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Summary

  • We have developed a statistically reliable share price model for Bank of America based on the consumer price index of food at home and the index of rent of shelter.
  • The model does foresee significant price changes in April 2014.
  • The model standard error is $2.86 since July 2003, that corresponds to the level of intermonth price fluctuations.

Here we introduce a new pricing model for Bank of America (NYSE: BAC). We have been trying to build a reliable model for BAC since 2008. Price modeling is based on our concept of stock pricing as a decomposition of a share price into a weighted sum of two consumer price indices (CPIs). The background idea is a simplistic one: there is a potential trade-off between a given share price and goods & services the company produces/provides. It is well known that the energy consumer price does influence the price of energy companies. In this study, we express the influence of various goods and services by related consumer price index. For example, the influence of energy is expressed by consumer price index of energy.

One CPI is not enough, however. Any company competes with all other companies on the market. Therefore, the influence of the driving CPI on the company's stock price also depends on the competitive power of all other CPIs. In our model, the net change in market prices is expressed by one reference CPI. This CPI represents the dynamics of price environment. Hence, the pricing model has to include two defining CPIs.

The model searches for driving and reference CPIs. The BLS reports the estimates for hundreds CPIs, but we have selected only 92 representatives for our study (see Appendix). The selected CPIs include all major categories as well as quite a few minor subcategories. To obtain two defining CPIs, we use linear regression of a given stock price on all pairs of 92 CPIs. The defining CPIs may lead the modeled price or lag behind it because of possible time delays between action and reaction (the time needed for any price changes to pass through). The model includes such delays (up to +-11 months) for both CPIs. Thus, the number of tested models for each stock approaches 1 million and only one is selected.

Bank of America was included in our study of bankruptcy cases in the USA. The initial model was not stable and the prediction for 2009 - 2011 was not fully correct. In March 2012, we presented a model for monthly closing (adjusted for splits and dividends) price based on two consumer price indices: other food at home (OFH) and housing (H). This intermediate model was also biased. In December 2012, we published a paper comparing BAC with four financial companies and revised the previously obtained model. The model estimated in December 2012 includes the index of food away from home (SEFV) and the index of rent of shelter (RSH).

Here we update the last model using new data between December 2012 and March 2014. The December 2012 model has not changed. Table 1 lists defining parameters for BAC between March and October 2012, and from August 2013 to March 2014. For each month, the best (from 1 million) model is based on the same defining CPIs - the index of food away from home (SEFV) and the index of rent of shelter . In all cases, the lags are the same: zero and one month, respectively. Other coefficients and the standard error suffer just slight oscillations or drifts.

Figure 1 depicts the overall evolution of both involved consumer price indices: SEFV and RSH, as well as those for the previous model: OFH and H. There are some differences between two pairs of defining CPIs which result in the change of the best fit model in March 2012. It is worth noting that these differences become prominent in 2011/2012 (OFH vs. SEFV). Before 2011, the relevant CPIs are similar and this might be the reason of the wrong model selection in 2012.

The best-fit models for BAC(t) in March 2014 and December 2011 are as follows:

BAC(t) = -5.54SEFV(t-0) + 2.43RSH(t-1) + 19.49(t-2000) + 431.49, March 2014

BAC(t) = -2.31OFH(t-0) +1.12H(t-0) + 2.18(t-2000) + 167.83, December 2011

The price of BAC share is relatively well defined by the behavior of the two defining CPI components. Figure 2 also depicts the high and low monthly prices for the same period, which illustrate the intermonth variation of the share price. These prices might be considered as natural limits of the monthly price uncertainty associated with the quantitative model. Figure 3 demonstrates the failure of the March 2012 model to predict the future of BAC price. The current model is valid since March 2012 (25 months is a row) and thus is more reliable than the previous one. Figure 4 displays the residual error which has standard deviation $2.86 for the period between July 2003 and March 2014. This is the uncertainty of the model for the future predictions.

