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• Banks are custodians of the economy in which they render surplus funds of investors available to borrowers as loans.

• (CLICK) Liquidity therefore fundamental, also highlighting the importance of asset and liability management (“borrow long, lend short”)

• Credit risk represents the loss of both principal and revenue, and disrupts cash flows, possibly pre-empting a liquidity crisis if this disruption is sufficiently large

• Risk management in general involves techniques to reduce the volatility of revenue and avoid large losses by reserving funds, the basis of another undiscussed Exercise called Loan Loss Provisioning

• (CLICK) Conceptually, the proportion reserved should depend on the credit risk of a borrower as well as on the loan amount granted (which should also depend on the inherent credit risk)

• (CLICK) In compensation for undertaking the associated (and estimated) credit risk, the bank charges service fees and interest rates on the principal.

• Again, the interest charged should depend on the inherent credit risk (the basis of risk-based pricing)

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• Growth of consumer credit over past few decades unimaginably large, hailing from the 1920s when Henry Ford and A.P Sloan started offering vehicle financing

• During 1960s, credit cards became universal and their widespread use was a noticeable sign of the growth in consumer credit – even though credit cards only accounted for roughly 15% of consumer credit

• (CLICK) As of 2007, total consumer credit debt in the USA amounted to $13 trillion (13 followed by 12 zeros) – including mortgages, credit cards, personal loans, vehicle financing, overdrafts, and other revolving loans

• Consumer debt is 40% greater than industry debt ($9.2 trillion) and more than double than corporate debt ($5.2 trillion) – which includes SME and agriculture

• Although consumer debt is greatest in the USA, other countries are not far behind, e.g., UK has grown from £1 trillion in 2004 to £1.4 trillion in 2007

• Considering the exponential growth in the demand for consumer debt, it is reasonable to state the credit risk management should also escalate accordingly in importance

• Consider that consumer debt has also exceeded the national annual income of consumers in the USA since 2000, thereby highlighting affordability factors in granting credit

• While economic literature is extensive on modelling the income and consumption of consumers (typical elements of affordability assessments), its interaction with credit risk management appears to be limited

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• Despite differences between the organizational structures and business units amongst lenders, most activities of a lender can be grouped within 3 function types: strategy, operational, and corporate functions

• E.g., credit risk management and marketing (2 sides of the same coin) are sub-functions of the strategy function

• Akin to “breaking the whole into parts”, the organizational structures within banks have led to tasking individual business units to solve (or model) parts of the whole

• E.g., a separate team for response modelling, another for application scorecard development, and another for pricing loans

• This was a logical consequence to the immense complexity (and workload) associated with credit risk management

• However, this approach also necessitated the fabrication of several assumptions in the statistical modelling within each respective business units

• E.g., formulating default definition without considering risk-based pricing or response modelling, or reserving capital without considering default definitions

• Considering but the two sub-functions of strategy (credit risk and marketing), disparities often occur in the analytical goals

• E.g., attracting more loan volumes (marketing), and rejecting more loan applicants likely to default (credit risk)

• In this research, we have limited our scope to 4 such typical modelling activities (called Exercises) within Credit Risk Management – each pending discussion

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• (CLICK) To explain how each of these 4 Exercises fits within the global scheme of things (also known as the 5 phase Credit Management Flowchart), a lender often starts with Response Modelling (green) to estimate the chances of a potential borrower actually taking up offered credit

• (CLICK) After initiating contact with these potential customers, each one is formally credit scored (red) to estimate the chances of a borrower actually repaying credit in full

• Note that during the Marketing phase (in which Response modelling typically occurs), the pool of customers likely to respond is also typically filtered based on a light version of the credit scorecard in production (often called pre-screening/pre-scoring)

• (CLICK) The next Exercise (Pre-classification – yellow) does not fit within the 5 phase Credit Management Flowchart and is performed prior to developing the credit score-card

• It supports many other analytical exercises since it constitutes formulating a set of default definitions

• (CLICK) The last Exercise (Pricing – blue) occurs both outside and inside the 5 phase Credit Management Flowchart

• Outside, it involves setting base prices (including loan features) for the portfolio and its various segments (including risk grades, or income brackets)

• Inside, it involves modifying these base prices (loan features) to the individual new applicant’s risk profile – hence the concept of “personalized interest rate”

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• 1: Response Modelling• Within the Marketing sub-function of the Strategy function, lender

interested in devising campaigns and soliciting customers to apply for a pre-designed credit product

• Goal is to maximise the pool of potential customers and, more importantly, maximise the proportion of customers who eventually accept the offered product, i.e., the take-up rate

• Basis of response modelling, typically involving the use of logistic regression

• Probability of a customer with characteristics 𝑥 accepting an offered loan with pre-specified features 𝑣 𝑖𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔 𝑝𝑟𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑟𝑦 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝒾

• 2: Pre-classification (CLICK)• Devising a loan performance variable (CD, Days past Due, etc.) based on 2

fundamental variables across time: Expected Instalment and the Actual Repayment

• Goal of classifying historical loan records based on their performance• This loan performance variable often becomes the target (dependent)

variable within other exercises such as the variety of scorecards (application, behavioural, collection, etc.)

