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EXECUTIVE WHITEPAPER
Understanding Price Elasticity to
Drive Portfolio Profit
In today’s challenging lending environment, setting prices to optimally balance customer
demand and lender profitability is critical. Lending institutions that understand and utilize
consumer sensitivity to price will be in a better position to increase consumer response and
product usage to drive portfolio profitability.
“To make profitable decisions a lender needs to understand how
consumers value its offerings. Despite the substantial impact that
price has on profit, it is surprising that many lenders do not have
analytic solutions that directly classify customers based on price
sensitivity.”
------Dr. Robert Phillips
Nomis Solutions, Founder, Chief Science Officer & Vice President, Research & Development
Professor of Professional Practice in the Decision, Risk and Operations Division,
Columbia University
EXECUTIVE WHITEPAPER
Executive Summary
Background
In today’s challenging lending environment, setting prices
to optimally balance customer demand and lender
profitability is critical.
Despite the substantial impact that price sensitivity has on
profit, we find that many lenders do not have analytic
solutions that directly classify customers based on price
sensitivity --hampering their ability to target promotions
and pricing programs in a way that both meets customer
needs and maximizes expected profitability (See Figure 1).
Lending institutions that understand and utilize
consumer sensitivity to price will be in a better
position to increase consumer response and
product usage to drive portfolio profitability.
While risk and response scores are commonly
used tools, they do not isolate and predict
individual sensitivity to price. Strategies that
utilize only these scores result in lost profit
opportunity.
Predicting consumer level price sensitivity to
credit offerings is complex. Analytic estimation of
price sensitivity at an individual level requires
highly sophisticated statistical techniques.
Furthermore, accurate estimation of price
sensitivity should be based on data derived from a
variety of products, lenders and other sources.
The Nomis Score™ provides a customer-level estimation
of price sensitivity that can be efficiently integrated into
acquisition, origination and customer management
strategies. Based on credit file and other readily available
data sources, the score capitalizes on Nomis Solutions’
unique pricing experience and research data to produce a
price sensitivity score that is robust across product,
channel and lender. The score captures predictive
interactions distinct from those captured by risk or
response scores and, when properly calibrated, can be
used to estimate the change in demand resulting from a
change in price.
To make profitable decisions a lender needs to know how
customers value its offerings, reputation and brand
relative to the competition. Most lenders use a risk score
to understand the variation in riskiness among potential
borrowers. Other, more analytically sophisticated
lenders, such as credit card issuers apply complex
champion/challenger testing to understand the overall
response of consumers for particular products. However,
in our experience, most lenders have devoted less
analytic attention to understanding customer price
sensitivity.
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Nomis Solutions developed the Nomis ScoreTM in order to
help lenders better understand the price sensitivity of
their existing customers and prospects. The Nomis Score
is an individual price sensitivity score – that is, it is a
number that measures the relative sensitivity of an
individual to the price of credit. Individuals with higher
Nomis Scores are more sensitive to the price of a credit
product than individuals with lower scores. The Nomis
Score can be used to segment customers based on price
sensitivity or to more directly estimate the change in
response to a change in price in order to develop more
refined and profitable strategies for prospecting,
acquisition and retention. Experience has shown that
using the Nomis Score can increase the profitability of
credit products by 10% - 20% or more.
This paper describes the basic concept of price sensitivity
and the properties that make this amenable to a broadbased scoring approach as well as an overview of how the
Nomis Score is calculated. It then discusses how the
Nomis Score can be used to segment customers to
support pricing decisions across the customer life cycle,
and how the Nomis Score can be leveraged to improve
the profitability of credit offerings.
What is Price Sensitivity?
It is hardly news that consumers are sensitive to prices.
For the vast majority of products and services, increasing
the price will result in fewer units sold. Typically, the
dependence of demand on price can be represented by a
continuous downward-sloping price-response curve such
as the one shown in Figure 2.
A market price-response curve such as the one in Figure 2
is an aggregation of independent decisions made by many
different customers. An individual customer will purchase
from a seller if the price is sufficiently low or, if the price is
too high, he will either purchase from another seller or
not purchase at all. As the price is changed, the
population of customers who will purchase also changes,
with more customers purchasing if the price is low.
While customer price sensitivity is ubiquitous across all
consumer markets, we are interested in the specific case
of consumer lending. Despite the complexity of some
loan offerings, the fundamental principles of price
sensitivity operate the same in lending markets as they do
elsewhere. Namely, holding everything else the same,
reducing the price of a loan will result in a higher
response and vice versa. This is true whether the price is
reduced by lowering the APR or by lowering fees or by
some combination of both. In what follows, we will refer
to “APR” or “rate” as the “price” of a loan with the
understanding that the same variation in response will
hold for other elements of loan price as well, while
‘response’ will be used as a generic measure of the
change in consumer demand.
