Share price modeling: Computer Science Corporation

Four years ago, we first presented a share price (monthly closing price adjusted for splits and dividends) model for Computer Science Corporation (NYCE: CSC). All predictions were based on our concept of share pricing as decomposition into a weighted sum of two CPI components.  The intuition behind our concept is simple; a faster growth in the CPI directly related to the share price (e.g. energy consumer price for energy companies) relative to some independent and dynamic reference (e.g. some goods and services which price does not depend on energy) should be manifested in a higher pricing power for the company. Our model selects (using the LSQ method) a defining CPI and the best reference index from a set of 92 CPI with estimates started before 2000. This set is fixed - it is important for model stability. Both CPIs for a given model must define the studied price for at least 8 months in a row, i.e. the model has to be the same for a relatively long time: the longer – the better.

 Approximately three years ago we revisited the original CSC model using all data available through March 2011.  The defining indices were estimated five years ago (in 2008): the consumer price index of motor vehicle parts (MVP) and the index of sporting goods (SPO). (All details are provided by the Bureau of Labor Statistics.) It is crucial for the model that the defining CPI components are leading by 0 and 5 months, respectively. Figure 1 depicts the evolution of both defining 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, March 2011

      

where CSC(t) is the share price in US dollars, t is calendar time. In April 2011, we predicted the curve in the upper panel of Figure 2 which is synchronized with the observed one. The residual error was 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 had a slight negative trend, we predicted that the share price would not be growing in 2011. We revisited the CSC pricing model in 2012 and obtained the same defining indices as in 2008: 

CSC(t) = -3.81MVP(t-1) + 3.35SPO(t-7) +15.97(t-1990) – 158.37, January 2012 

with slightly increased time delays of 1 month and 7 months, respectively. In the middle panel of Figure 2 the predicted and observed prices are depicted.  

Here, we revisit the original model with the data available on March 18, 2014. The best fit model is the same: 

CSC(t) = -3.13MVP(t-1) + 3.30SPO(t-7) +12.51(t-2000) – 51.97, March 2014

 

Slight drift in coefficients expresses the time trend in indices and observed for all pricing model from the very beginning. The functional dependence and time delays for both indices are the same. The lower panel of Figure 2 depicts the current model together with the high and low monthly prices expressing the intermonth price uncertainty. Thus, the pricing model for CSC is valid since 2008. The error term is presented in Figure 3. The standard deviation is $3.56 since July 2003.

One cannot excluded that the  MVP will suffer some further decrease  and the SPO will retain its long-term level. Then the positive price trend defined by the linear time term and negative MVP coefficient will result in further CSC share increase. 

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

 

Figure 2. Observed and predicted CSC share prices for three revisions: 2011 (upper panel), 2012 and 2014 (lower panel). 

Figure 3. The model error, i.e. the difference between the observed and predicted price; stdev = $3.56 for the period between July 2003 and March 2014.

 

Share price prediction for Hewlett Packard

Two years ago we presented a quarterly report of the performance of our share price model for Hewlett Packard (NYSE:HPQ). This company provides a good example of a successful share price prediction at a several month horizon.  We have already published our predictions at a four month horizon five times (July 2010, January 2011, March 2011, July 2011, and September 2011, February 2012). This is a revision of the original model which validates our concept of share pricing.  

All predictions were based on our concept of share pricing as decomposition into a weighted sum of two CPI components.  The intuition behind our concept is simple; a faster growth in the CPI directly related to the share price (e.g. energy consumer price for energy companies) relative to some independent and dynamic reference (e.g. some goods and services which price does not depend on energy) should be manifested in a higher pricing power for the company. Our model selects (using the LSQ method) a defining CPI and the best reference index from a set of 92 CPI with estimates started before 2000. This set is fixed what is important for model stability. Both CPIs for a given model must define the studied price for at least 8 months in a row, i.e. the model has to be the same for a relatively long time: the longer – the better. Our model for HPQ was stable between 2010 and 2012 and showed an excellent predictive power at a four month horizon for more than 30 months without gaps. The current revision extends the model by another 24 months of successful prediction. Altogether, the model is valid since the beginning of 2010 with just minor changes. 

