Pitney Bowes shares on decline

We would like to introduce another deterministic model for a share price from the S&P 500 index.  This time we present a company from consumer goods category - Pitney Bowes (NYSE: PBI) which “provides software, hardware, and services to enable physical and digital communications”. The 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. Hence, our stock price model tries to find one defining CPI and the best reference. Both CPIs are taken from a set of 92 different (not seasonally adjusted) CPIs and the best model has the smallest RMS error between July 2003 and February 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 (February 2012 is included) and the CPI estimates through January 2012 are published by the BLS.  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). The defining time lag is the same for both CPIs – one month.   The best-fit model for PBI(t) is as follows:  

PBI(t) =  -2.09 SEVF(t-1) - 4.87IT(t-1)  + 7.66(t-1990) + 381.64,  February 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 uncertainty.  The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $1.53.  

Since April 2011, the price of food away from home has been growing at a rate much higher than the rate of the IT index growth. This proportion of growth rates has affected the PBI price and it has been falling. We can not exclude that the price will fall below the level of $15 per share by May 2012. The IT price index does not show any sigh of faster growth and food price will likely grow till 2014.  

Figure 1. The evolution of defining indices.

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

Figure 3. The model residual error: sterr=$1.53.

Genuine Parts will be rising in 2012

We continue modeling share prices for selected companies from the S&P 500 index and here we (first time) address the stock price model for Genuine Parts (NYSE: GPC) which is a company from services sector which “distributes automotive replacement parts, industrial replacement parts, office products, and electrical/electronic materials”. The model has been obtained using our concept of share pricing as a decomposition of a share price into a weighted sum of two consumer price indices. The intuition is simple; a faster growth in the CPI related to GPC (e.g. motor vehicle maintenance and repair) relative to some independent but dynamic reference (e.g. prescription drugs) should be manifested in a higher pricing power for the studied company. Hence, our stock price model seeks for a defining CPI and the best reference which we both take from a set of 92 different (not seasonally adjusted) CPIs. 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 GPC from Yahoo.com (February 2012 is included) and the CPI estimates through January 2012 are published by the BLS.  The evolution of GPC share price is defined by the consumer price of the index of motor vehicle maintenance and repair (MVR) and the index of prescription drugs (PDRUG). The defining time lags are as follows: the MVR index has a one month lead and the PDRUG index leads by 9 months. The relevant best-fit model for GPC(t) is as follows: 

GPC(t) =  -1.87 MVR(t-1) + 0.65PDRUG(t-9)  + 9.86(t-1990) + 42.72,  February 2012

where GPC(t) is the GPC share price in U.S. dollars,  t is calendar time. Figure 1 displays the evolution of both defining indices since 2002.  The PDRUG index has a positve slope and grows much faster than the MVR one, Therefoer, the PDRUS index drives the rise in the share price since 2009.

Figure 2 depicts the high and low monthly prices for an GPC share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the bounds of the share price uncertainty.  The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $1.74.  

Since all prices related to medical goods and services are on a healthy rise without any sign of deceleration, the GPC price should not be decreasing unless the MVR index starts to grow fast. Fortunately for GPC, there are no real forces to pull the MVR index up.  Hence, we expect GPC to rise further in 2012.  

We have also reported on AutoNation’s share price.

Figure 1. The evolution of the index of Motor vehicle repair and maintenance (MVR) and the index of prescription drugs (PDRUG).  

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

Figure 3. The model residual error: stdev=$1.74.

Employment - only marginal improvements expected

The BLS has published a monthly “Employment Situation” report for February 2012. For establishment survey data, the BLS has estimated that “nonfarm payroll employment rose by 227,000 in February”. This is a good figure which is subject to revision.

Here we focus on the household survey data, which include the level of employment and the rate of unemployment. Figure 1 presents the estimated number of employed since 1990. There is a fall between 2008 and 2009 from ~147,000,000 to ~138,000,000, i.e. by 9,000,000. This is a huge drop. Since 2010, the level of employment has been steadily increasing and is of 142,065,000 in February 2012.  There is a step between December 2011 and January 2012 which is induced by a large revision to population controls, which is also seen in Figure 2 depicting the evolution of civilian non-institutional population.  The population curve is a bit weird due to such corrections and revisions (we have explained and accounted for this effect here). One should be careful with the BLS data.  

The level of employment is driven by the overall population and the rate of participation in employment. Figure 3 displays the employment/population ratio since 1990. Unlike the level of employment, the rate has not been growing since 2010. There were weak fluctuations between 58.7% and 58.3%. This is close to the inherent uncertainty of employment measurements. In February 2012, this rate is 58.6% which is marginally (+0.1%) above that in January. This might be a transient improvement if the curve will repeat the pattern observed in 2010 and 2011, when local peaks (as in February) were followed by falls.  

All in all, the rate of employment is at its lowermost level since 1983. And it does not show any strong signs of recovery.  

