We have been modeling AutoNations' (AN) stock price since 2009. This is a company from services sector (as defined by the S&P 500) and operates as an automotive retailer in the U.S. here we present the current model which has 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 AN share price (e.g. energy consumer price for energy companies) relative to some independent by dynamic reference should be manifested in a higher pricing power for the company. Therefore, the task is to find two best (say, in sense of RMS residual error) defining CPIs. It allows testing of the underlying concept (decomposition into CPIs) and to estimate time lags and coefficients for AN.
We have borrowed the time series of monthly closing prices of AN from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. The evolution of AN share price is defined by the consumer price of rent of primary residence (RPR) and the index of financial service (FS). The defining time lags are as follows: the RPR index leads the price by 10 months and the FS index leads by 5 months. The relevant best-fit model for AN(t) is as follows:
AN(t) = -1.89RPR(t-10) - 0.36FS(t-5) + 15.47(t-1990) + 270.31, February 2012
where AN(t) is the AN share price in U.S. dollars, t is calendar time. This model is valid since August 2011 with the same lags and coerffcients. Figure 1 displays the evolution of both defining indices since 2002. Due to the negative coefficient (slope), the sharp drop in the FS index in 2009 best explaines the jump in the share price five months later.
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 January 2012 of $1.63.
Both CPIs have negative influence on the share price. Therefore, the price should decrease when the indices grow fast. From Figure 2, we expect no large changes in the first half of 2012. At least the price will be inside the uncertainty bounds defined by monthly high/low prices, which were volatile during the previous 4 to 6 months.
Figure 1. The evolution of the index of rent of primary residency (RPR) and the index of financial service (FS).
Figure 2. Observed and predicted AN share prices.
Figure 3. The model residual error: stdev=$1.63.