3/31/14

Modeling share prices: JDS Uniphase to hold


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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