Originally, the long term model for HPQ share price was defined by the index of food without beverages (FB) and that of rent of primary residency (RPR). The former CPI component led the share price by 4 months and the latter one led by 5 months. The current model includes slightly different components of the CPI: the index of other food at home (OFH) and the index of housing operations (HO), which are quite similar in the overall evolution to the originally used components. Figure 1 depicts the overall evolution of all four involved indices through February 2014. Below we present five best-fit models for HPQ(t) obtained at different times:

 

HPQ(t) = -3.20FB(t-4) + 2.91RPR(t-5) + 3.64(t-1990) - 50.82, July 2010

HPQ(t) = -3.34FB(t-4) + 3.41RPR(t-5) + 0.51(t-1990) - 85.44, June 2011

HPQ(t) = -3.46FB(t-4) + 3.68RPR(t-5) – 0.72(t-1990) - 99.88, September 2011

HPQ(t) = -3.40FB(t-5) + 3.60RPR(t-6) – 0.57(t-1990) – 97.72, December 2011

HPQ(t) = -3.27FB(t-4) + 3.46RPR(t-5) – 0.39(t-1990) – 95.71, February 2012

HPQ(t) = -1.58OFH(t-4)+3.15HO(t-11) – 4.03(t-2000) – 89.35, February 2014

 

where HPQ(t) is the price in US dollars, t is calendar time. All coefficients have been slightly drifting but very close. This process expresses the trade-off between the linear trend in the difference between  the defining CPIs and the time trend term in the above equtions.  

Currently, HPQ price is predicted to decline a little in March and April 2014. This fall is a marginal one ($1) and lays within the uncertainty bounds of the model prediction – standard deviation of the model residual is $2.9 since 2003. Figure 3 depicts the model error. It is worth noting that the residual is an I(0) process that means that the predicted and observed prices are cointegrated time series. This makes all statistical estimates valid. 

 

 Figure 1. Evolution of the price of OFH and HO relative to FB and RPR.  

Figure 2. Observed and predicted HPQ share price.

Figure 3. The model residual error; sterr=$2.91.

The price of steel and iron will be falling

For price prediction of various commodities, our general approach is based on the presence of long-term sustainable (linear and nonlinear) trends in the evolution of the CPI and PPI in the United States [1, 2]. The difference between components of these indices is not a random one but is rather a predetermined process. Using these trends, one can predict consumer and producer price indices for select goods, services and commodities.  

On Seekingalpha, we first reported on the evolution of the producer price index (PPI) for iron and steel in July 2009. We compared our earlier prediction from 2008 with the actual evolution of the difference between the PPI of steel and iron and the headline PPI and made the following forecast: 

“In the short run, one can expect a fast recovery of iron and steel prices to the level observed in January-March 2008, i.e. the index will reach the level 210 to 220. However, this recovery will not stretch into 2011, and the index of iron and steel will be declining in the long run to the level of 2001, as depicted in Figure 3. In other words, the period between 2008 and 2010 is characterized by very high volatility, which will fade away after 2011.” 

Figure 1 reproduces Figure 3 from the 2009 post, where the green line gives a prediction of the future evolution. Since 2009, we made several updates considering new data on both PPIs (June 2010, February 2012,  December 2012, and August 2013). Here we revisit the previously predicted fall in the producer price index of steel and iron and formulate a preliminary hypothesis on the evolution in 2014-2016.   

Figure 2 displays the difference between the PPI and the index for iron and steel (BLS code 101) since 1985. Between 1985 and 2000, the curve fluctuates around the zero line, i.e. there was no linear trend in the absolute difference. The difference is characterized by a sharp decline between 2001 and 2008. Our main assumption described in the aforementioned post was absolutely right - the negative trend observed before 2008, after a short period of large fluctuations, started its transformation into a positive trend after 2010. In Figure 2, the (slightly updated according to actual data between 2009 and 2011) new trend is shown by green line. This trend suggests that the PPI grows faster than the index of steel and iron by approximately 2 units of index per year.  

Figure 3 demonstrates the most recent period and confirms that our prediction for 2013 was correct – the difference fluctuates around the green line. A short-term growth in the price of iron and steel observed in November 2013 and January 2014 is a transient one (a fluctuation) and the difference will return to green line in the second quarter of 2014.   

We confirm our forecast  that the difference will be growing fluctuating around the green line till 2016. The price of iron and steel will be declining further before the difference reach ~10 to 20.  Investments is iron and steel related assets are likely not profitable. 

Figure 1. The prediction of steel and iron price made in 2009.

 

Figure 2. The difference of the PPI and the index of steel and iron for the period between January 1985 and January 2014. The green line was first introduced in 2008. 

Figure 3. Same as in Figure 2 for the period between January 2005 and January 2014. Green line predicts the evolution of the difference after 2009. 

WWIII

The logic of the current international conflict successfully unwinds into a WWIII. There is no way back for both sides because of lost face of the powers. Many politicians forget "mutual assured destruction", which is around the corner. Both powers approaching the edge definitely  put in danger the whole mankind not thinking about people. and thus, do not deserve the power. Recklessness.