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Risk-based pricing: When does it work and when does it not? An adverse selection approach

| Risk-based pricing: When does it work and when does it not?

Executive summary .....................................................................................................................................2

Introduction ..................................................................................................................................................3

Risk-based pricing .......................................................................................................................................5

Risk-based pricing — When does it work and when does it not? .....................................................10

Risk-based response function and risk-based pricing ........................................................................12

Numerical examples .................................................................................................................................16

Conclusions ................................................................................................................................................21

Bibliography ...............................................................................................................................................22

About Experian Decision Analytics ........................................................................................................23

About Experian Decision Analytics’ Global Consulting Practice ......................................................24

About the authors ......................................................................................................................................25

Table of contents


Executive summaryRisk-based pricing is often recommended as a better way to set prices on consumer credit products. In theory, risk-based pricing will help align price and costs by increasing the pricing for higher-risk/higher-cost customers and decreasing the price for the lower-cost and better-risk customers. However, there are limitations such as imperfect segmentation, negative customer reactions and adverse selection. In looking at the risk-response function, there are additional factors affecting risk-based pricing such as risk-response relationship and affordability — all of which will impact the forecasted profitability of any risk-based pricing strategy. Accurate assessment of the true responding populations (impacted by both internal and external marketplace factors) is essential to successfully implementing any pricing strategy.

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IntroductionRisk-based pricing is not a new concept. It has been around for many years and has been recommended by many credit risk managers as a way for businesses to compensate for the risk of different customer segments. The theory is relatively simple. With fixed pricing, the cost of risk is evenly distributed among customer segments despite the fact that certain segments have high risk and others lower risk. This situation results in the lower-risk customers “paying” more than their risk — essentially being overcharged — while the higher-risk customers pay less than their risk.

Figure 1: The concept of risk-based pricing

In theory, risk-based pricing will help align price and costs by increasing the pricing for higher-risk/higher-cost customers and decreasing the price for the lower-cost and better-risk customers. It is even said to provide some positive selection, as the lower prices for good customers will increase applications and retention of such low-risk customers, while the higher price for higher-risk customers will discourage these clients from applying or remaining within a portfolio.

However, this rather simple depiction of risk-based pricing may be misleading. While risk-based pricing can be successful, there are situations where the risk-based pricing approach will not only fail to deliver improved profitability, but also will be detrimental to overall portfolio profitability.


The purpose of this paper is to discuss how risk-based pricing works in theory and in practice and to identify situations where risk-based pricing will not generate the expected results. Throughout the paper, we assume that banks use credit scoring to rank risk and that this scoring is an effective risk ranker. We will demonstrate:

1. There is a simple relationship between the true probability that the borrower will repay the loan and what the lender considers the likelihood of loan repayment and that this difference is mainly due to adverse selection.

2. If the risk distribution (risk score) is skewed to the left, the quantity effect might exceed the price effect, and therefore the risk-based pricing strategy might be unprofitable as the lower price given to “goods” outweighs the increased price charged to the “bads.” Alternatively, if the quantity of “bads” exceeds the quantity of “goods” in the market, the risk-based pricing strategy might be unprofitable as the increased losses outweigh the increased gains. These conditions are considered true within the bottom of subprime segments. By differentiating the interest rates charged to each identified risk group, lenders may inadvertently worsen the average level of risk of their portfolio as a whole. If the lender has insufficient information to reliably distinguish good risk from bad, it might be convenient to set a flat interest rate strategy rather than using a customised pricing.

3. Modelling response or take-up probability is not enough. Price response function, adverse selection estimation and affordability proxies are prerequisites to develop a successful risk-based pricing strategy. In the consumer lending context, Lyn C Thomas, (2009) points out that adverse selection is important in estimating the interaction between the quality of the applicant and the probability of them taking the loan.1

As Jeremy Williams shows in his “Price Optimization in Retail Consumer Lending” white paper, “the problem (with risk-based pricing) is that the profile of customers that take up the loan is likely to be different to the population that does not take the loan. The result is that increasing the price not only reduces volume, but also increases loss rates to a greater level than that simply predicted by the risk score. Consequently, increasing prices increases losses and eventually reduces overall profits.”2 We will try to show how to deal with this problem called “adverse selection” in the context of risk-based pricing and to offer some guidance on situations when a risk-based pricing strategy may fail.

