This is the first time we present a share price model for CarMax (KMX). This company from services category of the S&P 500 index is a retailer of used vehicles in the United States. Several days ago we published a price model for a similar company - AutoNations (AN) which is valid since 2009. Both models have been obtained by decomposition of the time series of monthly closing share prices (adjusted for splits and dividends) into a weighted sum of two consumer price indices. One might presume that a fast growth in the CPI inherently linked to the KMX share price (e.g. motor vehicle parts and equipment) relative to some independent by dynamic reference (e.g. food) should be manifested in a higher pricing power for the company. We seek for two best (say, in sense of the RMS residual error) defining CPIs. It allows testing of the underlying concept (decomposition into CPIs) and to estimate time lags and coefficients for KMX.
We have borrowed the time series of monthly closing prices of KMX from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. The evolution of KMX share price is defined by the consumer price of food (F) and the index of motor vehicle parts and equipment (MVP). The defining time lags are as follows: the food index leads the price by 3 months and the MVP index leads by 4 months. The relevant best-fit model for KMX(t) is as follows:
KMX(t) = -1.37F(t-3) + 1.20MVP(t-4) + 10.33(t-1990) + 170.88, February 2012
where KMX(t) is the KMX share price in U.S. dollars, t is calendar time. This model is valid since August 2011 with the same lags and coefficients. Figure 1 displays the evolution of both defining indices since 2002.
Figure 2 depicts the high and low monthly prices for the share together with the predicted and measured monthly closing prices. The predicted prices are well within the bounds of the share price uncertainty. The model residual error is shown in Figure 3 with the standard deviation between July 2003 and February 2012 of $2.30.
From Figure 2, we expect no large changes in the first half of 2012. (Same conclusion was made for AN.)
Figure 1. The evolution of the index of rent of food and the index of motor vehicle parts (MVP).
Figure 2. Observed and predicted KMX share prices.
Figure 3. The model residual error: sterr=$2.30.