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 [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 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

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.

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 24^th 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.

Comparison of SunTrust Banks (STI) and Franklin Resources (BEN) models

The price model for SunTrust Banks (STI) is a brand new one.  Like Franklin Resources (BEN) reported four days ago, it is a financial company and was analyzed previously as a candidate for a bankruptcy [1]. The newly obtained model is based on is our stock pricing concept and includes the consumer price index of food less beverages (FB) (it was food at home, FH,  for BEN) and the index of tobacco and tobacco products (TOB). The former defining CPI component led the share price by 4 months and the latter one by 6 months (5 and 8 months, respectively for BEN). Therefore, the model has a natural 4-month forecast horizon. It is worth noting that there are two financial companied driven by the same CPIs.

Figure 1 depicts the overall evolution of the involved indices. These two defining CPI components provide the best fit model between March 2011 and July 2010.  Both coefficients are negative, as in many models already reported in this blog, and thus the increasing prices result in decreasing share price. (However, the sensitivity to the TOB index is much lower than to the FB index, as was also valid for BEN). The slope of time trend is positive and would provide a $36 increment per year if both CPIs are fixed. The best-fit 2-C model for STI(t) is as follows:

STI(t) = -5.46FB(t-4)  – 0.19TOB(t-6) + 36.07(t-1990) + 627.06     

where STI(t) is a share price in US dollars, t is calendar time.  The standard deviation of $3.77  between July 2003 and March 2011. There was no growth during  the first quarter of  2011 since no one of the defining indices has demonstarted any big movement. In the second quarter of 2011, the price may drop to the level of $23 (and then to $18) from the current $28, as follows from the predicted and observed curves presented in Figure 2.  Figure 3 displays the model error.

Figure 1. The evolution of the difference between FB and TOB.

Figure 2. Observed and predicted STI share prices. The predicted curve leads by 4 months and was shifted ahead for synchronization with the observed one. Notice excellent prediction of major turns in the price.

Figure 3. The model residual, i.e. the difference between the observed and predicted STI

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

Allergan (AGN) share price model

It’s time to revisit the price model for Allergan (AGN) first estimated in January 2011.  As before, we model the monthly (adjusted for dividends and splits) closing prices between July 2003 and March 2011. It is found that the best fit model obtained in January is still valid in April 2011 with almost the same coefficients and time lags (see Appendix for details of our deterministic share pricing concept).

Briefly, we decompose a share price into a weighed sum of two individual CPI components, linear time trend component and constant free term. We allow positive and negative time lags between variables and seek to minimize the RMS model error by varying all 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 (photo and related materials). When both defining components lead the modeled price, one can predict future evolution of the stock; at least in the near future. The bets-fit two-component (2-C) model for AGN is as follows:

AGN(t)= -1.90FH(t-3) – 1.63THI(t-0) +16.56(t-1990) + 337.58       

where AGN(t) is the price of a share in US dolars, FH in the index of food at home leading the stock price by 3 months, THI is the index of tenants’ and household insurance, (t-1990)  is the elapsed time. Quantitatively, the best fit model provides RMSE=$3.37 for the period between July 2003 and March 2011. Also, it has been valid during the past seventeen months and we expect it to be valid in the first half of 2011, at least.  The defining CPI indices are displayed in Figure 1. The FH index has been growing at a high rate during since December 2011. This effect did not overcome the positive time trend of $16.6 per year and the fall in the THI during the same time. The share may grow in the second quarter if all the observed trends hold.

Figure 1. The price indices THI and FH between 2002 and 2011

Figure 2. Observed and predicted share prices AGN.

 Appendix

In its general form, our pricing model is as follows:

sp(t_j) = Σb_i∙CPI_i(t_j-t_i) + c∙(t_j-2000 ) + d + e_j                                                              (1)

where sp(t_j) is the share price at discrete (calendar) times t_j, j=1,…,J; CPI_i(t_j-t_i) is the i-th component of the CPI with the time lag t_i, i=1,..,I; b_i, c and d  are empirical coefficients of the linear and constant term; e_j is the residual error, which statistical properties have to be scrutinized. By definition, the bets-fit model minimizes the RMS residual error. The time lags are expected because of the delay between the change in one price (stock or goods and services) and the reaction of related prices. It is a fundamental feature of the model that the lags in (1) may be both negative and positive. In this study, we limit the largest lag to eleven months. Apparently, this is an artificial limitation and might be changed in a more elaborated model.

System (1) contains J equations for I+2 coefficients. For POM we use a time series from July 2003 to March 2011, i.e. 94 monthly readings.  Due to the negative effects of a larger set of defining CPI components their number for all models is (I=) 2. To resolve the system, we use standard methods of matrix inversion. As a rule, solutions of (1) are stable with all coefficients far from zero. In the POM model, we use 92 CPI components. They are not seasonally adjusted indices and were retrieved from the database provided by the Bureau of Labor Statistics.

Due to obvious reasons, longer time series guarantee a better resolution between defining CPIs. In general, there are two sources of uncertainty associated with the difference between observed and predicted prices. First, we have taken the monthly close prices (adjusted for splits and dividends) from a large number of recorded prices: monthly and daily open, close, high, and low prices, their combinations as well as averaged prices. Second source of uncertainty is related to all kinds of measurement errors and intrinsic stochastic properties of the CPI and its components. One should also bear in mind all uncertainties associated with the CPI definition based on a fixed basket of goods and services, which prices are tracked in few selected places.  Such measurement errors are directly mapped into the model residual errors. Both uncertainties, as related to stocks and CPI, also fluctuate from month to month.