Franklin Resources is likely overvalued

Here we present a new price model for Franklin Resources (NYSE: BEN).  The firm provides its services to individuals, institutions, pension plans, trusts, and partnerships. It manages, through its subsidiary, separate client-focused equity, fixed income, and balanced portfolios. BEN is a financial company and  we analyzed it three years ago as a candidate for  bankruptcy. 

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. Our model also includes a linear time trend and an intercept in order to remove mean and trend components from all involved time series.  The intuition behind our pricing model is obvious – we link a given share to those goods and services which are produced/provided by the company. In order to provide a dynamic reference we also introduce in the model some relative and independent level of prices (also expressed by CPIs). Hence, one needs two different CPIs to define the model. These CPIs we select from a big set of 92 CPIs by minimizing the residual model error.  

The current BEN model is driven by the consumer price index of food at home, FH, leading the price by five months and the index of other goods and services, O, which leads by nine months:  

BEN(t) = -5.47FH(t-5) – 1.81O(t-9) – 59.55(t-2000) + 1327.36, February 2012     

where t is calendar time.  The standard error between July 2003 and February 2012 is $7.55.  

The BEN model includes almost the same CPIs as the model for Apartment Investment and Management Company (NYSE:AIV), which we presented several days ago. For AIV, the index of food and beverages is defining instead of the index of food at home, but the difference is very small:

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

Both models allow prediction at a five month horizon. 

It is interesting to compare the overall evolution of both prices since 2003 and to understand their similarities and differences. Figure 1 displays both prices as they are. Their shapes are mainly similar but the amplitudes are quite different. Figure 2 depicts the same curves but normalized to their respective peak values between 2003 and 2012. The similarity and the presence of a sharp fall in October-November 2008 are obvious. This might be the reason behind the similarity in defining CPIs and the time lead. In any case, it is very important to have a hint on the future fall in the prices five(!) months in advance, as it was in 2008.  

Figure 1. The evolution of BEN and AIV share prices.

Figure 2. The evolution of BEN and AIV share prices, both normalized to their peak values beteen 2003 and 2012.  

Here we present the new BEN model in a standard way. Figure 1 shows the evolution of both defining indices between 2002 and 2012. Figure 4 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. The real time prediction (green curve) leads the observed price by 5 month. As for AIV, all major turns in the price were well foreseen by the model, including those in April 2007, May 2009, and May 2011. The residual error is also shown in Figure 5 with standard deviation of $7.55.

Figure 5 shows that BEN price is likely overvalued (same for AIV). One might expect that BEN shares will likely to fall slightly in the second quarter of 2012 and then will stay at $105.  

Figure 3. The evolution of defining CPIs.

Figure 4. Observed and predicted BEN share prices together with the high/low monthly prices.

Figure 5 . The residual model error.

Can we expect oil price deflation in 2012?

The price index of energy comprises approximately 10% of the headline CPI. It is highly correlated with oil price. The surge in oil price observed since November 2011 (Figure 1) has been the most important driver of the elevated consumer price inflation.

In August 2011, we discussed the evolution of crude price and compared prices with one year spacing.  This allows foreseeing the level of crude price index needed for a given rate of price inflation. Figure 1 presents an updated version of that in the previous post with data available through February 2012. One can see that the level of crude (domestic production) index approaches the peak value observed a year ago.  

The monthly rate of inflation is an important but only a transient indicator of the overall price change. Therefore, we have calculated the annual rate from the curves in Figure 1, where red line is the original price index (black line) shifted by one year ahead. The ratio of black and red line is the rate of oil price inflation, as shown in Figure 2.  The rate of inflation is characterized by two peaks in 2008 and 2010. Obviously, the rate of inflation is defined by two factors: the current level of oil price and that one year ago. The difference between black and red line can be considered as a crude estimate of the inflation rate. When the red line is above black line, the rate of inflation is negative. Otherwise, the rate is positive.

What can we expect in the second half of 2012 with the price index of oil peaking in the middle of 2011?  Almost inevitably, the rate of (oil price) inflation will be negative during several months, say, from May to October 2012 despite oil price is high.

Figure 1. The (producer) price index of oil (domestic crude petroleum). Red line is the original price index shifted one year ahead. The ratio of black and red line is the rate of oil price inflation shown in Figure 2.   

Figure 2. The annual rate of oil price growth.

Devon Energy is undervalued

A month ago we presented an annual report on the performance of our pricing model for ConocoPhillips (NYSE: COP) and found an excellent agreement between the predicted and measured monthly closing prices since 2000. Here we compare the overall behavior of the COP model and a model estimated for Devon Energy Corporation (NYSE: DVN) by the same technique.

