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 (RSH). 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 behaviour 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.
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
|
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
|
receration
|
|
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
|
persocal 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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