Here we model
the evolution of JDS Uniphase Corporation (NYSE: JDSU) stock price. JDSU is a
company from technology sector which “provides communications test and measurement
solutions, and optical products for telecommunications service providers,
wireless operators, cable operators, network-equipment manufacturers, original
equipment manufacturers, enterprises, government organizations, distributors,
and strategic partners 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. It should be taken into account that one defining consumer price (or
relevant CPI) has to be related to the share and the other CPI should be an independent
one as representing a dynamic reference. We expect a higher relative growth of
the defining CPI to manifest itself in a higher pricing power for the company. Both defining CPIs may lead the price of lag behind
by a few months.
We
have borrowed the time series of monthly closing prices of JDSU from Yahoo.com and
the relevant (seasonally not adjusted) CPI estimates through February 2014 are published
by the BLS. It is instructive that the evolution of JDSU share
price is defined by the consumer price index of postage
and delivery services (POST) and the index of all items (the headline CPI) less
energy index (CE). The defining time lags are as follows: the CE index leads the share
price by 4 months and the POST index is contemporaneous with the price. The relevant best-fit model for JDSU(t) is as follows:
JDSU(t) = 0.934POST(t-0) – 3.14CE(t-4)
+ 7.49(t-2000) + 486.18, February 2014
where JDSU(t) is the JDSU 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 JDSU share together with the
predicted and measured monthly closing prices (adjusted for dividends and
splits).
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 7 months. In 2012, the same model
was obtained, as listed in Table 2. Therefore, the estimated JDSU model is
reliable over time. For 2010 and 2011,
the model included another reference CPI – the consumer price index of alcohol
beverages, AB, which has cross correlation coefficient 0.996 with CE (see
Figure 1). Statistically, the model for 2010/2011 was indistinguishable from
the current version. The model residual error is shown in Figure 3. The
standard deviation between July 2003 and February 2014 is $3.38.
Considering
the overall evolution of the POST and CE indices we do not expect significant
changes in JDSU price. The difference between the headline CPI and the energy
index is on a negative trend, i.e. the CPI grows at a higher rate than the consumer
energy price. The index of all items
less energy gets some acceleration and this might be a general factor
suppressing the JDSU price since CE has a negative coefficient. The growth in POST index has a positive effect
and we observe a few steps affecting the JDSU price in the past. Such a step
may raise the price.
Table
1. The best fit models for the period between August 2013 and February 2014
|
Month
|
b1
|
CPI1
|
lag1
|
b2
|
CPI2
|
lag2
|
c
|
d
|
sterr,
$
|
|
February 2014
|
0.9337
|
POST
|
0
|
-3.1359
|
CE
|
4
|
7.4919
|
486.1826
|
3.3783
|
|
January 2014
|
0.9732
|
POST
|
0
|
-3.1225
|
CE
|
4
|
7.2528
|
479.9811
|
3.3666
|
|
December 2013
|
0.9786
|
POST
|
0
|
-3.1091
|
CE
|
4
|
7.1699
|
477.1218
|
3.3797
|
|
November 2013
|
0.9763
|
POST
|
0
|
-3.1464
|
CE
|
4
|
7.3463
|
483.8175
|
3.3926
|
|
October 2013
|
0.9855
|
POST
|
0
|
-3.1293
|
CE
|
4
|
7.2357
|
479.8867
|
3.4003
|
|
September 2012
|
0.9872
|
POST
|
0
|
-3.1443
|
CE
|
4
|
7.2982
|
482.2951
|
3.4122
|
|
August 2013
|
0.9872
|
POST
|
0
|
-3.1284
|
CE
|
4
|
7.227
|
479.5591
|
3.4261
|
Table 2.
The best fit models for 2012
|
Month
|
b1
|
CPI1
|
lag1
|
b2
|
CPI2
|
lag2
|
c
|
d
|
sterr, $
|
|
December
|
1.163
|
POST
|
0
|
-3.131
|
CE
|
4
|
6.466
|
463.155
|
3.33
|
|
November
|
1.163
|
POST
|
0
|
-3.126
|
CE
|
4
|
6.433
|
462.370
|
3.33
|
|
October
|
1.164
|
POST
|
0
|
-3.116
|
CE
|
4
|
6.386
|
460.441
|
3.33
|
|
September
|
1.158
|
POST
|
0
|
-3.105
|
CE
|
4
|
6.351
|
459.243
|
3.32
|
|
August
|
1.154
|
POST
|
0
|
-3.112
|
CE
|
4
|
6.392
|
460.948
|
3.32
|
|
July
|
1.156
|
POST
|
0
|
-3.129
|
CE
|
4
|
6.461
|
463.677
|
3.32
|
|
June
|
1.190
|
POST
|
0
|
-3.143
|
CE
|
4
|
6.370
|
461.592
|
3.31
|
|
May
|
1.214
|
POST
|
0
|
-3.171
|
CE
|
4
|
6.408
|
463.963
|
3.29
|
Figure
1. The evolution of POST and CE indices
Figure 2.
Observed and predicted JDSU share prices.
Figure 3.
The model residual error: stdev=$3.38.
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