Our simplest model links share prices of energy companies with the difference between the headline and core CPI. In essence, we were trying to use the core CPI as an energy independent (dynamic) reference to the headline CPI which includes energy and, in turn, is related to oil price. Then the difference between these CPIs might be manifested in the energy pricing power relative to all other goods and services.

Formally, our original pricing model states that a share price, for example, that of Devon Energy, DVN(t), can be approximated by a linear function of the difference between the core CPI, cCPI, and headline CPI:

DVN(t) = A + B[cCPI(t) - CPI(t)] (1)

where A and B are empirical constants (as obtained by linear regression); t is the elapsed time. Figure 1 shows the observed and predicted DVM share prices since 2000. The best fit model is characterized by A=$93, B=-7.5, and a standard model error, sterr=$11.51, for the period between January 2000 and February 2012. One can observe a good agreement between January 2000 and April 2011, when the predicted curve started to deviate from the observed one. The period after May 2011 has introduced the largest model error and is absolutely different from the behavior of the COP model which has proven its predictive power. (We have been reporting on its performance since 2009.) Figure 2 depicts the observed and predicted monthly closing prices for ConocoPhillips since 2002 with A=$75 and B=-5.5. The standard model error is only $8.31 for the period between 2002 and 2012.

Comparing the COP and DVN models one can conclude that the current price of Devon Energy is undervalued by about $15. In February 2012, the price closed some portion of the gap and this process should extend into March and April.

Figure 1. The observed DVN price and that predicted from the core and headline CPI. A=$93, B=-7.5; sterr=$11.51.

Figure 2. The observed COP price and that predicted from the core and headline CPI. A=$75, B=-5.5; sterr=$8.31.

FedEx is slightly overvalued

Here we present a tentative model for the evolution of FedEx (NYSE: FDX) stock price. 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. 

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:  

FDX(t) =  -4.87F(t-3) – 5.09CO(t-5)  + 26.50(t-1990) + 1039.05,  February 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 that here we present a tentative model which is fresh and needs to be validated by new data (new CPI estimates will be published tomorrow). 

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $6.33. It is not excluded that the share will have a negative correction in April/May.

Figure 1. The evolution of F and CO indices  

Figure 2. Observed and predicted FDX share prices. 

Figure 3. The model residual error: sterr=$6.33.

JPMorgan Chase & Co.: a negative correction is not excluded

Here we present a tentative model for the evolution of JPMorgan Chase & Co. (NYSE: JPM) stock price. JPM is a company from financial sector which provides various financial products and services worldwide. The model has been obtained using our general concept of share pricing as based on a decomposition of a share price into a weighted sum of two consumer price indices. Our main assumption is a natural one – all goods and services produced (provided) by a given company should define the share price evolution relative to other companies. In other words, relative pricing power of the company is related to the pricing power of its G&S. Since other companies are also driven by prices for their goods and services, which compete with the studied company, one need two defining sets of G&S to estimate the relative pricing power. Presumably, the studied share price can be defined by two CPIs.


The best CPIs are selected from a set of 92 CPIs with estimates available from 2000. The best fit (in the LSQ sense) consumer price indices are that of food and beverages (F) and the index of owner’s equivalent rent of residence (ORPR). 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:

JPM(t) = -1.99F(t-3) + 1.15ORPR(t-2) + 6.81(t-1990) + 39.30, February 2012

where JPM(t) is the JPM 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 well within the bounds of the share price uncertainty and lead by 2 months. However the measured price volatility is much higher than the predicted one. This means that large deviations from the predicted level are possible but such excursions are always ended on the predicted curve. One can use this observation for a qualitative forecast of price movements.
It should be noted that here we present a tentative model which is fresh and needs to be validated by new data.

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $2.84. It is not excluded that the share will have a negative correction in April/May.

Figure 1. The evolution of F and ORPR indices

Figure 2. Observed and predicted JPM share prices.

Figure 3. The model residual error: sterr=$2.84.

Procter and Gamble - a negative correction is not excluded before May 2012

In January 2012, we updated our share price model for Procter and Gamble (NYSE: PG) and showed that the original PG model had been working since September 2009 without any change. We presented the evolution of the model since 2009 in a series of figures. The original model does not show any sign of possible failure and here we re-estimate it using new data which are available in March 2012.

Our pricing concept is based on the decomposition of a share time history into a weighted sum of two consumer price indices, linear time trend and constant. 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. It should also be taken into account that any change in the defining CPIs may lead the share price reaction by months. Apparently, demand and supply are separated in time.