Throughout this paper, the terms “bank” or “lender” will refer to any financial institution, and the term “price” will refer to interest rate (APR).

1 Lyn C.Thomas, Consumer Credit Models: Pricing, Profit and Portfolios, 2009

2 Jeremy Williams, Price Optimization in Retail Consumer Lending


Risk-based pricing Robert Philips in “Pricing and Revenue Optimization” describes price differentiation as the tactic of charging different prices for different customer segments for the same (or nearly the same) product or service.3 In credit risk situations, risk-based pricing refers to charging different interest rates according to customer risk profile. In other words, in risk-based pricing or customised pricing, the financial institution can quote a different price for each loan application. The reason is to match the expected revenue and expected cost associated with the different default risks for each individual. Also, different prices could be set for each kind of product, to each customer segment, and through each channel — or even regional prices (except where there are legal ceilings on the rates that can be charged on loans).

For many financial institutions, pricing is a complex process involving real-time decisions. Usually, setting prices is not a simple decision, but involves many decisions simultaneously. Without a process of analysis and evaluation, it is unlikely that the pricing strategy maximises the profits.

The situation may be even worse, since many consumers better understand the pricing strategy than do financial institutions, and they can act accordingly, extracting surpluses from financial institutions and increasing their own benefits.

The pricing process In order to maximise total profitability, the pricing process has two main components:

1. A consistent business process focused on pricing as a critical set of decisions

2. The software and analytical capabilities required to support the process

Much of the development of a pricing strategy is usually placed on the use of mathematical analysis. The use of analytics is the key to optimising the pricing process. However, such analytical capabilities cannot provide a sustainable improvement if they are not immersed in a correct process.

Traditional approaches to pricing Traditional approaches to pricing are cost-plus pricing, market-based and value-based.

Cost-plus pricing is a strategy where one establishes a markup over costs. It has the advantage of being simple and always covers costs, but may not be appropriate in a competitive environment because it does not take into account the pricing strategy of competitors.

Market-based pricing refers to setting different prices in different contexts, where prices are set usually by a market leader. Obviously this approach does not take into account the costs themselves, but only the possibility of following in the market where the leader is defining the price.

Value-based pricing means that the price is set according to the customer value. That is, the customer value is the key driver of the price.

It is common practice to use a combination of the three approaches or to have all three aspects considered during the pricing process.

3 Robert Phillips, Pricing and Revenue Optimization, 2005


Price-response function, willingness to pay, optimal pricing4 Price-response functionA central issue in the analysis of the price to set for any product is the price-response function — the level of demand for a product varies, as does the price. In the context of a bank, the consumer relationship, price-response function can be interpreted as the probability q(r,o,x) that a borrower with characteristics “x” will take the loan, which is the willingness to accept the offer of a loan with interest rate “r”, and other characteristics “o” made by a bank.

The price-response function is not a market demand function. It is the demand for loans of a single seller as a function of the price offered by the seller. This is a significant difference because each seller in the same market faces different price-response functions.

We can describe a price-response function by its slope and elasticity. The slope of the price-response function measures how demand changes in response to a price change. The price-elasticity function measures a percentage change in demand due to a 1 percentage change in price.

Let “q(r)” be the probability of accepting a loan, which only depends upon the interest rate. We supposed that “q(r)” has desirable properties of good behaviour. That is “q(r)” is continuous, monotonically nonincreasing in “r”, and differentiable in “r”.

Slope (1)

Elasticity (2)

We will use this definition to find the optimal price to a hypothetical loan overleaf.

4 These sections follow Robert Phillips, Pricing and Revenue Optimization, 2005 and Lyn C. Thomas, Consumer Credit Models: Pricing, Profit and Portfolios, 2009.


