Interactive Visualization and Statistical Interpretation of Market Share, Competitive Price, Stock, and
Mortgage Loan Data Using JMP® 3.1
James Daughtry, Principia Information Research Group
Dr. Jonathan Pinder, Wake Forest University
Dr. Edwin Tang, Chinese University of Hong Kong
William Gjertsen, SAS Institute Inc.
Introduction and Abstract
The Information Age is here! The "Information Highway" and all of its features including market data
retrieval, the downloading of text and images, real time payment via credit/ debit cards and just in time
production and inventory control are part of our current business world. However, whatever the
source, we will still be presented with business and market data that needs to be visualized, analyzed,
and understood before it becomes meaningful information.
New interactive computer tools, such as }MP, make this visualization and understanding possible. This
presentation will draw on dynamic linking of screens, the 1, 2, 3 and N-dimensional representations of
outliers and the analytic discovery tools available in}MP. Included will be examples for 1) Market
Share and Competitive Price Analyses, 2) Stock Tracking and Selection and 3) Mortgage Loan Portfolio
Analysis using Multinomial logit analysis. Consideration will be given to how the data can be
retrieved, structured, and transformed. Data access and retrieval into JMP relational data tables will be
discussed.
Market Share and Competitive Price Analyses
All busiTIess enterprise in the USA and the "Global Market" is currently deluged with data. The
bombardment of data consists of thousands and millions of records. These records are for instance:
financial, accounting, customer, inventory, purchasing, production, manufacturing, market, and sales
in nature. The data sources can be internal and external; national and international. For the
government the source can be city, county, state and federal. The mode of data can be cross sectional
or longitudinal in time, and can appear as text, numbers, or multimedia images.
A corporation's top management: the board of directors, the chief executive, financial, and information
officers, all need high technology solutions that can analyze data easily and present it as information.
IMP is an excellent analytical engine to implement the conversion of data to information.
To the CEO, the consumer and the investor community, market share is one of the most important
"bottom line" financial measures of a successful business. Witness the recent concern of Mr. Michael
Spindler, CEO, Apple Computer Company, when Compaq knocked Apple out of first place in market
share of the PC market. His response was to set new goals and rejuvenate Apple's sales force in an
effort to regain market share over the next few years.
For any market share analysis it is first important to define the market. In our example the market
definition is the total resurfacing and construction program for the highway system of an entire
southern state. The data is first entered and edited as SAS data sets and then brought over to JMP for
data exploration and outlier detection.
The data originated as SAS data sets but was outputted to us in a PC DOS formatted file as a text file
with SAS PUT statements. The PC DOS diskette was read directly into Microsoft Word® on a
Macintosh with a Power Macintosh 7100/66. Word let us view the incoming text file and confirmed
that backslash, • , was the field delimiter. Next it was easy to import the data directly via the Text
selection under Import within JMP. We even kept the same variable names by choosing Labelwithin
the import dialog. The only modification occurred with amounts of money which were in a SAS Dollar
format (leading $ sign and commas). We had to read a number such as $60,448.50 as a character
866
variable and create a second variable which is numeric that eliminates the $ and , entries and converts it
to a continuous number such as 60448.50. This is done with the JMP Calculator formula as shown:
t1¢=.O
t2¢=.llum item(j, of BTEXTAMT, delimited by "$,")
t1 ¢=. {t(ll,· 1000 +12, if t2;to
otherwise
results 0
j~2
results t1
The JMP Tables retrieved consisted of the following files:
DB10TABS (and DB1OTABS2): Bid tabulations on all items.
DPRJlTQ: Project items. Item quantities and prices of all projects that were let.
DPROPOSL: Contract Awards. Contract 10, vendor, date and award amount.
ITEMLIST: A list of construction items per contract.
VENDOR: A list of vendor IDs and names.
VENDADDR: A list of vendor addresses.
The market share analysis provides comparative market share for all contractors, subsets of contractors,
over different time periods and different counties within the state. The market share data is expressed
as: number of contracts bid, number of contracts awarded, total market dollars, percentage of dollars
per contractor, total dollars and percent of dollars for particular construction items by contractor.
