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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