This time, we would
like to revisit our deterministic model for a share price of Pitney Bowes (NYSE:
PBI) which “provides
software, hardware, and services to enable physical and digital communications”. In
March 2012, we presented a preliminary model and did not exclude
that the price would fall below the level of $15 per share by May 2012. This
was a correct prediction and the (monthly closing) price fell to $13.28 in May
(as borrowed from Yahoo
at 11/10.2012). This level was below the
predicted one and the actual price has been hovering near $14 since June. The
updated model as based on the data between March and October 2012 has validated
our concept of share pricing. Since the consumer index of IT does not show any
sign of a faster growth and the food price index will likely grow till 2014 the
PBI’s share will suffer further fall. We would not recommend buying this share
in the near future.

The PBI model
is deterministic since it has been obtained by decomposition of a share price
into a weighted sum of two consumer price indices. One may follow up our simple
assumption that the growth in a CPI related to PBI (e.g. information technology)
relative to some independent but dynamic reference (e.g. food away from home) should
be seen in a higher pricing power for the studied company. But this is the
outcome of modeling. To obtain this result, our stock price model tries to find
one defining CPI and the best reference from a set of 92 different (not
seasonally adjusted) CPIs. The best model has to have the smallest RMS error
between July 2003 and October 2012. This set includes the headline and core
CPI, all major categories from food to other goods and services, and many minor
subcategories with long enough history (i.e. continuous estimates should be
available since 2000).

We
have borrowed the time series of monthly closing prices of PBI from Yahoo.com and
the CPI (not seasonally adjusted) estimates through October 2012 are published
by the BLS. As mentioned above, the evolution
of PBI share price is defined by the consumer price of the index of information
technology (IT) and the index of food away from home (SEVF). In the original model, the
defining time lag is the same for both CPIs – one month. In the
updated model, the time lag of the IT index is zero. The
best-fit models for

*PBI(t)*are as follows:*PBI(t) =*-2.09 SEVF

*(t-1) - 4.87IT(t-1) +*7.66

*(t-*1990

*) +*381.64, February 2012

*PBI(t) =*-1.90 SEVF

*(t-1) - 4.62IT(t-0) +*6.82

*(t-*2000

*) +*420.30, October 2012

where

*PBI(t)*is the PBI share price in U.S. dollars,*t*is calendar time. Figure 1 displays the evolution of both defining indices since 2002. Both indices have negative slopes and the IT index defines the growth of the price. Higher food prices suppress the level of PBI share price.
Figure 2 depicts the
high and low monthly prices for an PBI share together with the predicted and
measured monthly closing prices (adjusted for dividends and splits). The
predicted prices are well within the limits of the share price variation within
the corresponding months. The model
residual error is shown in Figure 3 with the standard deviation between July
2003 and October 2012 of $1.37.

Figure 1. The
evolution of defining indices.

Figure 2. Observed and predicted monthly closing prices for a PBI share.

Figure 3. The model
standard error is $1.37.

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