The rate of unemployment, UER, is 8.3%, i.e. at the same level as in January. Figure 4 illustrates the evolution of UER which has been falling since October 2010. We have projected the rate of unemployment to fall to 7.8% in December 2012. This may also result in a slight improvement of the E/P. However, the UER has been falling due to diminishing labor force. Figure 5 shows that the level of labor force has been falling rather than rising since 2008.

We expect the rate of unemployment to drop but this process will not be accompanied by rising employment/population ratio.  The level of employment will be growing proportionally to the civilian population.

Figure 1. The number of employed. Notice a step between December 2011 and January 2012 related to the change in population controls. 

Figure 2.  Civilian non-residential population. Notice several corrections induced by population controls.

Figure 3. Employment/ population ratio. Almost no change since 2009.

Figure 4. The rate of unemployment.

Figure 5. The level of labor force. 

Loews Corporation share price Q2 2012

This is a report on the performance of our share price model for Loews Corporation (NYSE: L). The model is based on the decomposition into a weighted sum of two consumer price indices (selected from a larger set of CPIs), linear trend and constant; all coefficients and time lags to be estimated by a LSQ procedure. A month ago we presented a quarterly report and confirmed the stability of the original model obtained in September 2009 for the period through October 2008. Here we test the previous model and make a regular update using new data through February 2012 (March 2012 for the share price). All in all, the original model is valid since October 2008 and does not show any clear sign of changes in the future. This is a reliable model valid during the past 52 months!  

A preliminary model for Loews Corp. was obtained in September 2009 and covered the period from October 2008. This old model included the index of food without beverages (FB) which led by 6 months and the index of transportation service (TS) with a 4 months lead: 

L(t) = -2.52FB(t-6) – 1.38TS(t-4) +27.93(t-1990) + 377.24, stdev=$2.04,  September 2009 

where L(t) is the share price in US dollars, t is calendar time.  

Since November 2010, the defining indices were the same: the index of food and beverages (F) and the TS index. Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2003 and February 2011.  The food and beverages index leads by 5 months and the TS index by 4 months.  The model does not show any tangible change with time - only coefficients have been slightly fluctuating:  

L(t) = -2.04F(t-5) – 2.08TS(t-4) +28.09(t-1990) + 441.81, November 2010

L(t) = -2.03F(t-5) – 2.12TS(t-4) +28.23(t-1990) + 448.98, March 2011

L(t) = -2.01F(t-5) – 2.09TS(t-4) +27.96(t-1990) +440.65, September 2011

L(t) = -2.03F(t-5) – 2.02TS(t-4) +27.65(t-1990) +431.99, December 2011

L(t) = -2.01F(t-5) – 2.01TS(t-4) +27.49(t-1990) +428.70, stdev=$2.41, February 2012      

The current model is depicted in Figure 2 together with high and low monthly prices as a proxy to the uncertainty bound of the share price. The predicted curve leads the observed one by 4 months. The solid red line presents the contemporary prediction, i.e. one sees four months ahead. Major falls and rises are well forecasted four months in advance. It is worth noting that the model obtained in March 2011, accurately predicted the small fall observed in the second and third quarters of 2011.    

The model residual error is of $2.41 for the period between July 2003 and February 2011, as shown in Figure 3. In the first quarter of 2012, the model foresees essentially no change. In the second quarter, the price is expected to rise to $40 per share.

Figure 1. Evolution of the price indices F and TS.

Figure 2. Observed and predicted share prices.

Figure 3. The model residual error; stdev=$2.41.

Aflac Incorporated: no change in March

A month ago we routinely revisited the stock price model for Aflac Incorporated (AFL), which we has obtained in October 2011 using our concept of share pricing. We decompose a share price into a weighted sum of two consumer price indices. This allows linking the share price with relative pricing power of goods and services associated with the company. Here we revise the recent model using the new CPI estimates published by the BLS for January 2012. Accordingly, our goal is to test the original model and to update time lags and coefficients.  

As in three previous models, the AFL share price is defined by the consumer price index of household furnishing and operations (HFO) and that transportation services (TS). In December 2011, the defining time lags were as follows: the HFO index led the share price by 1 month and the TS by 6 months. Therefore, four relevant best-fit models for AFL(t) are as follows:  

AFL(t) =  -5.02HFO(t-2) – 2.87TS(t-6)  + 20.42(t-1990) + 997.71,  March 2011

AFL(t) =  -4.63HFO(t-0) – 2.90TS(t-5)  + 20.41(t-1990) + 953.49, September 2011

AFL(t) =  -4.63HFO(t-1) – 2.87TS(t-6)  + 20.23(t-1990) + 948.72, December 2011

AFL(t) =  -4.65HFO(t-1) – 2.86TS(t-6)  + 20.20(t-1990) + 949.35, February 2012  

where AFL(t) is the AFL share price in U.S. dollars,  t is calendar time. 

