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.