At heart, individual price sensitivity is a measure of the
extent to which a customer weights price relative to other
characteristics in choosing a credit product. Some
individuals are extremely price sensitive and will spend
considerable time and energy searching for a loan at the
lowest possible APR. At the other extreme, there are
individuals for whom price is not the critical factor in
choosing the credit product. These borrowers are more
interested in such factors as convenience, lender identity
and reputation, rewards and brand. Note that these
differences hold true even after we adjust for the
riskiness of the consumer for whom the availability of
credit will play a role in their price sensitivity.
While a response score captures the overall response
level of a segment of customers, it provides no
information on which customers would change their
response if the lender changed its price. This is the
purpose of the Nomis Score.
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The Nomis Score and Consumer Demand
Consider a population of potential borrowers. If we offer
all of the prospective borrowers the same product at the
same rate then we would expect response to the offer to
follow a price-response curve such as the one shown in
Figure 3. One way to think about such a price-response
curve is that it is the result of a distribution of maximum
willingness-to-pay (W.T.P) for loans over the population
(Phillips, 2005). As an example, assume that Acme Bank
offers unsecured consumer loans of $10,000 at a single
rate. It is reasonable to expect that each successful
applicant has a “ceiling APR” – or maximum willingnessto-pay – such that they will accept the loan if the APR
quoted by Acme Bank is lower than their ceiling APR and
they will not take the loan if the quoted APR is higher. If
every borrower had the same maximum willingness-topay – say 5%, then all of the customers would take the
loan if Acme’s quoted rate were 5% or lower and none of
them would take the loan if the quoted rate were greater
than 5%. This would correspond to a case of “perfect
competition”.
However, in reality, there is always variability in the W.T.P
among borrowers in a population and W.T.P can be
modeled as a random variable with a normal distribution
as shown in Figure 3. For example, potential borrowers
for the $10,000 from Acme Bank might have a W.T.P.
distribution with a mean of 5% and a standard deviation
of 2.5. Thus, if Acme Bank sets its rate at 5%, half of its
applicants – those with willingness-to-pay above 5% -- will
take the loan. If it raises its rate to 7.5%, then only 16% of
applicants will accept its loans. If it lowers its rates to
2.5%, then 84% of applicants will accept its loans.1 In
general, if the bank offers a rate of y%, the fraction of
applicants that will accept its offer will be 1-Θ [(.01y.05)/.25] where Θ[x] is the standard cumulative normal
distribution function.
Now, assume that the lender used the Nomis Score to
segment the population. For simplicity, let us assume
that the lender creates just two segments: “high-price
sensitivity” customers and “low-price sensitivity”
customers. Note that the price sensitivity of the
population is related to the standard deviation of the
W.T.P distribution – a population with a lower standard
deviation is more price sensitive than one with a higher
standard deviation in the sense that demand falls off
more quickly as the price is increased. In other words, this
population will have a smaller standard deviation, while
the “low price-sensitive” population will have a higher
standard deviation. This illustrates a critical difference
between price sensitivity and response: price sensitivity is
a measure of the rate at which demand changes as a
function of price while response is a measure of absolute
demand.
In Figure 4, both distributions demonstrate the same level
of demand at an APR of 5%; however demand changes
much more quickly as a function for the price when the
standard deviation is 1% than when it is 5%.
1
We note that the acceptance percentages can be calculated using the fact that the probability that a normally distributed random
variable will be within one standard deviation of the mean is 68%. Because the normal distribution is symmetric about its mean, there
is a 16% chance that the random variable (here, willingness to pay) will be more than one standard deviation higher than the mean. In
this case, the mean is 5 and the standard deviation is 2.5, so the offered rate of 7.5% is one standard deviation above the mean.
Similarly, there is an 84% chance that willingness-to-pay will be higher
than 2.5%,the
which
is one standard
deviation
below the
Specifically,
“high-price
sensitivity”
segment
willmean.
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demonstrate price response in accordance with priceresponse curve A and the “low-price sensitivity” segment
will demonstrate price response in accordance with curve
B.
Acme Bank could use this information in a number of
different ways. For example, assume the bank plans to
offer two different products– one with a higher rate but
an enhanced points program and one with a lower rate
and a standard points program. Then it should offer the
higher rate card to the less-price sensitive segment and
the lower rate to the higher price-sensitive segment. By
doing this, it can increase both take up and profitability
relative to, say, targeting products based solely on risk
score or offering both products to all customers.
