4/2/14

Predicting share prices: Texas Instruments to hold


In this post, we describe a stock pricing model for Texas Instruments (NYSE: TXN). TXN is a company from 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 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 months 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

Month
b1
CPI1
lag1
b2
CPI2
lag2
c
d
Feb-14
-1.466
PETS
3
-0.327
NDUR
5
11.030
201.333
Jan
-1.449
PETS
3
-0.322
NDUR
5
10.890
199.133
Dec-13
-1.440
PETS
3
-0.320
NDUR
5
10.822
198.049
Nov
-1.423
PETS
3
-0.315
NDUR
5
10.686
195.910
Oct
-1.384
PETS
3
-0.311
NDUR
5
10.441
191.660
Sep
-1.364
PETS
3
-0.309
NDUR
5
10.295
189.531
Aug
-1.348
PETS
3
-0.308
NDUR
5
10.184
187.997
Jul
-1.337
PETS
3
-0.307
NDUR
5
10.106
186.976
Nov-12
-1.425
PETS
3
-0.326
NDUR
5
10.747
199.049
Oct
-1.443
PETS
3
-0.328
NDUR
5
10.883
200.752
Sep
-1.458
PETS
3
-0.324
NDUR
5
10.965
201.424
Aug
-1.464
PETS
3
-0.320
NDUR
5
10.991
201.319
Jul
-1.470
PETS
3
-0.317
NDUR
5
11.017
201.414
Jun
-1.482
PETS
3
-0.315
NDUR
5
11.096
202.045
May
-1.490
PETS
3
-0.316
NDUR
5
11.164
202.738
Apr
-1.503
PETS
3
-0.318
NDUR
5
11.279
204.068
Sep-11
-1.510
PETS
3
-0.330
NDUR
5
11.362
93.490
Aug
-1.506
PETS
3
-0.333
NDUR
5
11.337
92.904
Jul
-1.498
PETS
3
-0.342
NDUR
5
11.321
92.841
Jun
-1.500
PETS
3
-0.339
NDUR
5
11.327
91.595



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.

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