Market share analysis over periods of time for all competing contractors is very important to all
bidders. Analysis over time indicates the stability of a contractor's market share and determines its
present and future capacity. Market share is highlighted in Figures 1, 2, 3.
Another important issue for corporate CEOs is competitive price analysis. This is particularly true in
our case where contractors must bid on complete construction jobs. To launch a new product or be the
low bidder in the marketplace it is imperative for success to have a firm understanding of the
competitive price at the item level. Item price analysis can include average summary statistics,
regression analysis, cluster analysis, and control charts of competitive bids and awards as in Figure 4.
In many cases price-quantity relationships can be analyzed in a cross section of time, over a range of
time, in a geographic region, for a subset of competitors or the whole market, and for a particular item
or group of items. Figure 5 is an example of portraying the price-quantity relationship for asphalt
cement (AC) bids for the year of 1992. As expected as quantity increases price per unit should decrease
and interesting competitive prices and patterns can be identified.
867
(AWDAMTBy CNDTLET )
4000000.00 -
• NORT08
.WOOD10
.APAC40
3000000.00-
.EARNlO
.EARN10
Eo-<
~
~ 2000000.00-
• JOURlO
..::
•
•
1000000.00 ,
,
0.00-
.IDEAlO
,
,
• I
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11/15/89 7/5/90
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2/21/91 10/11/91 5/29/92 1/16/93
CNDTLET
'1'.
I
I
9/4/93
•
;Ii t
I
I
4/24/94
·
Figure 1: Vendors with highest market share of individual contract awards,
a first look at the data_
868
Market Share Leaders by Award Amount and Number of Contracts
WHIT40
BAUG10
ATLA10
SALTlO
SEAR10
DEQUlO
M-TP10
NORT08
PLAN10
FORS10
MIDS20
APAC40
,;;;;~~
I!!!
!;;;;;;;;~
ROWL10 ~~~!!!!!
DELTlO !!
APAC20
JETAlO
COURlO
EARN10
WooD10
o
2500000
5000000
7500000
10000000
Sum(AWDAMT)
12500000
Figure 2: Display the Market Share Leaders and select the Top 10 by drawing a
reference line at $5,0000,000 and label each company with # of contracts.
Top 10 in Total Dollar Market Share
_WOOD10
_
EARN10
_
COUR10
_
JETAIO
1IIIIIIII
APAC20
•
DELTlO
IIITIl
ROWLlO
~mj APAC40
f:.,('J MIDS20
m FORSlO
Figure 3: Our Top 10 Vendors captured 52.5% of total $146.69 million market.
869
15000000
(BTUPRICE By CONTID )
30-
.DELTlO
. MCBR20
~
U
p:)
..... -- ..
.
~
8
.JETA10
.COURIO
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.FORS10·
25-
---------~-------------
20-
I:I88*18
· .
--.--------~--.----------------~
.
· -- ...................... -- ........ -_ .. -- ...................... -1-"" -_ .. -- ........
·
··
:
15-
I
40000
20000
0
··
I
I
60000
CONTID
=-- -- ...... -- -- .....
I
I
80000
100000
12000
Figure 4: Bid Unit Price vs. Contact ID "Control Chart"
(BTUPRICE By BTOQTY
unr
350
~
A1(1
,TJ::TA 1(1
300
U
)
250
~
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.
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.
.
1000
BTOQTY
.. ...................... -- ................ ---- .....
------ii-·_ .. ----
____ a.
-------- ---- .. ---- .. . .
. _-- .....
.
.
1500
Figure 5: Unit Price vs. Quantity for Asphalt Cement Contracts for 1992
870
2000
Stock Tracking and Selection
An application well suited for JMP is market timing, technical analysis of stocks and selection of a
stock based on your own fundamental criteria.
"The stock market is an incredibly inefficient engine for making money. Market timing is merely an
attempt to try to make it more efficient") Whether you are a portfolio manager or an individual
investor its very important to know not only the individual equity's characteristics but the profiles of
the sector and overall market as well. You don't want to invest in a stock, no matter how attractive, in
an overall bear market.