Value of a Broad-Based Price Sensitivity Score
The Nomis Score is a unique measure of the relative price
sensitivity of an individual consumer to credit prices. The
viability of the Nomis Score is predicated on four
properties of price sensitivity:
1. Customers differ in terms of their price sensitivity
for lending products. Some customers are highly
sensitive to the price of a loan – others are less
sensitive.
2. The price sensitivity of individual customers is
statistically stable over time and over
transactions – that is, a customer who
demonstrates a high-level of price sensitivity in
one transaction is highly likely to demonstrate a
high level of price sensitivity in a future
transaction.
3. Ordinal price sensitivity holds across lending
products and channels. That is, if customer A was
more price-sensitive than customer B in choosing
a home-equity loan, then customer A is likely to
be more price-sensitive than B in choosing a
credit card. Similarly, if customer A was more
price-sensitive than customer B in choosing a loan
through an on-line channel, they will also be more
price-sensitive in choosing a loan when shopping
at a branch (even though the average price
sensitivity of on-line customers may be higher
than the average price sensitivity of in-branch
customers).
4. The relative price sensitivity of two customers
can be estimated from information available in a
standard credit file supplemented with
demographic information and historic pricing
transaction data.
Nomis experience and research has found that these four
properties hold true across a wide variety of lending
products, channels, and geographies.
The first property is non-controversial – the fact that
customers vary in their willingness-to-pay for loan
products is reflected in the fact that lending markets
support a wide range of price variation. The second
property – the stability of individual price sensitivity – is
also not surprising. Indeed it is consistent both with the
experience of other retail industries as well as the
experience of credit rating agencies. Stability reflects the
fact that the Nomis Score is measuring an underlying
element of customer behavior that does not change
quickly over time. Note that this does not mean that
price sensitivity never changes. For example, events that
result in a change in a person’s financial situation and
their need and desire for credit – e.g., a better job or the
birth of a child – will result in changes in price sensitivity
that will be captured in the score the next time that it is
calculated and so it is important to obtain the freshest
score
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The third property – the independence of individual price
sensitivity from product and channel – is related to the
second. Namely, it is another way of stating that there is
an element of price sensitivity that is idiosyncratic and
independent of the details of any specific transaction.
Mathematically, it means that the personal element of
price sensitivity can be separated from the underlying
characteristics of a particular channel or product. We
have called this the “decomposition principle”. For
example, customers applying on-line for a loan tend to be
more price sensitive (all else being equal) than those who
apply in a branch. Nonetheless, we find that the Nomis
Score effectively ranks the relative price sensitivity among
customers who are applying through different channels.
In essence, the Nomis Score “decomposes” individual
differences in price sensitivity from the underlying
characteristics of the product or branch.
The fact that price sensitivity can be estimated using
credit file data is also not surprising – such data
incorporates a rich record of financial transactions and
current financial position. It is also very useful from two
additional points of view. First, such data is readily
available and already leveraged by lenders for most credit
decisions and is accepted as being regulatory compliant
for credit decisions. Secondly, the use of this data in
price sensitivity scoring means lenders can segment
customers on price sensitivity using the same underlying
data that they would use for underwriting or for “riskbased pricing”.
We note that the four properties of price sensitivity listed
above also hold for “customer riskiness” – which is why
credit-bureau based risk scores are such an effective and
ubiquitous approach to segmenting customers. Like price
sensitivity, “riskiness” is an individual characteristic that
varies among borrowers, is largely stable over time for a
particular borrower, has a component that is product and
channel independent, and can be estimated using credit
file data. In both instances, developing the scores based
on representative samples of consumers with credit files
(as opposed to those in the particular market niche of the
lender) provides a breadth of perspective that adds value
over and above lender-specific risk models. However, the
development of a broad-based price sensitivity score also
requires access to pricing data across a variety of
industries and products.
Developing the Nomis Score
Leveraging our deep pricing experience, the Nomis Score
was developed using predictive information from the
potential borrower’s credit file along with other
demographic data (if available). This was combined with
performance data based on Nomis’ proprietary research
data that includes information on price points and
consumer reaction for a variety of products, lenders and
channels. The specific mathematical formulae and
variables used to calculate the Nomis Score are based on
an extensive set of historical regressions to determine
which variables, under what transformations, and in
which combinations are most predictive of customer price
sensitivity. In order to isolate the consumer aspect of
price sensitivity, it is essential to include data from many
different products, channels and lenders. The final model
identifies those specific customer characteristics that are
the strongest determinants of price sensitivity and is used
to estimate a score based on these characteristics.