Logistic price-response functionLogistic or logit price-response functions describe with accuracy the credit market and customer behaviour, and it has desirable properties. Graph 1 shows the s-shape that shows that at a very high (or a very low) price level, the elasticity is low (demand is inelastic), higher changes in price lead to a small change in demand, and when the price is near to the “market” price, small changes in prices lead to a huge change in demand (demand is elastic).

The logit response rate function satisfies:

(3)

Figure 2: Graph 1 – Logistic price-response function


This graph shows that the log-odds of take/no-take are linear in respect to the interest rate charged. That is, as the interest rate goes up, the probability of taking the loan goes down.

Properties of the logistic price-response function:

Demand at 0% (4)

Slope (5)

Elasticity (6)

In this case, “b” describes a kind of price sensitivity related to the interest rate. When “b” is large, the borrowers are more sensitive to interest rates, and “a” could be interpreted as the overall take-up when the interest rate is 0 percent.

Maximum willingness to payIn many cases, price-response functions can be considered as an alternative for a portion of potential borrowers whose maximum willingness to pay is greater than certain interest rates.

In other words, every potential borrower has a maximum price (their reservation price) at which they are willing to take the loan. Let “w(r)” be the density function5 of this maximum willingness to pay across the population of potential borrowers, then:

(7)

The equation (7) shows that there is only a fraction of the population willing to pay r1 or more.

Furthermore, note that q’ (r)= -w(r), which means that only those with a maximum willingness to pay of exactly “r” will turn down the loan as the interest rate goes up by an infinitesimal amount above “r”.

In the case of a logistic price-response function, the willingness-to-pay distribution is:

(8)

The maximum willingness to pay occurs when:

(9)

Next, we will show what the theory suggests about the kind of price-response function used in practice to get the optimal risk-based interest rate.

5 In probability theory, a probability density function (pdf), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. The probability for the random variable to fall within a particular region is given by the integral of this variable’s density over the region.

Optimal risk-based interest rate At this point in the discussion, we want to know: What is the optimal interest rate to be charged for our loans? We assume that the probability of accepting the loan q(r) regardless of their default risk is the same for everyone.

Let rf be the opportunity cost or risk-free interest rate, “LGD” the loss given default and

“p” the probability of being good. One unit of profit is set as “spread” between (r-rf ), and if they default, the losses are the LGD plus the opportunity cost rf.

So the expected profit maximisation is:

(10)

It is easy to see that the formula (10) expresses the probability “p” to earn one unit of profit (r-rf ) or lose (LGD+rf ) with (1-p) probability given the take-up probability q(r).

Differentiating and equating the derivative to zero gives:

Optimal interest rate

(11)

We can rewrite (11) as;

(12)

The left side of the equation (12) is the marginal decrease in revenue if interest rate changes infinitesimally. The right side is the increase in revenue for those who will still take the loan but at a higher interest rate. This represents the following known result: at optimal interest rates, the marginal revenue is equal to the marginal cost.

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Risk-based pricing — When does it work and when does it not?Limits to price differentiationWhile credit scoring is effective and does rank-order risk, it is not perfect. While the probabilities can be effectively identified, for each score, it is only a probability — the score cannot identify which accounts at each score range will pay and which ones will not.

Robert Phillips states that: “There is no technology to determine the precise willingness to pay of each customer. The best that can be done is to create market segments such that the average willingness to pay is different for each segment.”6

Negative customer reaction, fair/unfair feelingIn different ways, customers can react negatively to a risk-based pricing strategy. The standards of fairness can be disturbed if the customer response is based on comparison of the current price to a hypothetical willingness to pay, which encompasses deep notions of fairness.

Or it could be perceived as a form of class, racial or sexual discrimination, because the result would be, as Barnett states in The Observer: “Those who are able to pay the most are required to pay the least.”7

Also, there are three types of interaction between that risk and response that affects the risk-based pricing performance as well as one more related to the risk distribution which may lead to unexpected results.

Risk-response relationshipThe potential borrowers with high credit scores and the highest odds of being good payers are likely to be the target of many lenders. They are offered better deals than those with lower credit ratings. It is well established that there is usually an inverse relationship between risk and response. Hence, the probability that the low-risk customers will take a particular loan is likely to be lower than higher-risk customers.

