We revisited our price model for Wal-Mart Stores (NYSE: WMT) two months ago. Originally, the model was estimated in June 2010 and the same model still worked well in December 2011. This suggests the overall robustness and reliability of the share price model for WTM.

Our concept of share pricing is based on the decomposition into a weighted sum of two selected consumer price indices. The intuition is simple; a faster growth in the CPI related to a given company relative to some independent but dynamic reference should be manifested in a higher pricing power for the studied company. This reference is needed since all consumer prices change over time and those associated with the company should be measured in relative terms. Hence, our stock price model seeks for a defining CPI and the best reference which we both select from a set of 92 different (not seasonally adjusted) CPIs. This set includes the headline and core CPI, all major categories from food to other goods and services, and many minor subcategories with a long enough measurement history (i.e. continuous estimates should be available since 2000).

Here we re-estimate the original model with data available in March 2012, i.e. the closing price for February and CPIs for January 2012. This model is defined by the (seasonally not adjusted) index of hospital and related services (HOSP) and the price index of miscellaneous personal services (MISS), as reported by the US BLS. The former CPI component leads the share price by 9 months and the latter one evolves in sync with the price. Figure 1 depicts the overall evolution of both involved indices through January 2012. A very specific feature of both indices is their linearity over time: they are close to straight lines with small fluctuations.

The newly estimated model allows validating the initial model and demonstrating its reliability. The previously obtained defining components are the same and provide the best fit model between June 2010, March and December 2011 with only one month change in the lag for the HOSP index. All coefficients are slightly different for the new model (see below). The slope of the time trend is negative. The best-fit 2-C model for WMT(t) is as follows:

WMT(t) = 0.50HOSP(t-10) + 1.42MISS(t) - 28.39(t-1990) – 158.12 (January 2011)

WMT(t) = 0.46HOSP(t-9) + 1.49MISS(t) - 28.03(t-1990) – 165.50 (March 2011)

WMT(t) = 0.46HOSP(t-9) + 1.30MISS(t) - 26.06(t-1990) – 141.92 (December 2011)

WMT(t) = 0.48HOSP(t-9) + 1.33MISS(t) - 26.75(t-1990) – 145.13 (February 2012)

where t is calendar time. The predicted curve in Figure 2 evolves in sync with the observed price. The residual error is $2.15 for the period between June 2003 and February 2012.

With both indices growing along their respective trends, we foresaw in December 2011 a slight increase to the level of $60 to $65 per share in 2012Q1. It really happened and the price was at the level $62.06 in February. The current model supposes a slight negative correction which also follows from the positive residual error shown in Figure 3. A no change scenario is also possible with the predicted price rising to the level of the measured one in March 2012. In a week, we will re-estimate the model using both CPIs for February.

Figure 1. Evolution of the price of HOSP and MISS.

Figure 2. Observed and predicted WMT share prices.

Figure 3. Residual error of the model; sterr=$2.15.

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