The Nomis Scoring Model calculates a Nomis Score
between 200 (low sensitivity) and 800 (high sensitivity)
that measures the relative price sensitivity of the
borrower. In the sense of rank ordering consumers, the
Nomis Score is analogous to a risk score. In both cases,
the consumers’ relative rank ordering of performance
(risk or price sensitivity) will hold true regardless of
product, lender or channel, while the exact performance
will vary depending upon these exogenous factors.
However, unlike a risk score, which estimates the
expected probability of default, each Nomis Score band
represents an entire price-response curve that reflects the
change in demand corresponding to a change in price as
opposed to a single estimate of default.
We note that developing a price sensitivity score such as
the Nomis Score is significantly more complicated than
developing a “response score”. Price sensitivity is
proportional to the derivative of response with respect to
price. For that reason, it requires substantially more data
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to derive a price sensitivity score than it does a response
score. And, while a response score is, by its nature,
specific to a set of product/channel/lender attributes, a
broad-based price sensitivity score must be based on
experience from a wide range of different products,
channels, and lenders.
Development of a price sensitivity score is further
complicated by another difference between response and
price sensitivity. With a response score, the predicted
response for two different customers will always have the
same relative ordering of response. However, with the
Nomis Score, highly price sensitive customers will be less
responsive than less price sensitive customers to
unattractive offers but more responsive to more
attractive offers.
between the two is positive with r2 = .35. This means that
the variation in risk score only explains about 35% of the
variation in Nomis Score within this population. The
remainder of the variation in price sensitivity is
independent of risk score. As can be seen in the figure, a
high fraction of customers have a high risk score and a
low Nomis Score and vice versa. This means that the
Nomis Score will add additional value when used in
conjunction with a risk score to create customer segments
based both on price sensitivity and on risk.
The Nomis Scoring Model changes over time, for two
reasons. First of all, Nomis continually performs research
to improve the accuracy of the Nomis Scoring Model. As
improvements are discovered, they are incorporated into
the model. Secondly, changes in the macroeconomic
environment over time lead to changes in price
sensitivity. Obtaining the freshest score available will
result in scores that more accurately predict price
sensitivity on a forward-looking basis.
The Nomis Score can be used directly to segment
customers based on their price sensitivity by adding the
score as an additional dimension to an existing pricing
strategy. However, when product, channel and lender
attributes are available, Nomis can calibrate the score to
provide more specific estimates of the price-response
curve for the various Nomis Score bands.
Nomis Score and Risk
Today, many lenders use risk as a surrogate for price
sensitivity. To some extent this is true, due to the fact
that riskier customers have fewer options and are
therefore, in general, less price sensitive. However,
Nomis research has shown that price sensitivity is only
weakly correlated with riskiness. Figure 5 shows a graph
of Nomis Score as a function of risk score for a random
population of credit card applicants. The correlation
Using the Nomis Score
The Nomis Score provides a statistically accurate and
stable measure of relative individual price sensitivity. It
can be used to guide segmentation decisions so that
customers will receive the offers that are most suited to
them. This will result in higher profitability – both
through increased take-up or usage, as well as from more
profitable offers.
First consider an acquisition campaign. The Nomis Score
can be used to guide pricing decisions, offering the best
price point to prospects with higher Nomis Scores and
higher rates to consumers with lower Nomis Scores. The
Nomis Score can also be used for origination decisions in a
de-centralized lending environment, for example in the
Auto industry. Here, the Nomis Score can be used to
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determine the magnitude of pricing discretion that should
be allowed by dealers or branch personnel. Finally, the
Nomis Score can be useful in segmenting customers’ price
sensitivity for a variety of customer management
decisions such as offering a competitive price to
customers more likely to attrite in a mortgage portfolio,
or determining how much to increase or decrease the
price of a revolving loan to in order to increase utilization
while maximizing profitability and reducing likelihood of
attrition.
As noted above, the price sensitivity of a customer in a
particular situation depends not only on his idiosyncratic
price sensitivity as measured by the Nomis Score but also
on other factors such as the type and size of loan under
consideration, the customer channel, the risk, previous
relationship with the offering lender, etc. Using the
Nomis Score in conjunction with your other existing
attributes (risk and response scores for example) provides
opportunity for optimal customer assessment and offer
creation.
The Nomis Score, by itself, captures only the differences
in underlying individual price sensitivity – it does not
capture differences in price sensitivity due to product,
channel, or relationship influences and therefore cannot
be translated directly into a “price-elasticity” or “response
probability” for a particular transaction. It can, however,
be used as an input to the Nomis Price Optimizer or other
optimization tools to provide a more accurate estimate of
price elasticity for a segment, and hence better
recommendations regarding prices to offer.