We will first illustrate technical analysis indicators that are easy to implement withinJMP for the
overall market and apply similar ideas to track an individual stock. We will first look at a few analytic
and graphical tools for momentum and overbought/ oversold conditions and then apply some of these
same ideas to a particular stock.
Market timing using trend line analysis:
The Cumulative Haluran Index (Cum HST) has a high correlation
withDJI
(DJI By Cum HST )
4000.00
3900.00
3800.00
3700.00
3600.00
3500.00
5' 3400.00
3300.00
3200.00
3100.00
3000.00
2900.0°i===l--r-r----r----r--,---r---,.--,.----r---r---,---,--,---,r--r-rl
o 10000 20000 30000 40000 50000 60000 70000 80000 90000
CumHST
_
Bivariate Normal Ellipse P=0.950
[Bivariate)
Variable
Mean
CumHST
DJI
48636.94
3494.543
Std Dev Correlation Signif. Prob
27285.73
272.7042
0.948034
0.0000
Number
855
Given that this indicator is highly correlated with the Dow Jones Industrials index, JD, we can use it to
illustrate trend line confirmations and divergences, our first market timing technique.
871
DJI breakout on 12114
CumHST breakout confirms the same day
87000
3950.00
3900.00
Confirm ed
bya
breako ut in
CumHS T
3850.00
_ 3800.00
5'
3750.00
84000
3700.00
83000
3650.00
3600.00 -hi-r-. ...,..,..,..,..,.,-/
9/Zl/9 4 10/31/9 4
'7!7o'!r'"..,..,,m
82000 -I-r-r,...,...,....,r-r-T"T........r-r-,....,...,...,...,....,-r
9/27/9 4
10/31/ 94
Da~
12/5/9 4
1/9/95
Da~
Drawin g correct trend lines is one of the easiest and most powerf ul
tools available to a technical
analyst . The way to draw correct trend lines is described by Speare
d:
"For an uptren d within the period of consideration, draw a line from
the lowest low, up and to the
highes t minor low point preced ing the highes t high so that the line
does not pass through prices in
between the two low points. For a downtr end, draw a line from the highes
t high point to the lowest
minor high procee ding the lowest low so that the line does not pass through
prices in between the two
highs."2. The above two charts indicate a change of trend from down trend
to uptren d since the
correct short term trend lines have been been broken throug h in an
upwar d direction. Use the
Annota te or "A" tool in JMP to draw correct trend lines.
Polariz ed Fractal EffiCiency
Althou gh trend lines can and should also be used effectively with individ
ual stocks, it is instruc tive to
introdu ce anothe r tool, an oscillator based on fractal climension. A
fractal is an object in which the
parts are in some way related to the whole. Trees branch accord ing
to a fractal scale. Each branch ,
with its smalle r branch es, is similar to the whole tree. The time series
of a stock or index in the same
way has self-similarity with respect to time. Below is snapsh ot of daily
and weekly charts from the
same stock. Can you tell which is which?
Daily or Week ly?
Daily or Weekly?
"8o'"
"0
::E
54.000+-------1/7/93
«.ooo+-~-----------
3/31/9 4
Date
Date
872
Polarized Fractal Efficiency for Cisco WeekI y prices
100
80
60
40
~
20
O~----~------------~----------~H----+~----~----~------­
-20
-40
-60
~O~--~--~--~--.---.--.---'---'---'---r---r---r---r--,
10/28/90
6/17/91
2/3/92
9/22/92
5/11/93
12/29/93
8/17/94
Date
Footnote: + = Buy x = Sell
The Polarized Fractal Efficiency measures price change distances two ways and takes the ratio to
create an oscillator. When the oscillator crosses above 0 from below it is a buy and when it
descends below 0 from above it is a sell. The FE numerator measures the "long ruler" straight line
distance, F, between Gosei and Gosei+10 and each Di distance in the denorrtinator is the "short
ruler" distance between CloSei and Gosei_l. The FE denorrtinator, G, is just the overall "short ruler"
distance between Gosei and Gosei+1()' FE is then smoothed with a 5 period EMA. The smoothed
PFE will oscillate between +100% and -100%.