Adverse selection8 If one assumes that the take-up probability is a function of the quality of the applicant, then there is a second interaction between the quality of the applicant and the chance of him or her taking the loan — namely, adverse selection.

Adverse selection occurs when there is asymmetric information between the buyer and the seller of a contract. A bank suffers asymmetric information when it is unable to distinguish between two applicant projects with different risk levels, when assigning credit.

6 Robert Phillips, Pricing and Revenue Optimization, 2005

7 A. Barnett, Policy Forum: Poor Kept on the Outside Looking In, Business Section, The Observer, 1997

8 It is important to recognize that when one introduces a loan with a higher interest rate, both the risk-response relationship and adverse selection work to increase the bad rate over that which might have been expected. However, one should recognize and try to separate the two effects, because often all the impact is put down to adverse selection, whereas the risk-response relationship is making a significant change in the bad rate (Lyn C. Thomas, Consumer Credit Models: Pricing, Profit and Portfolios, 2009).


Also, adverse selection means that riskier borrowers are willing to pay higher interest rates than safer borrowers. Under differential pricing, there is a powerful motivation for customers in high-price segments to find a way to avoid revealing their true willingness to pay and pay the lower price. In this situation, the bank knows that it has less information than the applicants, so it protects itself by raising the interest rate charged on every applicant. When it does so, safer borrowers are excluded from the market (they have a lower willingness to pay), and only the riskier borrowers apply for loans. Then the bad rate will be higher than the expected one. This can explain why banks prefer rationing credit9 (by setting high cutoffs) instead of raising interest rates.

AffordabilityThe third type of interaction between risk and response rate is where the interest rate charged on the loan affects the borrower’s affordability to pay back the loan and therefore on the bad rate. The argument is that a borrower with limited resources might be able to service the interest rate payments of a five percent loan quite easily, and so the probability of a good behaviour would be high. However, if the rate were 25 percent, then the borrower’s disposable income might not be enough to cover the interest rate payments and so the probability of being good would drop substantially. Lyn C. Thomas claims: “It could be argued that this was one of the causes of the subprime mortgage crisis in 2007. The mortgages offered to credit-impaired borrowers were at very favourable interest rates for an initial period, but at the end of this period when the rates reverted to much higher levels, the default rate increased considerably.”10

Risk distribution skewed or uncertainty over the distribution of risksWhen banks customise prices to each identified group of risks, they may involuntarily worsen the average risk level of loans in their portfolio as a whole. Risk-based pricing can cause adverse selection if risk distributions are nonuniform (skewed distributions). However, even where there is a uniform distribution of risks, banks may remain adverse to customising prices if there are doubts about the true shape of the distribution. “It is possible, for example, that the number of potential borrowers in each of the risk categories could vary considerably over time. So although the lender may have some working estimate that points to a uniform distribution of risks, an added layer of uncertainty in the lending decision may deter lenders from actually implementing risk pricing. A similar outcome may arise if the lender is unable to clearly distinguish risk categories. If risk assessment procedures can only place a borrower in the correct risk category with a probability less than unity, then ceteris paribus, the narrower the risk category, the lower the accuracy.”11 (Pryce, 2003)

9 A seminal paper related to this issue is Stiglitz, J. E., & Weiss, A. (1981). Credit rationing in markets with imperfect information. The American Economic Review, 393–410.

10 Lyn C. Thomas, Consumer Credit Models: Pricing, Profit and Portfolios, 2009

11 G. Pryce, Worst of the Good and Best of the Bad: Adverse selection consequences of Risk Pricing, 2003


Risk-based response function and risk-based pricingRate-based probabilities of being goodThe most obvious form of customised pricing in consumer lending is risk-based pricing where the interest rate “r” charged on a loan to a potential borrower is a function of the risk of the borrower defaulting. We noticed that adverse selection and affordability issues mean that the probability “p” of the borrower being good (or (1 – p), the probability of being a bad) may depend on the interest rate of the loan, that is “p(r)” and so we need to be very careful about our definition of “p” to avoid having “r” as a function of “p” which is in turn a function of “r”.12 This is called an endogeineity13 problem.

