Recently, the BLS has reported the CPI estimates for March 2011. It is natural to revisit our models for the first quarter. Johnson & Johnson (JNJ) is one of the companies we have been following since 2009. A preliminary model was obtained in September 2009. The latest model was reported in January 2011.
Originally, the stock price 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 coefficients well explained by the uncertainty of the monthly closing price as a parameter characterizing the stock behavior and the estimation accuracy of these two defining CPIs.
In the previous post on JNJ we presented a model based on the CPIs for November 2010 and the December closing price of JNJ. Our concept of share pricing and 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 March 2011, i.e. two years or 24 months. Since the index of appliances has been on a steady decline since the early 2000s, its negative coefficient of -1.35 (-1.40 in January) has actually resulted in the growth of the share price. The negative influence of TS, -1.47 (-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) = -1.35APL(t-2) – 1.47TS(t-6) + 11.13(t-1990) + 332.20
Actually, the predicted curve in Figure 2 leads the observed price by 2 months with the residual error of $2.35 (see Figure 3) for the period between March 2003 and March 2011. 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.
In January, we expected that this share would experience a slight growth in the first quarter of 2011. The price actually has stalled at the level of $60. In the second quarter 2011, the price should not change much.
Figure 1. Evolution of the price of APL and TS.
Figure 2. Observed and predicted JNJ share prices. Red line – contemporaneous prediction which forecasts major pivot points in advance.
Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.35. The largest errors were observed in 2007 and 2010. Currently, the model overestimates the share price.
I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.