if is; 10
otherwise
•,
ifi<1O
L
G:
(~(CSCO j-CSCO j_/+l),
j=(i-9)
.,
F
FE:
ifis;10
'G.IQO,
-(.f·IQO),
ifCSCO j 2:CSCO j _
if is; 11
. {(FE.•0.333+PFE. 1.0.667\
1
1O
otherwise
FE.,
PFE:
otherwise
otherwise
1-
873
4/6/95
CSCO & 30week MA with PFE Buy & Hold Signals
12
10
8
6
4
2
10/28/90
2/20/91
6/16/91
10/10/91
2/2/92
5/28/92
9/21/92
Date
CSCO & 30week MA with PFE Buy & Hold Signals
28,-------------.-------------,------------,----~------T
261-------------+-------------~----_f~~~~~--~~~241-------------+-------------~--~------~----------~~
20-r--~--r_-----+------~----~----~._----~~----_r------
2/16/93
12/21/92
4/15/93
6/12/93
Date
CSCO & 30week MA with PFE Buy & Hold Signals
40
pI\
35
30
25
20
~
h
-
/
.875_ _ _
'y
-.....
I-(~
~2.~75
--........
.A~
J
/
I"-Y .. . .
.J
--~
15
8/8/93
12/1/93
3/27/94
7/21/94
11/13/94
3/9/95
Date
Here we see the benefit of market timing vs., just buy and hold. If you are aggressive, make each sell a sell
short signal as well as sell the stock you bought previously signal. So the PFE market timer sells the stock at
34.75 that he bought at 27.875 and sells it short at 34.75 and buys it back later in 1994 at 24.625. The net gain is
6.875 + 10.125 =17 for the market timer and 25.675 - 24.625 = 1.0 for the buy and hold individual. Note that
basic trend line analysis should also be used on Cisco prices. Weinstein4 offers yet another set of buy / sell
rules based on stage analysis which can act as a second confirmatory tool to PFE rules. In practice the
technical trader uses several indicators (i.e. trend lines and oscillators) simultaneously to make market
decisions.
874
A stock selection example:
From our universe of stocks to be selected (i.e. Investor's Business Daily highlights a new industry
group every day) ,choose those that have a percentile ranking of 80 or more for both earnings per
share (EPS Rnk) and relative strength to all other stocks (ReI Str). We can use the dynamic linking
between histograms to visually make this first filter and subset the data. Then spin the resulting
dataset using fundamental indicators and discover hidden gems like Micron Technology! Then begin
tracking that stock in earnest.
(EPS Rnk )
70
80
90
100
(ReI Str )
Components
~
Net % Prof Margin
y Ret on Equity
Undervalued index
Z Last Q Sales
0.0
80.0
Mortgage Loan Portfolio Analysis
MultinomitlI Logit Model
In a situation described involving loan accounts, there are three states, rather than two, in which an account
may be categorized: default, prepayment, or an active. To extend the two-state model to a set of three
alternatives, with no particular ordering, let: Yij = 1 if the ith observation chooses alternative j, j = 1,2,3. In
the situation of interest here, i represents the accounts in a portfolio and j represents the states of default,
prepayment, or an active account. In a similar fashion as above, let Pij = P(Yij = 1), then for the three-state
model:
··Pi1+Pi2+Pi3=1,
which generalizes to
J
L 7r:ij
=1
for the general case with for the general case with J alternative states for the qualitative
j=l
875
dependent variable. Thus, for the generalized multinomial model:
exp(uj + /3i Xi)
ltij = J
..
I. exp(lXj + /3 jXi)
j=1
In the three-state model, solving for (U2 + /32 Xi) and (U2 + /32 Xi) yields:
(lti2) = u2 + /32 xi
log (lti3)
ltil = u3 + /33 xi
ltil = 1 -lti2 - lti3
log ltil
where Ul
= ~l = 0 and state one is the benchmark for comparison (Theil (1969».