Endogeneity has long been recognised as an important consideration in price-sensitivity estimation because lenders can often anticipate exogenous changes in demand and adjust prices accordingly. Several studies have shown that not accounting for endogeneity can result in significant underestimation of price sensitivity.14

Optimal risk-based interest rate and risk-based response functionOne of the objectives of a lender is to determine the risk-based interest rate which maximises the expected profit over a portfolio of potential borrowers when the interest rate of the loan depends on the probability of being good, and then the take-up probability has to depend on the probability of being good and the interest rate as well. If we suppose that “r” negatively affects the probability of being good (as we have seen in the previous section), we get the following:

(13)

The equation shows that if there are either adverse selection or affordability problems (which will most often be the case, because this is the credit business!), the quality of the borrower is lower than in the previous definition of “p”, because now we add the effect of interest rate into the risk assessment.

(14)

The logistic risk-based response function or take-up rate which depends on ‘r’ and ‘p’ would be:

(15)

12 Lyn C. Thomas, Consumer Credit Models: Pricing, Profit and Portfolios, 2009

13 In a statistical model, a loop of “causality” between the independent and dependent variables of a model leads to endogeneity.

14 Robert Phillips, Ahmet Simsek and Garrett van Ryzin, Endogeneity and Price Sensitivity in Customized Pricing, 2012


The meaning of the equation (15) is the same as in equation (3) but adding the probability of being good “p”, with “c” measuring the sensitivity of the function with respect to “p”. In this case, the maximum willingness to pay occurs when:

(16)

This implies the riskier the borrower is, the higher the rate he or she is willing to pay.

Substituting equation (15) into equation (11), the optimal risk-based interest rate is:

(17)

This equation captures the effect of “p” on the optimal interest rate, in the same way as parameter “r“ does, too. This is a nonlinear equation, with the interest rate at both sides of the equation. Therefore, a numerical method has to be used to get the optimal interest rate.

Impact of adverse selection on risk-based pricingIf there is adverse selection, then “p ̃(r,p)“ should decrease as the interest rate “r” increases. Thus we can address this relationship with the following: to let the probability of being good be a decreasing linear function of the interest rate, or let the log odds score be a linear function of the interest rate and being “d” the sensitivity of “p ̃“with respect to “r”.

We call the first of these alternatives a linear probability adverse selection function and define:

(18)

This form comes from taking “errors” from a lineal regression scorecard.15

The impact of adverse selection can be measured modelling the errors made when the scorecard is developed with logistic regression, and they are not based on complete and accurate information about all past borrowers.

Suppose we are interested in the true probability of being good “p”̃ of an applicant who has accepted an offer from a lender, who believes the applicant’s probability of being good is “p*”, and so has an error “I I*”.Bo Huang and Lyn C. Thomas show that if the errors are uniformly distributed from –dr to dr and there are N potential lenders in the market, the linear log-odds adverse selection function is:

(19)

15 Bo Huang and Lyn C. Thomas, Credit Card Pricing and Impact of Adverse Selection, 2009


The equation (19) shows the true probability of being good as a function of the probability that we usually get from a logistic scorecard and the “error correction term” or the effect due to adverse selection which is captured by:

Applying any of these adjustments (linear or logistic) before substituting in the pricing formula, the profitability of each borrower will be improved.

The most important practical issue at this point (which we don’t treat here) is to estimate “d“.

Usually “d“ is called the price-sensitivity parameter.

How do banks set the interest rate charged to a specific loan?16

Given that the ultimate goal of a financial institution is to maximise profits, they achieve this goal by modelling the price-response function and the default risk of the loan applicant.