• Other times, it becomes another predictor within other models, e.g., bespoke pre-scoring models

• In general, this variable is a reflection of the chosen default definition

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• 3: Credit Scoring (Application) (CLICK)• Within the credit risk sub-function of the Strategy function, one is

concerned with estimating a pragmatic measure of creditworthiness called probability of default (PD)

• Considered pragmatic since each lender will have a different view of what creditworthiness constitutes (primarily due to differences in the Pre-classification Exercise and, in turn, the default definition)

• Main goal is to keep eventual bad debt at a minimum, which may conflict with the goal of the Response Modelling Exercise

• Mostly cross-sectional models involving two points in time, modelling the previously devised loan performance variable as a linear function of characteristics 𝑥 observed at 1st point in time

• Historically includes LDA, QDA, Linear/logistic regression. Also newer innovations such as SVMs, recursive partitioning algorithms (decision trees), artificial neural networks.

• 4: Risk-based Pricing (CLICK)• In pricing loans (interest rates), a lender has to incorporate many

components into this eventual price• Including the administrative/operational costs and fees associated

with servicing the loan;• A Risk premium for the Expected Loss of a loan, to be accumulated

within a pool (related to the Provisioning Exercise);• Compensation for undertaking the inherent credit risk (related to

profitability)• Lenders have started varying loan features (including interest rate) since

the 1990s on their products based on segmenting their portfolio by creditworthiness (or risk grades)

• Each segment is associated with a specific interest rate (and other loan features)

• Typically consists of a tree-like structure wherein each particular segment splits into other categories, e.g., for PD between 0.3 and 0.5, if salary >= 15k then loan amount = 25k

• Loan features within these categories are mostly policy-driven and/or based on management consulting

• Other forms include a similar tree-like graph involving behavioural scorecards (limit increases) and actuarial cash flow models calculating the ROE at a particular interest rate

• Most forms of optimization in pricing involve a champion/challenger approach – a cumbersome and time-sensitive approach, often spanning many months wherein a very small portion of a loan book is given a different set of loan features and their performance (and profitability compared to the remaining loan book) is scrutinized over time.

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• There exists three broad classes of interactions/relationships between a customer and a bank, based on the actions and characteristics of each

• 2 of these interactions are well documented (e.g., adverse selection dating back from the 1980s even), with the exception of the relatively new interaction, Price-Risk relationship (Unaffordability)

• It is argued that these interactions exist partly due to the incongruence between the aforementioned Exercises

• All 3 interactions can be encapsulated into a central concept, i.e., the price-risk-response relationship

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• Fundamental to any pricing activity is the price-response function• Measures the degree of product demand fluctuations given a change in

price• Also known as the elasticity of a response model

• (CLICK) In the credit risk management context, this implies that the response probability 𝑃(𝐴) of a potential borrower either accepting or rejecting an offered loan, depends directly on the quoted interest rate 𝒾 (EXPLAIN GRAPH)

• However, while this concept is basic in principle, it also assumes that the population of potential borrowers is largely homogenous in their response – an insidious assumption

• I.e., this assumes that two borrowers from very different socio-economic classes will respond similarly – an obviously unrealistic assumption

• From an analytical perspective, the exact nature of the Price-response relationship is unclear – it may be a smooth and fluid linear relationship or it may have peaks and valleys

• Largely data-dependent and, by extension, market-dependent

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• Credit scoring has the main objective of risk-ranking applicants and granting credit only to those applicants having scored above a certain probability threshold –called the cut-off score

• As such, the credit risk sub-function of the strategy function has the objective to keep bad debt at a minimal level

• Naturally, this may conflict with the goal of the marketing sub-function, i.e., attain a maximum of applicants

• The documented existence of adverse selection may be attributed in part to this gap between credit scoring and response modelling

• Incorporated within another universal idea called asymmetric information between lender and borrower

• I.e., the lender does not have the same level of information on the financial capacity of a borrower than the borrower himself

• While credit scoring aims to give a limited view on the inherent creditworthiness, it does not nearly account for all pre-cursor events of default

• E.g., divorce, sickness and death, fixing a geyser in an emergency and other unplanned expenses circumventing paying off debt