To demonstrate the implementation of the decision analysis/multinomiallogit model, consider the
following specific loan portfolio circumstance. The loans in this portfolio are for mobile homes and involve
three parties: the mobile home purchaser ("the customer"), the mobile home seller ("the dealer"), and the
loan originating institution ("the bank"). State lending regulations prevented banks from granting loan
terms longer than 12 years for mobile homes. Therefore, the bank created a "dealer participation plan" in
which the customer received a 15 year loan, of which the bank received the first 12 (satisfying the
regulations) and the dealer received the final 3 years of payments in exchange for acting as guarantor for
the customer. Thus, in the event of default during the first 12 years, the dealer was responsible for
repaying the balance of the principal. In the event of prepayment, the dealer received the difference
between the customer's principal balance and a lesser balance for which the dealer was guarantor.
For several of reasons dealers failed to honor their financial obligations of the participation agreement. At
which time, in accordance with the contractual agreement, the bank seized the rights to the 'participation'
account payments in a failing dealer's portfolio. These payments then became the subject of legal
proceedings. Thus, a valuation was necessary to determine a fair market value of portfolios for which there
is no existing market.
In one failing dealer's portfolio there were a total of 89 participation accounts. Of these accounts, 28 had
either prepaid or defaulted prior to the dealer's failure and comprised a set of closed accounts. The dealer
filed a claim of $628,285 for the 3 years of payments from the remaining 61 open accounts. Thus, a valuation
was prepared for the 61 open accounts and was dependent upon estimates of the effects of future defaults
and prepayments.
To begin the valuation process, the two sets of accounts were combined and the status of each account was
categorized as either default, prepaid, or open. In order to estimate the multinomiallogit model, variables
had to be available for each type of account. The variables available from the bank's database were:
1. Sialus
- Account status: default, prepaid, or open; the dependent variable.
2. Dale
- Loan origination date.
3. Balance
- Principle balance owed by the customer.
4. RemPmls
- Number of remaining payments.
5. InlRalel
- Original interest rate.
6. IniRale2
- Current interest rate (for accounts with variable interest rates).
7. 30
- Number of payments 15-30 days late.
8. 60
- Number of payments 31-60 days late.
9. 90
- Number of payments 61-90 days late.
10. 90+
- Number of payments more than 90 days late.
To develop the multivariate multinomiallogit model, each of variables were test in various models and the
.significant variables reduced to a model containing the independent variables 60, RemPmls, and InlRale2.
The results of this model are given in Table 1.
876
Table 1: Multivariate Multinomial Logit Model Results
Dependent Variable: Status
r2(U) 0.5913
n
89
Whole-Model Test
-Lo2:Likelihood
ChiSquare
Source
OF
Prob>ChiSq
Model
6
44.208872
88.41774
0.000000
Error
81
30.551364
CTotal
87
74.760237
EffedTest
NpmTII
Source
DF
Wald ChiSquare
Prob>ChiSq
2
60
2
7.569479
0.0227
RemPmts
2
2
9.693357
0.0079
IntRate2
2
2
14.230615
0.0008
Parameter Estimates
Term
Estimate
Std Error
ChiSquare
Prob>ChiSq
49.115
intercept
17.077865
8.27
0.0040
-1.9755
0.7181072
0.0059
60
7.57
-0.13792
RemPmts
0.0447098
9.52
0.0020
-219.75
IntRate2
85.625495
0.0103
6.59
28.956
0.0773
intercept
16.390795
3.12
-1.8306
0.7364416
6.18
0.0129
60
-0.089853
RemPmts
0.0400944
5.02
0.0250
IntRate2
-110.71
0.1847
83.466043
1.76
To deterrrune the state predIction (Plj) equations, let the states default, prepaId, and open be represented by
the indices 1, 2, and 3 respectively and let state 1 (default) be the benchmark state (paraIneters = 0). From
the paraIneters in Table 1 are used to calculate the linear terms:
Linear2 = 28.956-1.830660-O.089853RemPmts-llO.71IntRate2.
Linear3 = 49.115-1.975560-0.13792RemPmts-219.75IntRate2.
Using these linear terms the equation for estimating thePlj's are:
1
Pl1 - 1 + exp(Linear2) + exp(Linear3) .
Pi2 = exp(Linear2) Pl1 .
