One, three, and nine months ago we reported on a share price model for Alcoa (NYSE: AA), which is company from Materials subcategory of the S&P 500 list specialized in aluminum. Our concept is intuitive and straightforward. A company is what it produces. There are price setters and price takers. Some goods and services drive economic development and some follow up. Let’s imagine a company producing some goods (services) very attractive to people right now. The company may raise the overall price for its goods (services). Accordingly, stocks go up, likely with some time lag. One of the indicators of the overall price is the consumer price index (CPI) for these specific goods and services or some very intimately related G&S. Then it is not excluded that the company’s share depends on this CPI in a statistically reliable way and one can obtain a good link between the price and this CPI. Since the headline CPI evolves under the pressure of a big set of goods and services, one need to find some dynamics reference (another CPI) which would be most independent on the CPI related to the company. Hence, we have to find two CPIs which describe the evolution of the price the best (in the LSQ sense). When both CPIs lead the price, a deterministic model can be obtained and we are looking for such companies in the S&P 500 list. Alcoa is one of the companies with a deterministic model – both defining CPIs lead by three months at least.
Here we test and update the AA model using new data, including the monthly closing price in February 2012 and the estimated CPI components for January 2012. The principal result is that the model has the same defining CPI components and time lags with slightly changing coefficients. Therefore, the model is a reliable tool to predict the evolution of Alcoa shares.
According to our general approach to share price modeling we decompose the observed time history of the monthly closing AA stock price (adjusted for splits and dividends) into a weighted sum of two CPI components, time trend and free term. Two defining CPI components are selected to minimize the model (RMS) error and may lead or lag behind the share.
The original and current AA model is defined by the (not seasonally adjusted) index of food away from home (SEFV) and the price index of rent of primary residence (RPR), as reported by the US BLS. The former CPI component leads the share price by 3 months and the latter is 5 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through August 2011. It seems these indices have been evolving in sync since 2002 with the only step-like change in the SEFV index in 2008. We present three empirical models as estimated in April, October, December 2011, and February 2012:
AA(t) = -6.71SEFV(t-2) + 3.34RPR(t-4) + 19.23(t-1990) + 298.87, Aril 2011
AA(t) = -6.61SEFV(t-2) + 3.22RPR(t-4) + 19.51(t-1990) + 300.89, October 2011
AA(t) = -6.47SEFV(t-3) + 3.08RPR(t-5) + 19.58(t-1990) + 302.45, December 2011
AA(t) = -6.38SEFV(t-3) + 3.01RPR(t-5) + 19.53(t-1990) + 301.93, February 2012
where AA(t) is a share price in US dollars, t is calendar time. Figure 2 illustrates the observed and predicted models for December 2011. The residual error in Figure 3 is $3.04 ($3.05 in December, $3.04 in October, and $3.12 in April) for the period between July 2003 and February 2011. Figure 2 also shows monthly high and low prices as the uncertainty in the monthly closing price as the best share price estimate. Since the closing price has to characterise the whole month by one value the high and low prices might serve as strict statistical bounds.
One can expect the share price to fall a bit through March/April 2012 to the level of $7 to $8.
Figure 1. Evolution of the price of SEVF and RPR.
Figure 2. Observed and predicted AA share prices
Figure 3. The model error; sterr=$3.04.
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