US dollars, t is calendar time.
Both models are depicted in Figure 2. The residual error is of \$2.02 for the period between July 2003 and March 2011.  The dependence on time has been strong enough (\$22.5 per year) to overcome negative influence of both indices since 2009. Notice that the index of food away from home has been growing at a lower rate since 2009 and the index of communication has been falling steadily since the beginning.  From Figure 2, one can expect the share will be stable at the level of \$42 during the next half a year.

Figure 1. Evolution of the price indices SEFV and CO.
Figure 2. Observed and predicted ALTR 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

## 4/25/11

### Celgene Corporation stocks will not be growing

Here we present a share pricing model for Celgene Corporation (CELG). A preliminary model was obtained in September 2009 and covered the period from October 2008. This old model included the same indices as the current one: the price index of food at home (FH) and the index of housing (H). The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. The FH index leads by 6 months and the H index is synchronized with the CELG share price.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011.  The model is as follows:
CELG(t) = -1.87FH(t-6) + 2.86H(t-0) +4.21(t-1990) – 247.59
where CELG(t) is a share price in US dollars, t is calendar time.
The observed and predicted prices are depicted in Figure 2. The residual error is \$3.91 for the period between July 2003 and March 2011.  Since the dependence on time is weak (\$4.2 per year) and the index of food at home had a spurt during the last four months (\$7 since December 2010), one can expect a fall by \$10 in the next half a year. We assume that the housing index is not going to grow fast.
Figure 1. Evolution of the price indices FH and H.
Figure 2. Observed and predicted CELG share prices.

### Loews Corporation share price

Here we present a share pricing model for Loews Corporation (L) (see a brief description of the concept here). A preliminary model was obtained in September 2009 and covered the period from October 2008. This old model included the index of food without beverages (FB) and the index of transportation service (TS).
The most recent model also uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. Currently, the defining indices are almost the same: the index of food (F) and the TS index. The F index leads by 5 months and the TS index by 4 months.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between December 2009 and March 2011.  The models are as follows:
L(t) = -2.03F(t-5) – 2.12TS(t-5) +28.23(t-1990) +448.98
where L(t) is the share price in US dollars, t is calendar time.
Both models are depicted in Figure 2. The predicted curves lead the observed ones by 4 months. The residual error is of \$2.46 for the period between July 2003 and March 2011.  In the second quarter of 2011, the model foresees a fall to the level of \$39 per share.
Figure 1. Evolution of the price indices F and TS.

Figure 2. Observed and predicted L share prices.

## 4/24/11

### Cardinal Health in Q2 2011

Cardinal Health (CAH) is one of the companies with a long story of successful modeling. In September 2009, we first estimated a preliminary two-component model from the full set 73 CPI components. As in all our models, we predict the monthly closing price adjusted for splits and dividends. Here, we revisit the previous model using all data available on April 24th and an extended set of CPIs.  Also, all time series are 18 months longer what provides a better resolution and reliability.
For CAH, the defining indices are as a year and two years ago: the index of dairy and related products (DAIRY) and the index of pets, pet products and services (PETS). The CPI components are both leading by 2 months. Figure 1 depicts the evolution of both indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011:
CAH(t) = -0.38DAIRY(t-2) – 1.69PETS(t-2) +11.33(t-1990) + 136.12

where CAH(t) is the share price in US dollars, t is calendar time.
The predicted curve in Figure 2 is synchronized with the observed one. The residual error is of \$2.58 for the period between July 2003 and March 2011.  The next move in the price is likely down according to the growth in both defining indices.
Figure 1. Evolution of the price indices DAIRY and PETS.
Figure 2. Observed and predicted CSC share prices.

### Computer Science Corporation will not be growing

A year ago, we first presented a share price (monthly closing price adjusted for splits and dividends) model for Computer Science Corporation (CSC). In this post, we revisit the previous model using all data available on April 24th.  Longer time series provide a better resolution between defining CPIs and higher model reliability.
For CSC, the defining indices are as a year and two years ago: the index of motor vehicle parts (MVP) and the index of sporting goods (SPO). The CPI components are leading by 0 and 5 months, respectively. Figure 1 depicts the evolution of both indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011:
CSC(t) = -3.83MVP(t-0) + 3.16SPO(t-5) +16.31(t-1990) – 137.20
where CSC(t) is the share price in US dollars, t is calendar time.
The predicted curve in Figure 2 is synchronized with the observed one. The residual error is of \$3.28 for the period between July 2003 and March 2011.  Since the MVP index has been growing since 2002 and the SPO index has a slight negative trend, the share price will not be growing in the near future.
Figure 1. Evolution of the price indices MVP and SPO.
Figure 2. Observed and predicted CSC share prices.