In this post, we describe a stock pricing model for Texas Instruments (TXN). TXN is a company from the Technology sector, which "designs, manufactures, and sells semiconductors to electronics designers and manufacturers worldwide." The model has been estimated using our concept of stock pricing as a decomposition of a share price into a weighted sum of two consumer price indices (CPIs). The intuition is straightforward: there is a potential trade-off between a given share price and goods and services the company produces and/or provides. Texas Instruments might be a good example of stock price dependence on the goods it produces like some energy related companies depend on energy price. 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.
The TXN monthly closing prices (adjusted for splits and dividends) were borrowed from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through February 2014 are published by the BLS. It is worth noting that it takes approximately two weeks for the BLS to publish its estimates for the previous month. On April 2, we have the closing price for March 31, but the CPIs are available only for February. We have to update all models when we obtain new estimates for closing prices or CPIs, i.e. two times a month.
We have found that the evolution of TXN share price is defined by the consumer price index of nondurable goods (NDUR) and the index of pets, pet products and services (PETS) from Recreation CPI category. We assume that the index of nondurable goods is the price driver. The defining time lags are as follows: the NDUR index leads the share price by 5 months and the PETS index has a 3-month lead. The relevant best-fit model for TXN(t) is as follows:
TXN(t) = -1.47PETS(t-3) - 0.327NDUR(t-5) + 11.03(t-2000) + 201.33, February 2014
where TXN(t) is the TXN 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 TXN share 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 3 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 June 2011 and February 2014. These models all have the same defining CPIs, time lags, and similar coefficients. All models are practically identical. Therefore, the estimated TXN 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 $2.38.
The model predicts the level of $45 in May 2014, which is lower than the closing price on March 31 - $47.16. This monthly closing price is within the model uncertainty bounds for the predicted March value $44.94. It is not likely that TXN price will rise too much higher in the next two months.
Table 1. Selected best fit models for the period between June 2011 and February 2014
Figure 1. The evolution of PETS and NDUR indices
Figure 2. Observed and predicted TXN share prices.
Figure 3. The model residual error: stdev=$2.38.
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.