Here we model another company from the S&P 500 list. This is a company from Services category - Safeway Inc. (NYSE: SWY), which operates as a food and drug retailer in North America. Safeway share price is approximated by a linear combination of two consumer price indices; with the CPI of food, F, directly related to Safeway and the CPI of owner's equivalent rent of residence, ORPR, representing an independent but dynamic price reference. We suggest that one CPI moves the Safeway price but only relative to the overall prices, which evolve freely of Safeway. Thus, our stock price model tries to find one defining CPI and the best reference.
We have borrowed the time series of monthly closing prices of Safeway from Yahoo.com (March 2012 is included) and the CPI estimates through February 2012 are published by the BLS. (The CPI estimates for March 2012 will be reported by the BLS in the middle of April and we will revise all models accordingly). The best-fit model for Safeway(t) is as follows:
Safeway(t) = -1.59F(t-4) + 1.19ORPR(t-0) + 3.34(t-2000) + 28.85, March 2012
where Safeway(t) is the Safeway share price in U.S. dollars, t is calendar time. Figure 1 displays the evolution of both defining indices since 2002. The ORPR index has a positive influece on the price. Apparently, the negative slope of F implies that higher food prices reduce the Safeway return. This is not against common sense.
Figure 2 depicts the high and low monthly prices for a Safeway share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the limits of the share price uncertainty as defined by the monthly high/low prices.
The model residual error is shown in Figure 3 with the standard error between July 2003 and January 2012 of $1.86. The model predicts that all deviations are only short-term ones, i.e. the measured curve returns to the predicted one, which may be considered as a "fundamental" price level. Basically, the observed share price gravitates to the predicted curve.
Considering Figures 2 and 3, one can conclude that they current Safeway price is slightly overvalued and a negative correction is not excluded in the beginning of the second quarter of 2012. Such corrections have been observed many times in the past.
Figure 1. The evolution of defining indices.
Figure 2. Observed and predicted monthly closing prices for a Safeway share.
Figure 3. The model residual error: sterr=$1.86.