In July 2011, we reported that the original model gave a correct prediction of the fall in Q2 2011. In September 2011, we showed that the contemporary fall in the price had to stop and expected a positive correction in Q4 2011. A month ago we predicted that the price would likely not change much in 2012Q1. Figure 1 confirms our prediction – the closing price in January was $47.9 and $45.42 in February. It depicts the high and low monthly prices for an AFL share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The model residual error ($4.02 for the period between July 2003 and February 2012) is depicted in Figure 2. 

We do not foresee any large change in the price in March and likely in April 2012.  

Figure 1. Observed and predicted AFL share prices.

Figure 2. The model residual error $4.02.

Prudential Financial's share price: a negative correction is expected in March-April

Here we model the evolution of Prudential Financial (NYSE: PRU) stock price. Prudential is a company from financial sector which provides provides various financial products and services. The model has been obtained using our concept of share pricing as a decomposition of a share price into a weighted sum of two consumer price indices. The intuition is clear – there is a set of goods and services which any company produces and this set defines the share price evolution of a given company relative to other companies. These other companies are also driven by prices for some goods and services. Hence, for a given company one needs two defining sets of goods and services to estimate its relative pricing power – one related and one as an independent reference. Thus, the relevant stock price can be defined by two CPIs which include corresponding goods and services.  

Originally, we addressed the PRU model in 2009 and found two CPIs explaining the monthly closing prices of PRU since 2003. They were the consumer price index of food and beverages (F) and the index of transportation services (TS). The defining time lags were as follows: the food index led the share price by 5 months and the TS index led by 4 months:  

PRU(t) =  -6.09F(t-5) – 3.15TS(t-4)  + 59.76(t-1990) + 930.50,  September 2009 

In 2010, we revisited the original model and estimated new coefficients and lags. These estimates were close to the original ones: 

PRU(t) =  -5.45F(t-5) – 3.98TS(t-3)  + 59.66(t-1990) + 1055.38,  September  2010 

Here we revise the model and re-estimate all coefficients and lags. We have borrowed the time series of monthly closing prices of PRU from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS.  The best-fit model for PRU(t) is as follows:  

PRU(t) =  -5.14F(t-5) – 3.80TS(t-4)  + 56.20(t-1990) + 1005.63,  February 2012 

where PRU(t) is the PRU share price in U.S. dollars,  t is calendar time. One can conclude that the model has not been changing since January 2009 and thus provides a good estimate of the price at a four month horizon.  

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 well within the bounds of the share price uncertainty and lead by 4 months.  

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $5.58. The share price is expected to grow in the first half of 2012, but the current price level already corresponds to that expected in June. Therefore, a negative correction in March-April is not excluded. Otherwise, Prudential Financial has a good short-term (months) perspective.

Figure 1. The evolution of F and TS indices  

Figure 2. Observed and predicted PRU share prices.

Figure 3. The model residual error: stdev=$5.58.

Apartment Investment and Management Company's share price: a slight fall is not excluded

Here we present a simple two-component share price model for Apartment Investment and Management Company (NYSE:AIV). We presume that any share price can be represented as a weighted sum of two consumer price indices (not seasonally adjusted in our model) which may be leading the share price by several months. The model  also includes a linear time trend and an intercept in order to remove mean and trend components from the time series. AIV is a financial company listed in the S&P 500 market index. It “engages in the acquisition, ownership, management, and redevelopment of apartment properties.”

We have been following the evolution of AIV share price since 2008 and a preliminary model was presented in 2009. It was based on a selection from a smaller set of CPIs and thus subject to further improvement. The current model is based on the index of food and beverages (F) and the index of other (O); the former is five months and the latter is six months ahead of the price. Figure 1 shows both CPIs since 2002. This set of CPIs has been determining the best-fit model during the past 24 months. The best-fit two-component model for AIV(t) is as follows:

AIV(t)= -2.57F(t-5) -0.41O(t-6) +20.51(t-1990) + 520.76, February 2012

where AIV(t) is the AIV share price in U.S. dollars, t is calendar time. The stadard error of teh model is $2.15 for the period between July 2003 and February 2012.

Figure 2 depicts the observed and predicted monthly closing prices since 2003 and also provides an estimate of the model natural uncertainty as related to the high/low monthly prices. Actually, the predicted curve leads the observed price by 5 months and is shifted back for better visual comparison. In that sense all major turn in the price were well foreseen by the model, including those in April 2007, May 2009, and May 2011. In other words, AIV share price is completely defined by the behaviour of these two CPI components. The residual error is also shown in Figure 3 with standard deviation of $2.15 for the period between July 2003 and February 2012.

Figure 3 shows that the price is likely overvalued by about $5. From Figure 2, one can conclude that AIV share will likely to fall slightly in the first quarter of 2012 and then will go up. It could be a new turn up in the price evolution.

Figure 1. The evolution of defining CPIs.

Figure 2. Observed and predicted AIV share prices together with the high/low monthly prices.

Figure 3 . The residual model error.