To set the interest rate “r”, which will be charged on a loan of one unit to a borrower, lenders use a model that assumes that they can borrow money at the risk-free rate “rf “ and the loss given default is “LGD“. If the lender charges a rate “r” to an applicant whose probability of being good is “p”, then the probability that the applicant will accept the loan is “q(r,p)”. If the lender assigns the borrower a probability “p” of being good and a rate “r(p)” is charged for the loan, the lender is assuming the following expected profit:

(20)

This equation is the same as the equation (10) but with the probability of take-up “q()” and “r()” as a function of the probability of being good.

To obtain the optimal interest rate, we maximise the equation (20), resulting in the following formula:

(21)

Where the variables have the same meaning we have given this throughout this paper.

The bank’s estimate of the probability of being good is “p*”. However, as we have seen, the true probability is “p ̃”,which takes into account the adverse selection effect over “p”.

Consequently, if the lender can identify the true probability of being good “p ̃” the optimal profit can be derived from the following equation:

16 This section follows Bo Huang and Lyn C. Thomas, Credit Card Pricing and Impact of Adverse Selection, 2009

(22)

However, the lender’s estimate of the borrower’s probability of being good is “p*”, and so what the lender expects the profit to be is:

(23)

Even though the borrower’s true probability is “p ̃”.In fact, the borrower will not live up to this expectation, and the actual or true expected profit the lender will get is:

(24)

It’s easy to see in equations (22), (23) and (24) that the differences between “p ̃” and “p*” mean that the lender earns a lower profit because he sets the optimal interest rate with “p*” when the true probability of being good is “p ̃”. Next, we will show these core issues with some numerical examples.



Numerical examples We use the logistic price-response function, which depends on “r” and “p”. With the following parameters a=54, b=32 and c=50, we get:

(25)

Thus for applicants whose default rate is five percent (p=0.95), 96 percent of them will accept a loan at an interest rate of 10 percent while only four percent will accept one at 30 percent.

We’ll assume that LGD=50 percent and rf=5 percent:

(26)

(27)

Also, we’ll consider the assumption that the relationship between “p ̃” and “p*” is linear in log-odd and N=500, d=4 so the formula that includes the effect of adverse selection in the probability of being good is:

(28)

Applying these last two equations into equations (22, 23 and 24) of the previous section, we get the results shown in Table 1.

The results of Table 1 show that the optimal profit is always better than the actual profit the lender receives, but for high-risk customers, the expected profit is higher than the optimal possible profit. For most borrowers, the profit that the lender expects is higher than the profit that actually occurs, and this difference is considerable for the high-risk borrowers. This is because the lender thinks these borrowers are better than they really are, and so has to offer a lower interest rate to attract them. This means that the chance of the borrower actually taking the offer at this rate (0.90 compared with 0.68 that the lender expected) more than compensates for the fact they are more likely to default than the lender was expecting — even though for very good borrowers (even at p=0.98 for example), the expected profit is below the true profit. Bo Huang and Lyn C. Thomas point out that: “For low-risk customers, what the lender expects is below what he would get if he knew correctly the creditworthiness of the borrower. For high-risk borrowers (relatively low “p”), the differences between the rate one should charge knowing the correct creditworthiness of the borrower and the rate the lender charges because of the adverse selection error is considerable. Because of the errors in the scorecard, in fact he should only start taking borrowers when his belief that they are good is 0.88. This is a very large difference in whom to take.”17



Graph No. 2 shows that the optimal profit is hill-shaped with a single peak (p ̃=0,70) as expected, and also there is a “de facto” cutoff at p ̃=0,70 in true profit. This means that the optimal risk-based pricing could be totally different than the expected risk-based pricing strategy if we don’t take the adverse selection problem into account. As we saw above, this is one of the principal reasons that a risk-based pricing strategy can fail.

Source: Bo Huang and Lyn C. Thomas (2009)

Figure 3: Table 1 – True, optimal and expected profit


Graph 2. True, optimal and expected profit (for a US $1,000 loan).