According to our quantitative BAC model, the rise in its price since the end of 2011 has been driven by deceleration in the growth of SEFV index. The RSH has been growing at a constant rate. If the RSH and SEFV retain their trends BAC price will be increasing at a constant rate. In 2014, the consumer price index of food increases at a rate of approximately 1 unit per year. This forces all food related indices to grow, including the SEFV. Therefore, BAC price is expected to fall in the first half of 2014. From Figure 2, BAC price is approximately $20 in April 2014.

Table 1. The monthly models for BAC for eight months in 2012 and for seven months in 2014/2013.

MonthC1t1b1C2t2b2cd
2012
October-5.9217SEFV02.6567RSH220.7381447.5626
September-5.8865SEFV02.6484RSH220.5481443.7352
August-5.8953SEFV02.6542RSH220.5659444.0072
July-5.9408SEFV02.6744RSH220.7368447.1716
June-5.9322SEFV02.6797RSH220.6401444.8138
May-5.9688SEFV02.691RSH220.8133448.3051
April-5.9683SEFV02.6962RSH220.7737447.2148
March-5.9487SEFV02.6875RSH220.6911445.9155
2014and2013
March-5.5413SEFV02.427RSH119.4879431.4925
February-5.5254SEFV02.4246RSH119.41429.3975
January-5.5957SEFV02.4457RSH119.7611436.0936
December-5.6127SEFV02.4501RSH119.8513437.8585
November-5.6308SEFV02.4526RSH119.9578440.1902
October-5.6509SEFV02.4575RSH120.0682442.3
September-5.6788SEFV02.4623RSH120.2354445.6533

Figure 1. Evolution of defining pairs: OFH/H vs. SEFV/RSH.

Figure 2. Observed and predicted BAC share prices based on SEFV/RSH

Figure 3. Observed and predicted BAC share prices based on OFH/H, as estimated in December 2011.

Figure 4. Model residuals, standard error of the model $2.86.

Appendix. 92 defining CPIs

CPI CPI
Cheadline CPIMmedical care
Ffood and beveragesMCCmedical care commodities
FBfoodPDRUGprescription drugs
FHfood at homeMCSmedical care services
MEATmeats, poultry, fish and eggsMPRSmedical professional services
FISHfish and seafoodHOSPhospital and related services
DAIRYdairy and related productsRrecreation
FRUITfruits and vegetablesVAAvideo and audio
NABnonalcoholic beveragesPETSpets, pet products and services
OFHother food at homeSPOsporting goods
SEFVfood away from homeFOTOphotography
ABalcoholic beveragesORGother recreational goods
HhousingRSrecreation services
SHshelterRRMrecreational reading materials
RPRrent of primary residenceECeducation and communication
ORPRowners' equivalent rent of residenceEDeducation
THItenants' and household insuranceBOOKeducational books and supplies
FUfuels and utilitiesTUITtuition, other school fees, and child care
HHEhousehold energyCOcommunication
HFOhousehold furnishing and operationsPOSTpostage and delivery services
FABfurniture and beddingINFinformation and information processing
APLappliancesITinformation technology, hardware and software
OHEFother household equipment and furnishingOother goods and services
THOEStools hardware equipment and suppliesTOBtobacco and smoking products
HOShousekeeping suppliesPCpersonal care
HOhousehold operationsPCPpersonal care products
AapparelPCSpersonal care services
MAPmen's and boy's apparelMISSmiscellaneous personal services
WAPwomen's and girl's apparelLSlegal services
FOOTfootwareFSfinancial services
BABYinfant's apparelMISGmiscellaneous personal goods
JEWjewelry and watchesCMCPI less medical care
TtransportationCECPI less energy
TPRprivate transportationCFCPI less food
NUMVnew and used motor vehiclesCCcore CPI
NMVnew vehiclesCSHCPI less shelter
NCnew carsCOMMcommodities
MFmotor fuelDURdurables
MVPmotor vehicle parts and equipmentEenergy
MVRmotor vehicle maintenance and repairNDURnondurables
MVImotor vehicle insuranceOSother services
MVFmotor vehicle feesRSHrent of shelter
TPUpublic transportationsSERVservices
AIRFairline fareTStransportation services
OITother intercity transportationCFSHCPI less food and shelter
ITRintracity transportationCFSHECPI less food, shelter and energy

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Source: Modeling Share Prices: Bank Of America To Hold