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### Is Allergan stock price stable?

Here we present a quantitative price model for Allergan (AGN). We are modelling monthly (adjusted for dividends and splits) closing prices between June 2003 and December 2010. It is found that the final model has been valid with almost the same coefficients during the past year.

The pricing model assumes a linear link between a share price and a difference between CPI components. The intuition behind the original model was simple. A higher pricing power of goods and services associated with energy, and thus with energy companies, is expressed in a faster increase in corresponding price index. In the first approximation, the deviation between appropriate price indices is proportional to the ratio of pricing powers of related companies. However, one should be very careful in selecting proper indices: it was found that the index for energy itself does not explain the evolution of share prices for energy-related companies. The change in energy price influences the share prices through deeper economic chains which include price reaction of many goods and services. (Our concept and quantitative approach are described in the paper “Modelling share prices of banks and bankrupts” published in Theoretical and Practical Research in Economic Fields, ASERS, vol. I(1(1)_Summer), pp. 59-85.)

Briefly, we decompose a share price 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 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 (see the aforementioned paper) 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)= -1.85*FH(t-3) – 1.77*THI(t-1) +16.33(t-2000) + 346.8

where FH in the index of food at home leading the stock price by 3 months, THI is the index of tenants’ and household insurance leading by 1 months, (t-2000) is the elapsed time. Quantitatively, the best fit model provides RMSE=\$3.29 for the period between June 2003 and December 2010. Also, it has been valid during the past fourteen months and we expect it to be valid in the first half of 2011. The most recent period was characterized by a outburst in the price, which has ended near the predicted level for December 2010. Since the price index of food is on a negative trend relative to the overall CPI as well as housing index the stock price might not change much in the first quarter of 2011.

Figure 1. Observed and predicted share prices, AGN.