Figure 4: Graph 2 – True, optimal and expected profit example

Example of risk distribution skewed to the left18 It is possible that the overall selection effect caused by the risk-based pricing is adverse if the risk distribution shows positive skew. This is illustrated in Table 2, which provides a worked example for exhibition purposes. The table shows a market with five kinds of risks (default = probabilities of 0.05, 0.1, 0.2, 0.25 and 0.9, respectively). The distribution of 100 leads between risk types is given in row three (10, 10, 10, 50 and 20, respectively). Assume that there is initially a flat interest rate such that the first three types of risk are left out (indicated by square shadings of rows A and B). From the respective probabilities of default and number of applicants of the risk types 4 and 5 (i.e., those not excluded), the bank can calculate the expected number of defaults (12.5 and 18, respectively), leading to an overall default rate of 44 percent of loans.19

Suppose that the bank performed later identification tasks that allow you to position correctly to customers in one of two categories of risk, and thus charge interest rates apart.

18 This example is taken from G. Pryce, Worst of the Good and Best of the Bad: Adverse Selection Consequences of Risk Pricing, 2003

19 G. Pryce, Worst of the Good and Best of the Bad: Adverse Selection Consequences of Risk Pricing, 2003


Assume also that if the bank does this, the risk categories 1 and 4 will be left out, and the risk categories remaining are appropriate to accept the offer of credit given by the bank. This leads to a total number of defaults of 21 on 40 loans made, i.e., a default rate of 53 percent, which is higher than the default rate when there was an interest rate of pooling.20

Source: Pryce, 2003

Figure 5: Table 2 – Risk distribution positively skewed

Source: Pryce, 2003

Figure 6: Graph 3 – Risk distribution skewed to the left

20 G. Pryce, Worst of the Good and Best of the Bad: Adverse Selection Consequences of Risk Pricing, 2003


If the risk distribution (risk score) is skewed to the left, the quantity effect might exceed the price effect and therefore the risk-based pricing strategy might be unprofitable.

Alternatively, if the quantity of bads exceeds the quantity of goods in the market, the risk-based pricing strategy might be unprofitable, too.

These conditions are considered true within the bottom of subprime segments.

By differentiating the interest rates charged to each identified risk group, lenders may inadvertently worsen the average level of risk of their portfolio as a whole. If the lender has insufficient information to reliably distinguish good risk from bad, it might be convenient to set a flat interest rate strategy rather than using a customised pricing strategy.


ConclusionsRecently, variable pricing has become more common in consumer lending. Variable pricing assumes that adverse selection can occur, as lenders have limited information about the riskiness of the prospect borrowers. In this paper, we conclude that the relationship between the actual default risk of a borrower and the lender’s perceived view of this risk are simple, irrespective of the distribution of the errors in the lender’s scorecard. By developing a model of the profit that a lender derives from a loan, we analyse the impact of these adverse selection errors.

The conclusion is that whichever method is used to estimate the optimal profit of a risk-based pricing strategy, the actual profit could be lower, particularly for risky profiles.

Lenders could develop a strategy to manage this issue when modelling the profit-maximising interest rate to be obtained. This approach may lead to accept that the application scorecard required recalibration or redevelopment. In fact, the lender will probably try to build a new scorecard to reflect the true riskiness of the borrowers who actually take the loan.

However, the problem with this approach is that the population who takes the loan depends on the rates being offered (endogeneity), and one of the strengths of variable pricing is that one can vary the rates to respond to changes in the market (because the population who takes the loans is constantly changing). However, as Bo Huang and Thomas state, the simple relationship between the successful lender’s perceived probability of the borrower being good and the expected true probability of the borrower being good suggests that applying the transformation “p*→p ̃=p*-dr” is a feasible and more convenient approach. Applying this last adjustment before substituting in the pricing formula, it will improve the profitability of the borrowers, particularly the high-risk ones.21



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Thomas, Lyn C. Consumer Credit Models: Pricing, Profit and Portfolios OUP Catalogue. Oxford University Press, 2009.


About Experian Decision AnalyticsExperian Decision Analytics enables organisations to make analytics-based customer decisions that support their strategic goals, so they can achieve and sustain significant growth and profitability. Through our unique combination of consumer and business information, analytics, decisions, and execution, we help clients to maximise and actively manage customer value.