• Adverse selection states that significantly more not-so-good applicants apply and is granted credit than expected since these applicants scored marginally above the cut-off score

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• On a technical level, this implies that the good/bad odds ratio within higher risk grades (lower score bands) are affected, i.e., more bads than anticipated within those higher risk grades (lower score bands)

• Mainly explained by the second interaction found between the Credit scoring (risk) and Response modelling (response) exercises, i.e., the risk-response relationship

• Adverse selection is a special case of the more general risk-response relationship

• (CLICK) Due to the advent of most banks using similar credit bureau data and purchasable demographic datasets in developing response models, a particular phenomenon arose (especially in nearly saturated markets):

• Those lower risk customers (as scored in pre-screening models judging creditworthiness) are often simultaneously targeted by multiple lenders

• This explains the typical low response rates for the lower risk grades due to these customers being more discriminating in selecting a credit product from any particular lender

• (CLICK) On the converse, those higher risk customers often have higher response rates, likely explained by their exasperated need for credit in the first place – the basis of adverse selection

• The observed phenomenon of having more bads than anticipated affects not only the good/bad odds ratio, but subsequently also a lender’s risk appetite, cut-off decisions, loss provisions and overall profitability

• (CLICK) As with the Price-Response relationship, the exact nature of the Risk-Response relationship is unclear – it may be a smooth and fluid linear relationship or it may have peaks and valleys

• Largely data-dependent and, by extension, market-dependent

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• The Risk-based Pricing Exercise generally involves setting prices (interest rates & fees) for each risk segment within an existing portfolio

• After classifying a new applicant into one of these pre-existing risk grades, the associated price is then charged

• This approach generally coincides with selecting other loan features (allowable term, principal, etc.) within previously discussed tree-like graph

• However, all current risk-based pricing practices calculate a price after credit risk has been estimated

• This implies that the price is a function of the estimated PD, which implies that when varying the price without touching any other parameter, no feedback to the PD occurs.

• Also, most risk-based pricing activities do not consider the monthly shock a new loan will have in its instalment on a borrower

• This shock subsequently affects the default risk of said borrower• As en example, an applicant may very well be able to service a new loan at

10% interest pa• However, this may no longer be the case if and when this interest

rate rises to 20% during the loan life since the borrower’s disposable income might no longer be sufficient to cover the increased shock of the new instalment

• (when considering interest rate changes regardless of macroeconomic conditions or by contractual design)

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• The impact of this was clearly seen with Adjustable-Rate Mortgages (ARMs) in the US housing market during the 2008 financial crisis when the interest rates on these mortgages rose significantly (by contractual design) 2-3 years after origination – many borrowers defaulted, contrary to the initial PD estimation

• Too many defaulted to ascribe this occurrence simply to random statistical error

• A seemingly obvious solution would be to re-estimate the PD after setting the price

• However, since the price depends again on the PD, this would imply a new price as well – especially if this newly estimated post-pricing PD has edged away from acceptable risk parameters, thereby requiring an increased premium by the lender to compensate for the increased inherent default risk

• A typical chicken-or-egg situation

• (CLICK) This relationship is therefore intuitive with its ramifications on loss provisions, loan write-offs and profitability quite extensive

• As the price 𝒾 increases on a loan, so to must the inherent credit risk – and vice versa

• (CLICK) The Unaffordability interaction is a special case of this Price-Risk relationship, manifesting when the price increases to a certain point when it’s longer serviceable – leading to default

• (CLICK) As with the previous interactions, the exact nature of the Price-Risk relationship is unclear – it may be a smooth and fluid linear relationship or it may have peaks and valleys

• Largely data-dependent and, by extension, market-dependent

• The credit industry and its regulators were not inactive on this issue, especially considering the recent affordability calculation guidelines published by the South African Department of Trade and Industry in August 2014

• A typical measure of affordability include variants of the debt-service-to-gross-income ratio not exceeding hard thresholds

• In the UK, these are 25% for unsecured loans and 50% for both unsecured and secured loans

• Other typical measures include not having more than 4 active credit agreements, or by imposing interest rate ceilings or even allowable monthly expenses by income bracket as in the SA dti’s case

• However, these rules (and variants) have been criticised by scholars as overly static and ineffective as a blanket-approach to all borrowers

• In its essence, affordability guidelines should be centred on the net disposable income of a borrower (the difference between monthly income and consumption)

• However, when modelling income and consumption, one enters the domain of macroeconomic theory

• Scholars have been increasingly advocating the use of widely accepted

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economic theories over last 2 decades, coalescing into the hot topic today that is affordability assessments

