Here we model the evolution of Allstate Corporation's (ALL) stock price. It should be taken into account that the defining consumer price (or relevant CPI) has to be related to some independent and dynamic reference, which can also be a consumer price index. A higher relative growth of the defining CPI should be manifested in a higher pricing power for the company.
We have borrowed the time series of monthly closing prices of ALL from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. The evolution of ALL share price is defined by the consumer price index of food without beverages (FB) and the index of information and information processing (INF). The defining time lags are as follows: the FB index leads the share price by 4 months and the INF index leads by 6 months. The relevant best-fit model for ALL(t) is as follows:
ALL(t) = -1.83FB(t-4) - 4.05INF(t-6) + 6.21(t-1990) + 634.40, February 2012
where ALL(t) is the ALL 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 ALL 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 4 months.
The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $2.74.
One can foresee the price evolution at a 4 months horizon. Currently, the share price is expected to decline in the first half of 2012.
Figure 1. The evolution of FB and INF indices
Figure 2. Observed and predicted ALL share prices.
Figure 3. The model residual error: stdev=$2.74.