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