Meaningful information is key to effective decision-making, and Experian is expert in connecting, organising, interpreting and applying data, transforming it into information and analytics to address real-world challenges. We collaborate closely with clients to identify what matters most about their business and customers, then create and implement analytics-based decisions to manage their strategies over time.

In today’s fast-paced environment where developing, implementing, and sustaining an effective strategy is imperative, Experian Decision Analytics helps organisations unlock a wealth of benefits immediately—and set the stage for long-term success.

Increased revenue: Our products and services enable clients to increase revenue by providing the insight and agility they need to find and engage the right customers, target products more effectively, and grow market share.

Controlled risk: A broad range of risk-management products and services help organisations verify identity and manage and detect fraud, optimise collection and recovery, and balance risk and reward.

Operational efficiency: Experian Decision Analytics helps organisations quickly integrate various information and processes to enhance operational efficiency and boost agility. Our flexible, collaborative approach helps organisations increase speed to market, enhance business agility and improve the quality of customers’ experiences.

Compliance as differentiation: Proven expertise lets clients use compliance as source of competitive advantage. Experian Decision Analytics helps ensure compliance with essential regulations, while helping organisations better understand customers.


About Experian Decision Analytics’ Global Consulting PracticeExperian’s business consultants deliver powerful insight that is used by clients to enhance credit-management strategies across their consumer and small-business portfolios and the Customer Life Cycle. Experian’s Global Consulting Practice is a credentialed consultancy dedicated to creating measurable and sustainable value for organisations around the globe in financial services, banking, mortgage, automotive finance, telecommunications and utilities, microfinance, retail credit and debt collections. We specialise in analytics-based decision strategies, data-driven products and services, regulatory compliance and fraud risk management across acquisitions, customer management, collections and overall portfolio management.

Experian’s business consultants provide clients with exceptional credit and fraud risk-management strategic insight, detailed enhancement opportunities, and deployment strategies through deep business subject-matter expertise and client intimacy, as well as a client engagement methodology to ensure consistency. We have deep knowledge of data, analytics and software and have demonstrated the ability to synthesise this intelligence with the deep understanding of credit-management principles and practices to solve our clients’ complex business needs.

• Averageof20years’experienceperconsultant• Fifty-sixconsultantsbasedthroughoutAsiaPacific,Europe,the

MiddleEast,NorthAmericaandtheUnitedKingdom• Deepexpertiseinacquisitions,originations,customer

management,collectionsandrecoveryaswellasidentityauthenticationandfraudmanagement

• Teamswithlocalknowledgeofbestpractices


About the authorsLucas Acebedo — Business Consultancy Manager, LAC & Mexico, Associate Programme Global Consulting Practice, Experian Decision Analytics

Lucas Acebedo joined Experian in 2010 as a Senior Consultant, managing hosted solutions like Portfolio Management Package at large Latin American clients. He is responsible for the delivery of Portfolio Reporting Studio and Consulting on strategic topics in Credit Risk, Retail Credit Portfolio Management and Collections.

Prior to that, he spent three years at an Argentinean Bank as a Head of Portfolio Management and scoring, being responsible for Credit Risk Models Management, Reporting, Risk-based pricing and Basel II models implementations.

He also was Consultant at Inter-American Development Bank, INDEC (National Bureau of Statistics) and Inter-American Statistical Institute.

Acebedo teaches Macroeconomics and has also trained undergraduate students in Econometrics at University of Buenos Aires.

June Durnall — Principal Consultant, Global Consulting Practice, Experian Decision Analytics

June Durnall joined Experian in 2011. She is a senior consumer credit risk manager with experience in approximately 30 countries.

Since 2004, Durnall has been a Senior Managing Consultant (Credit Risk Management) at MasterCard Advisors. Here she was responsible for full life cycle consumer credit risk management globally with clients in North America, Latin America, Europe and Asia.

Prior to that, she spent five years at Fair Isaac as a Senior Consultant providing credit and risk consulting to the ASAM region (Asia, South America, and Mexico). P & L experience was obtained through senior risk management positions at Citibank and Bank of America.

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