Modeling Share Prices: Bank Of America To Hold

Apr. 7.14 | About: Bank of (BAC)

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.

Month C1 t1 b1 C2 t2 b2 c d
2012
October -5.9217 SEFV 0 2.6567 RSH 2 20.7381 447.5626
September -5.8865 SEFV 0 2.6484 RSH 2 20.5481 443.7352
August -5.8953 SEFV 0 2.6542 RSH 2 20.5659 444.0072
July -5.9408 SEFV 0 2.6744 RSH 2 20.7368 447.1716
June -5.9322 SEFV 0 2.6797 RSH 2 20.6401 444.8138
May -5.9688 SEFV 0 2.691 RSH 2 20.8133 448.3051
April -5.9683 SEFV 0 2.6962 RSH 2 20.7737 447.2148
March -5.9487 SEFV 0 2.6875 RSH 2 20.6911 445.9155
2014 and 2013
March -5.5413 SEFV 0 2.427 RSH 1 19.4879 431.4925
February -5.5254 SEFV 0 2.4246 RSH 1 19.41 429.3975
January -5.5957 SEFV 0 2.4457 RSH 1 19.7611 436.0936
December -5.6127 SEFV 0 2.4501 RSH 1 19.8513 437.8585
November -5.6308 SEFV 0 2.4526 RSH 1 19.9578 440.1902
October -5.6509 SEFV 0 2.4575 RSH 1 20.0682 442.3
September -5.6788 SEFV 0 2.4623 RSH 1 20.2354 445.6533
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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
C headline CPI M medical care
F food and beverages MCC medical care commodities
FB food PDRUG prescription drugs
FH food at home MCS medical care services
MEAT meats, poultry, fish and eggs MPRS medical professional services
FISH fish and seafood HOSP hospital and related services
DAIRY dairy and related products R recreation
FRUIT fruits and vegetables VAA video and audio
NAB nonalcoholic beverages PETS pets, pet products and services
OFH other food at home SPO sporting goods
SEFV food away from home FOTO photography
AB alcoholic beverages ORG other recreational goods
H housing RS recreation services
SH shelter RRM recreational reading materials
RPR rent of primary residence EC education and communication
ORPR owners' equivalent rent of residence ED education
THI tenants' and household insurance BOOK educational books and supplies
FU fuels and utilities TUIT tuition, other school fees, and child care
HHE household energy CO communication
HFO household furnishing and operations POST postage and delivery services
FAB furniture and bedding INF information and information processing
APL appliances IT information technology, hardware and software
OHEF other household equipment and furnishing O other goods and services
THOES tools hardware equipment and supplies TOB tobacco and smoking products
HOS housekeeping supplies PC personal care
HO household operations PCP personal care products
A apparel PCS personal care services
MAP men's and boy's apparel MISS miscellaneous personal services
WAP women's and girl's apparel LS legal services
FOOT footware FS financial services
BABY infant's apparel MISG miscellaneous personal goods
JEW jewelry and watches CM CPI less medical care
T transportation CE CPI less energy
TPR private transportation CF CPI less food
NUMV new and used motor vehicles CC core CPI
NMV new vehicles CSH CPI less shelter
NC new cars COMM commodities
MF motor fuel DUR durables
MVP motor vehicle parts and equipment E energy
MVR motor vehicle maintenance and repair NDUR nondurables
MVI motor vehicle insurance OS other services
MVF motor vehicle fees RSH rent of shelter
TPU public transportations SERV services
AIRF airline fare TS transportation services
OIT other intercity transportation CFSH CPI less food and shelter
ITR intracity transportation CFSHE CPI less food, shelter and energy
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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.