In practice, if supplemental information about the loan
product, channel, and prior customer relationship is
provided to Nomis by the user, the score ranges can be
translated directly into a “price-elasticity” curve or a
“response probability” curve for each Nomis Score
segment. These curves can be used to drive particular
targeting or pricing decisions and/or provide insight into
how loan prices should vary among channels or among
different loan products.
Price Sensitivity Scoring and Consumer Protection
The growing focus on consumer protection in financial
services requires that banks and finance companies offer
products that are suitable, transparent, and competitively
priced. Increasing transparency and standardizing terms
and conditions of loan products will make lending markets
more price-competitive which will benefit consumers.
However, as the Nomis Score has shown, not all
consumers are equally price sensitive and differences in
price sensitivity are driven by real preferences for brand,
access, service, product features, relationship and other
aspects of the overall value proposition.
The Nomis Score allows banks to determine which
customers value differentiated products and benefits, and
are willing to pay for these differentiated benefits.
Consumers who are very price sensitive care less about
product features and will prefer a competitively priced
low-frills offer over a premium-priced offer with
additional benefits. Conversely, consumers with low price
sensitivity may prefer premium products and be willing to
pay for the additional benefits and features offered.
Using the Nomis Score allows banks to target higherpriced premium products to the customers who value the
additional features and are willing to pay for them while
targeting lower-priced standard products to customers
who are driven primarily to price. This enables lenders to
better target the “right product” to the “right customer”
at the “right price thereby satisfying consumer financial
protection and “Treating Customers Fairly” guidelines.
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Nomis Score Case Study
A top-tier North American credit card issuer was
interested in growing receivables from existing customers
through a balance transfer campaign. However, they
realized they needed a new approach to targeting in order
to increase both response rates as well as average size of
balance transferred.
The card issuer’s existing approach consisted of
segmenting customers based on risk, historical behavior
and their likelihood to respond to an offer based on a
custom response score. This segmentation was used to
test potential ‘teaser’ and ‘go-to’ rates based on
competitive offerings in the marketplace at the time.
Customers in each segment were randomly assigned one
of three price points, all of which were competitive
relative to the marketplace. This strategy was the control
or ‘business as usual’ approach. While this approach
provided a segmentation scheme, it provided no
information on how customers within each segment were
likely to react to a change in rate.
In an attempt to improve performance, Nomis worked
with the issuer to develop a ‘Nomis Score strategy’ which
incorporated the Nomis Score as an additional
segmentation variable to determine the rate to offer.
Since the primary objective of the issuer was to increase
receivables, the high Nomis Score segment (those most
price sensitive) were offered the most attractive rate, the
low Nomis Score segment was offered the least attractive
rate and the medium segment was offered the medium
rate (See Figure 7). The ‘average’ rate was the same in
both strategies. Once the two strategies were developed,
customers were randomly assigned to either the ‘business
as usual’ or the Nomis strategy.
By identifying the highly-price sensitive customers, the
Nomis Score strategy enabled the bank to more
effectively align the interest rate offer with their
customers’ value for price and therefore achieve their
objectives of maximizing receivables. Offering the best
rate to the most price sensitive group of customers
allowed the issuer to significantly increase both response
rates and average balance transferred, resulting in a 20%
increase in receivables and a ~10% increase in profit. The
Nomis Score strategy returned an additional $35MM in
receivables for every 1MM customers mailed.
Conclusion
Understanding the value a consumer places on price
relative to other product attributes can have a significant
impact on a lenders’ profitability. The Nomis Score
provides a unique tool to enable lenders to segment
prospects or customers by their price sensitivity
independently of product, channel, or previous customer
relationship in order to make more profitable targeting,
acquisition, and retention decisions. This broad-based
score is calculated on readily available data, and can be
quickly and easily integrated into existing strategies to
improve pricing decisions.
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References
About Nomis Solutions
Phillips, R. L. (2005) Pricing and Revenue Optimization.
Stanford University Press, Stanford, CA
Nomis Solutions enables best-in-class Pricing and
Profitability Management for financial services
companies. Through a combination of advanced analytics,
innovative technology, and tailored business processes,
the Pricing and Profitability ManagementTM Suite
delivers quick time-to-benefit and improves financial and
operational performance throughout the customer
acquisition and portfolio management processes.
Visit www.nomissolutions.com or contact us at
info@nomissolutions.com or 650-588-9800.
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