A share price model for Procter and Gamble was originally published in July 2010. According to our concept, it was defined by the index of food away from home (SEFV - CUUS0000SEFV) and that of rent of primary residency (RPR); the evolution of these indices is presented in Figure 1. In the original model, the former CPI component led the share price by 3 months and the latter one led by 8 months:

PG(t) = -5.88SEFV(t-3) + 3.43RPR(t-8) + 17.60(t-1990) + 174.08, July 2010

In April 2011, we updated the original model using some new data (closing price for March 2011) and found that the same model was also applicable with a small change in the time lead for the SEFV – it was 4 months instead of 3 months in the original model. New coefficients were also slightly different, but very close to the original ones:

PG(t) = -5.40SEFV(t-4) + 2.93RPR(t-8) + 18.16(t-1990) + 187.47, March 2011

In September 2011, the updated model used the monthly closing price for September 2011 and CPIs for August 2011. It validated the model obtained for the previous period but is characterized by the same time lags and a small shift in the coefficients estimated by the LSQ technique.

PG(t) = -4.94SEFV(t-4) + 2.47RPR(t-8) + 18.15(t-1990) + 184.89, September 2011

In December 2011, the closing prices were estimated using the CPI data for December 2011 and thus both time shifts are one month longer. Accordingly, the best-fit models for PG(t) are as follows:

PG(t) = -4.76SEFV(t-5) + 2.27RPR(t-9) + 18.29(t-1990) + 187.61, December 2011

The current model is similar to all previously obtained models:

PG(t) = -4.42SEFV(t-4) + 2.00RPR(t-8) + 18.01(t-1990) + 185.91, February 2012

where PG(t) is the monthly closing price (dividend and split adjusted) in U.S. dollars, t is calendar time.

Figure 2 depicts the predicted curve which actually leads the observed price by 4 months with the residual error of $2.25 for the period between July 2003 and February 2012 (see Figure 3 for the model residuals). In other words, the price of a PG share is completely defined by the behaviour of these two CPI components.

The model does predict the share price in the past. There is a nonzero probability that the price will fall to $60-$62 by May 2012: the model error was $8 in February.

Figure 1. Evolution of the price of SEFV and RPR.

Figure 2. Observed and predicted PG share prices.

Figure 3. The model residual error.

Wal-Mart Stores is stable in March

We revisited our price model for Wal-Mart Stores (NYSE: WMT) two months ago. Originally, the model was estimated in June 2010 and the same model still worked well in December 2011. This suggests the overall robustness and reliability of the share price model for WTM.

Our concept of share pricing is based on the decomposition into a weighted sum of two selected consumer price indices. The intuition is simple; a faster growth in the CPI related to a given company relative to some independent but dynamic reference should be manifested in a higher pricing power for the studied company. This reference is needed since all consumer prices change over time and those associated with the company should be measured in relative terms. Hence, our stock price model seeks for a defining CPI and the best reference which we both select 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 a long enough measurement history (i.e. continuous estimates should be available since 2000).

Here we re-estimate the original model with data available in March 2012, i.e. the closing price for February and CPIs for January 2012. This model is defined by the (seasonally not adjusted) index of hospital and related services (HOSP) and the price index of miscellaneous personal services (MISS), as reported by the US BLS. The former CPI component leads the share price by 9 months and the latter one evolves in sync with the price. Figure 1 depicts the overall evolution of both involved indices through January 2012. A very specific feature of both indices is their linearity over time: they are close to straight lines with small fluctuations.

 

The newly estimated model allows validating the initial model and demonstrating its reliability. The previously obtained defining components are the same and provide the best fit model between June 2010, March and December 2011 with only one month change in the lag for the HOSP index. All coefficients are slightly different for the new model (see below). The slope of the time trend is negative. The best-fit 2-C model for WMT(t) is as follows:

WMT(t) = 0.50HOSP(t-10) + 1.42MISS(t) - 28.39(t-1990) – 158.12 (January 2011)

WMT(t) = 0.46HOSP(t-9) + 1.49MISS(t) - 28.03(t-1990) – 165.50 (March 2011)

WMT(t) = 0.46HOSP(t-9) + 1.30MISS(t) - 26.06(t-1990) – 141.92 (December 2011)

WMT(t) = 0.48HOSP(t-9) + 1.33MISS(t) - 26.75(t-1990) – 145.13 (February 2012)

where t is calendar time. The predicted curve in Figure 2 evolves in sync with the observed price. The residual error is $2.15 for the period between June 2003 and February 2012.

With both indices growing along their respective trends, we foresaw in December 2011 a slight increase to the level of $60 to $65 per share in 2012Q1. It really happened and the price was at the level $62.06 in February. The current model supposes a slight negative correction which also follows from the positive residual error shown in Figure 3. A no change scenario is also possible with the predicted price rising to the level of the measured one in March 2012. In a week, we will re-estimate the model using both CPIs for February.

Figure 1. Evolution of the price of HOSP and MISS.

Figure 2. Observed and predicted WMT share prices.

Figure 3. Residual error of the model; sterr=$2.15.