Here, we model the evolution of Textron's (NYSE:TXT) stock price. TXT is a company from the industrial goods sector which "operates in the aircraft, defense, industrial and finance businesses worldwide." The model has been obtained using our concept of stock pricing as a decomposition of a share price into a weighted sum of two consumer price indices (CPIs). The background idea is a simplistic one: there is a potential trade-off between a given share price and goods and services the company produces and/or provides. For example, the energy consumer price does influence the price of energy companies. Let's assume that some set of consumer prices (or relevant consumer price index - CPI) drives the company stock price. Obviously, this company competes not only with those producing similar goods and services, but also with all other companies on the market. Therefore, the influence of the driving CPI on the company's stock price also depends on all other CPIs. To take into account the net change in various market prices, we introduce just one reference CPI best representing the overall dynamics of the changing price environment. Hence, the pricing model has to include at least two defining CPIs. Because of possible time delays between action and reaction (the time needed for any price changes to pass through), the defining CPIs may lead the modeled price or lag behind by a few months.
We have borrowed the time series of monthly closing prices of TXT from Yahoo.com, and the relevant (seasonally not adjusted) CPI estimates through February 2014 are published by the BLS. We have found that the evolution of TXT share price is defined by the consumer price index of transportation services (TS) and the index of pets, pet products and services (PETS) from the recreation CPI category. We assume that the index of transport services is the price driver, i.e. the consumer prices of transportation services. It is instructive that Textron Inc. operates Cessna, Bell and Textron Systems, i.e. TXT is directly related to transportation systems. The defining time lags are as follows: the TS index leads the share price by five months, and the PETS index has a 3-month lead. The relevant best-fit model for TXT(t) is as follows:
TXT(t) = -2.78PETS(t-3) - 2.86TS(t-5) + 33.02(t-2000) + 832.91, February 2014
Where TXT(t) is the TXT share price in U.S. dollars, t is calendar time. Figure 1 displays the evolution of both defining indices since 2002. Figure 2 depicts the high and low monthly prices for TXT shares, together with the predicted and measured monthly closing prices (adjusted for dividends and splits). It is worth noting that the predicted curve actually leads the observed one by three months, i.e. the model sees three months ahead.
The model is stable over time. Table 1 lists the best-fit models, i.e. coefficients, b1 and b2, defining CPIs, time lags, the slope of time trend, c and the free term, d, for select models for the period between November 2009 and February 2014. These models all have the same defining CPIs, similar coefficients and time lags - they are practically identical. Therefore, the estimated TXT model is highly reliable over time, and predicts at a three-month horizon. The model residual error is shown in Figure 3. The standard deviation between July 2003 and February 2014 is $4.20.
The model predicts TXT price to rise to $45 in May 2014.
Table 1. Selected best-fit models for the period between November 2009 and February 2014
Figure 1. The evolution of the PETS and TS indices.
Figure 2. Observed and predicted TXT share prices.
Figure 3. The model residual error: stdev=$4.20.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.