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We have been following Johnson & Johnson (JNJ) share price from 2009. A preliminary model was obtained in September 2009. From the very beginning, this stock was defined by the index of appliances (APL) and that of transportation services (TS). We have revisited the stock in September 2010 and found that the model did not change, except a slight change in the defining coefficients well explained by the uncertainty of the monthly closing price as a parameter characterizing the stock behavior and the estimation accuracy of individual CPIs. In this post we present an updated model as based on the CPIs available up to November 2010 and the December closing price of JNJ. Our quantitative approach is described in . Briefly, we decompose a share price into a weighted sum of two individual CPI components and minimize the RMS model error.
Figure 1 depicts the overall evolution of both involved consumer price indices. These two defining components provide the best fit model between March 2009 and December 2010. Since the index of appliances has been on a steady decline since the early 2000s, its negative coefficient (-1.40) has actually resulted in the growth of the share price. The negative influence of TS (-1.26) has been also compensated by all other terms in the model. The best-fit 2-C model for JNJ(t) is as follows:
JNJ(t) = -1.40*APL(t-2) – 1.26TS(t-6) + 9.99(t-2000) + 298.88
Actually, the predicted curve in Figure 2 leads the observed price by 2 months with the residual error of $2.29 for the period between March 2003 and December 2010. One may conclude that the price of a JNJ share is well defined by the behaviour of the two defining CPI components.
Comparing the evolution of the observed and predicted prices since the start of modelling (2008) we have found that the model does predict the share price in the past and foresees at a two month horizon. One may expect this share will experience a slight growth in the first quarter of 2011. In January, the model predicts the closing price of $63.54. i.e. an approximately $2 gain (the December closing price of $61.85).
Figure 1. Evolution of the price of APL and TS.
Figure 2. Observed and predicted JNJ share prices.
Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.29. The largest errors were observed in 2007 and 2010.
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.