• Specifically, this includes basing affordability on current consumption which depends on something called the permanent/lifetime income of a borrower – hallmarks of the popular Permanent Income Hypothesis (PIH) of Nobel laureate Prof Milton Friedman

• The PIH is often cited alongside the Life-cycle Theory of another Nobel laureate Prof Franco Modigliani, which states that consumers smooth their consumption over time with current consumption being affected by permanent income shocks rather than short-lived income shocks

• E.g., younger borrowers will borrow against their future earnings, thereby explaining their higher risk appetite

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• These 3 interactions are also made clearer when factoring them together• An apparent paradox is then presented when examining the Risk-based pricing

Exercise from a response viewpoint (the same as viewing the price-risk-response relationship):

• Due to other lenders also pricing for risk, a risk-neutral lender may price lower risk customers at an even lower point than what would have been acceptable to those low risk customers – as per the price-response relationship

• However, due to the risk-response relationship, low risk customers are also more discriminating in selecting an offered credit product, giving more credence to the interest rate (price) than their higher risk counterparts

• This implies a lender has to lower the already-lowered price even more in order to acquire those low risk customers (or at least increase the chances of doing so) – all as a result of pricing for risk in the first place

• If continued ad infinitum and all lenders participate, the paradox lies in the fact that a lender would eventually have to offer credit free of charge –which is obviously nonsensical

• Holistically, this is the typical effect of the competitive nature of the credit industry, although the underlying credit models do not incorporate this yet

• The paradox also has a converse that manifests as adverse selection once again:• Higher risk customers would accept higher priced credit products

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inherently due to their exasperated need for credit coupled with the likely possibility of already having been rejected by some other lenders

• As per the risk-response relationship• This implies a risk-neutral lender may want to price these higher risk

customers even higher to compensate for the perceived increase in their credit risk (having been rejected by other lenders)

• Due to the unaffordability interaction (the price-risk relationship), this implies such a higher price would further increase the probability of default

• The paradox manifests then as the need to increase the price even more, thereby exasperating the situation further

• If a lender does not reprice the inherent credit risk, more bads are accepted than anticipated, leading to the manifestation of adverse selection

• Holistically, this cycle can only continue up to the maximum allowable interest rate ceiling (such as the In Duplum rule of South Africa)

• This paradox is only resolved when making the identified exercises congruent in such a manner that the resulting modelling approach is cognizant of all lending constraints

• E.g., incorporate the price-risk-response relationships and constrain the eventual price to be always above the risk-free interest rate (otherwise, it’s more profitable investing the lending capital instead of lending it)

• In general, the very existence of these 3 interactions implies that one must model these Exercises (Risk-based Pricing, Credit Scoring, and Response Modelling) together in order to capture what is essentially a game between the lender and the borrower

• This is perhaps clearly seen in the discrepancy between current pricing practices and the existence of these price-risk-response relationships

• As previously discussed, current pricing practices imply that the interest rate is a function of the PD

• However, the price-risk-response relationships imply that, amongst other things, the PD is a function of the interest rate – directly contrasting current practises

• (CLICK) Mathematically, this is expressed as shown (ask via email for PhD proposal for a much more thorough explanation) (CLICK – Explain terms)

• The objective becomes to find the optimal price incorporating the price-risk-response relationship by defining 𝒾 𝑝, 𝑞 as a function of risk (p) and response (q) – who are themselves functions of, amongst other things, the price (i).

• Such a rudimentary prototype was already developed by two leading credit risk scholars at the University of Berkeley, USA, based on finding the optimal price that maximises the ROE for a lender’s portfolio

• However, this only included the Risk-Response relationship (controlling to some degree for the effects of adverse selection)

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• An interesting consequence is the shift away from using cut-off scores in credit scoring and decision-making

• This is in line with the recent research trend of focusing on profit scoring over the past decade – which is, in itself, holistically similar to this unified framework

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• While this presentation only focusses on showcasing the identified problems on a very high-level (the incongruence) and not the in-depth researched and proposed solutions, we can conclude with the hypotheses of this research:

• Once the identified Exercises are viably reformed within one framework, it is hypothesized that the accuracy of desired outputs would be greatly enhanced

• These include more coherent probabilities of acceptance and default – coherent in terms of the price-risk-response relationships

• Truly optimal prices from a ROE-perspective – also coherent in terms of the price-risk-response relationships

• However, perhaps the greatest benefit of having more realistic probability estimates is their effect on other exercises – especially loan loss provisioning and Basel-compliant capital estimation

• Especially since these rely on PDs, LGDs, and EADs• Also note that we haven’t even touched on how these price-risk-

response relationships fits into an ever-changing dynamic macroeconomic environment – that is for another presentation

• (CLICK)

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