Pr3 = exp(Linear3) Pl1 .
Rather than using these estimates of Plj to forecast of the specific state of each account, the Plj's measure the
state probabilities associated with each account. Thus, they quantify the potential that every account has
for defaulting, prepayment, or remaining open.
After building the multivariate multinomiallogit model, univariate multinomiallogit models were
estimated to illustrate the qualitative effect on the status of each account of each Significant independent
variable in the multivariate model. The univariate logit models for are illustrated in Figures 6 -8 The
vertical spacing between the logit curves represents the likelihood of each state and is measured on the lefthand scale. The right-hand scale indicates the overall proportions of the three states. Thus, if the
dependent variable were not associated with the independent variable then the logit curves would be
horizontal lines located at the hash marks separating the three states.
Figure 6 demonstrates that the likelihood of default becomes critical at about 4 payments 60 days late.
Furthermore, at about 9 payments 60 days late the likelihood of default is nearly certain due to the
collection practices of the bank. Figure 7 shows that as the number of remaining payments decrease there is
less likelihood of default and that the likelihood of prepayment remains constant over a broad range of
remaining payments. Figure 8 shows that as the current interest rate increases there are sharp increases in
the likelihood of prepayment and default and that approxlinately 14% is the critical rate at which customers
shift towards prepayment and default.
877
1
1
Default
Prepaid
0.75
0.50
Default
Prepaid
0.75
0.50
Open
0.25
Open
0.25
0
0
0.09
-2 0 2 4 6 8 10 12 14 16
60 Days Late
0.11 0.13 0.15
Current Interest Rate
0.17
1
Default
0.75
0.50
0.25
. ."
......
Prepaid
~,
•
Open
10 30 50 70 90 110 130
Remaining Payments
Figures 6, 7, and 8; Logistic probabilities of Outcomes vs. # of 60 Days Late payments,
Current Interest Rate and # of Remaining Payments
After estimating the Plj's, the next step in the valuation process was to estimate the net present values
(NPVij) of each state for each account. As before, let the states default, prepaid, and open be represented by
the indices 1,2, and 3 respectively. For each open account, NPVil was determined by subtracting the
principal balance and the estimated cost of repossession from the estimated proceeds of selling the
repossessed asset. The cost of repossession was estimated from the costs of the previous defaults. Based on
the selling price of the previous defaults, at the age of the asset, a logarithmic model was regressed to
estimate the repossession sales proceeds.
NPVi2 was calculated as the difference between the customer's principal balance and a lesser balance for
which the dealer was guarantor. Finally, NPVi3 was calculated as the present value of the final 3 years of
payments to be received by the dealer if the loan proceeded to full term.
Thus, the portfolio valuation for the 61 open accounts was calculated by first estimating the state
probabilities, Pl} for each account. Next, the net present values (NPVijl for each state for each account are
computed as described above. Subsequently, the expected NPV for each account, E[NPV;j, is determined
by:
3
E[NPV;j = L frij NPVij
j=1
878
Finally, the portfolio valuation is calculated by summing E[NPViJ for all accounts. Thus, the portfolio
valuation is based on the relative risks inherent in each account rather than trying to specifically predict
which accounts will default or prepay. Using this method for the set of accounts in this example, the
portfolio valuation was calculated as $267,497; well below the $628,285 claimed by the dealer in the
lawsuit.
References for Stock TUning: and Selection
1. Wagner, Jerry (1995) Jerry Wagner; Fund Timer. Technical Analysis of Stocks & Commodities, Volume 13
January.
2. Victor Sperando and T. Sullivan Brown, Trader Vic- Methods of a Wallstreet Master
Wiley & Sons, 1991) p. 71.
(New York: John
3. Hannula, Hans (1994) Polarized Fractal Efficiency. Technical Analysis of Stocks & Commodities, Volume 12
January.
4. Stan Weinstein, Stan Weinstein's SecTets faT Profiting in Bull and BeaT Markets
(Homewood, IL: Business One Irwin, 1988)
Multinomial Logit Reference
Theil, H. (1969) A multinomial extension of the linear logit model. International Economic Review 10:251-259.
879