Here we model the evolution of Abbot Laboratories’ (NYSE: ABT) stock price since July 2003. Abbot is a company from healthcare sector of the S&P 500 index. We model a share price decomposing it into a weighted sum of two consumer price indices. Our concept presumes that there exist a trade-off between a given share price and goods and services the relevant company produces and/or provides. Obviously, the defining consumer price (or CPI) has to rely to some independent and dynamic reference, which can also be a consumer price index. The pricing power is related to the difference between the defining and reference CPIs.
We have borrowed the time series of monthly closing prices of ABT from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. Instructively, the evolution of ABT share price is defined by the consumer price index of medical care commodities (e.g. the discovery, development, manufacture, and sale of health care products) and the index of transportation services (TS). The defining time lags are as follows: the MCC index leads the share price by 9(!) months and the TS index leads by 8 (!) months. The relevant best-fit model for ABT(t) is as follows:
ABT(t) = 0.93MCC(t-9) – 1.00TS(t-8) + 1.92(t-1990) – 22.62, February 2012
where ABT(t) is the ABT share price in U.S. dollars, t is calendar time. Figure 1 displays the evolution of both defining indices since 2002. Figure 2 depicts the high and low monthly prices for an ABT share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the bounds of the share price uncertainty and lead by 8 months. However, the price has not been changing much since 2010 and the knowledge of the lead can not bring high return.
The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $2.38. Currently, the price is overestimated relative to its expected value and one can foresee a negative correction (~$3) in the first half of 2012. From Figure 2, the uncertainty of $5 (between the low and high monthly prices) is applicable to our prediction. It means that one may act on the price when it is beyond the $5 range relative to the expected level.
Figure 2. Observed and predicted ABT share prices.
Figure 3. The model residual error: stdev=$2.38.
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