Pitney Bowes' share price may continue its long-term fall

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.

Northeast Utilities May Fall To $37 Per Share by 2013

Here we revisit our pricing model for a company from Utilities category – Northeast Utilities (NYSE: NU), a public utility holding company, which provides electric and natural gas energy delivery services In April, we concluded that the price should rise in the second quarter of 2012 to the level of $37 per share, with the relevant standard error of $1.23. The closing monthly price (adjusted for splits and dividends) in June was $38.46. It has increased to $39.3 in October. The updated model indicates that the price has to decrease by approximately $2 in the next few months. Otherwise, the price has to be relatively stable over the next seven months, i.e. during the natural forecasting period. One may consider NU as a reliable company for investments but wait before buying at $37.   

Before presenting the best fit deterministic pricing model for NU we would like to brief on the underlying pricing concept.  Our approach consists in decomposition of a share price into a weighted sum of two consumer (or producer) price indices. One may test quantitatively our simple assumption that the growth in some specific CPI related to NU (e.g. housekeeping supplies, the BLS name is CUUR0000SEHN and we abbreviate it to HOS) relative to some independent but dynamic reference (e.g. food away from home, CUUS0000SEF or SEFV) should be seen in a higher pricing power for the studied company. In essence, our stock price model tries to find one defining CPI and the best reference.

In order to find the best pair of CPIs we calculate the RMS residual errors using all permutations from a set of 92 different (not seasonally adjusted) CPIs. In addition we allow for time lag (fixed between 0 and 11 months) between the studied price and both indices, and introduce a linear trend and intercept terms. The best model has the smallest RMS error between July 2003 and October 2012. The complete 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 2001).

We have borrowed the time series of monthly closing prices of NU from Yahoo.com (October 2012 is included) and the CPI estimates through October 2012 are published by the BLS.  The best-fit models for NU(t) in March and October are as follows:  

NU(t) =  -2.57SEVF(t-6) + 0.97HOS(t-7)  + 15.18(t-2000) + 267.79,  March 2012

NU(t) =  -2.60SEVF(t-7) + 0.98HOS(t-8)  + 15.25(t-2000) + 268.06,  October 2012 

where NU(t) is the NU share price in U.S. dollars,  t is calendar time. The changes in the model are just minor with the same principal CPIs, very close time lags, and slightly changed coefficients. One can conclude that the data for the past seven months have validated the original model.

 

Figure 1 displays the evolution of both defining indices since 2002.  The housekeeping supplies index has a positive influece on the price, i.e. the growth in HOS results in a higher NU price. Apparently, the negative slope of SEFV implies that higher food prices reduce the NU return. This is not against common sense.   

Figure 2 depicts the high and low monthly prices for a NU share together with the predicted and measured monthly closing prices. The high/low prices put natural limits for the variation of the monthly price. The predicted prices are well within the high/low share price curves.  The model residual error is shown in Figure 3 with the standard error between July 2003 and October 2012 of $1.20 (in March, the error was $1.23). All in all, the model is very accurate and all deviations are promptly recovered, i.e. the measured curve returns to the predicted one, which leads by seven months. One can foresee the share price behaviour seven months ahead, as shown by solid red line representing a contemporary prediction of the price.   

Considering Figure 2, one can conclude that the price should fall in the fourth quarter of 2012 to the level of $37 per share. It will likely stay that level in 2013Q1.   

Figure 1. The evolution of defining indices. 

 

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

 

Figure 3. The model residual error: standard error $1.20.

No big move in FedEx share price is expected

Here we revise our tentative model for the evolution of FedEx (NYSE: FDX) stock price. In March 2012, we suggested that this share is slightly overvalued and a negative correction was possible. Actually, the price has been hovering around $90. The updated model, which includes monthly closing price for October, foresees no big change in 2012. The positive residual through Q2 and Q3 was stable but fell to zero due to the change in defining variables, not the price. In any case, the predicted correction of $5 was within the model uncertainty of $6.4, which is the standard model error from July 2003.   

FDX is a company from Services sector of the S&P 500 index which “provides transportation, e-commerce, and business services in the United States and internationally”. We decompose a FDX share price into a weighted sum of two consumer price indices, one has to be related to the overall FDX activity and one index is independent on FDX services.  We assume that all goods and services produced (provided) by FDX should define the share price evolution relative to other companies. In other words, the FDX relative pricing power is defined by the pricing power of its G&S. Since other companies are also driven by prices for their goods and services, which compete with FDX, one need two defining sets of G&S to estimate the relative pricing power. It is not excluded that the studied share price can be accurately defined by two CPIs. There are some measurement errors in all CPIs which are directly mapped into the model errors. Since we model the monthly closing prices (CPIs are reported at a monthly rate) the intermonth variations (high/low prices) can be treated as natural uncertainty of the monthly closing prices. Therefore our pricing model has two sources of uncertainty.

As in the tentative model, the best CPIs are selected from a set of 92 CPIs with estimates available from 2000 (one may extend this set). The best fit (in the LSQ sense) consumer price indices are that of food and beverages (F - CUUS0000SAF) and the index of communication (CO - CUUR0000SAE2). The latter index is directly related to FedEx and the former one seems to be mainly independent and evolving according to own forces. The defining time lags are as follows: the food index leads the share price by 3 months and the CO index leads by 5 months. The tentative and updated models are as follows:   

FDX(t) =  -4.87F(t-3) – 5.09CO(t-5)  + 26.50(t-1990) + 1039.05,  February 2012

FDX(t) =  -4.70F(t-3) – 5.52CO(t-5)  + 25.78(t-2000) + 1314.97,  October  2012 

where FDX(t) is the FDX 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 a share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are mainly within the bounds of the share price uncertainty and lead by 3 months.  Since the measured price volatility is much higher than the predicted one there are some large deviations from the predicted level. In any case, such fluctuations have always ended on the predicted curve. One can use this observation for a qualitative forecast of the future price movements.  

It should be noted the tentative model is partly validated by new data. The model residual error is shown in Figure 3 with the standard deviation between July 2003 and October 2012 of $6.43.  

Figure 1. The evolution of F and CO indices

 

Figure 2. Observed and predicted FDX share prices.

Figure 3. The model residual error: sterr=$6.43.