Archive for the ‘Profit Model Analytics’ Category

You’ve got to know when to hold ‘em, know when to fold ‘em

Know when to walk away and know when to run

I’ve always wanted to use the lines from Kenny Rogers’ famous song, The Gambler, in an article. But that is only part of the reason I decided to use the game of Texas Holdem poker as a metaphor for the credit risk strategy environment.

The basic profit model for a game of poker is very similar to that of a simple lending business. To participate in a game of Texas Holdem there is a fixed cost (buy in) in exchange for which there is the potential to make a profit but also the risk of making a loss. As each card is dealt, new information is revealed and the player should adjust their strategy accordingly. Not every hand will deliver a profit and some will even incur a fairly substantial loss, however over time and by following a good strategy the total profit accumulated from those hands that are winners can be sufficient to cover the losses of those hands that are losers and the fixed costs of participating and a profit can thus be made.

Similarly in a lending business there is a fixed cost to process each potential customer, only some of whom will be accepted as actual customers who have the potential to be profitable or to result in a loss.  The lender will make an overall profit only if the accumulated profit from each profitable customer is sufficient to cover the losses from those that weren’t and the fixed processing costs.

In both scenarios, the profit can be maximised by increasing exposure to risk when the odds of a profit are good and reducing exposure, on the other hand, when the odds of a loss are higher. A good card player therefore performs a similar role to a credit analyst: continuously calculating the odds of a win from each hand, designing strategies to maximise profit based on those odds and then adjusting those strategies as more information becomes available.


To join a game of Texas Holdem each player needs to buy into that game by placing a ‘blind’ bet before they have seen any of the cards.  As this cost is incurred before any of the cards are seen the odds of victory can not be estimated. The blind bet is, in fact, the price to see the odds.

Thereafter, each player is dealt two private cards; cards that only they can see. Once these cards have been dealt each player must decide whether to play the game or not.

To play on, each player must enter a further bet. This decision must be made based on the size of the bet and an estimate of the probability of victory based on the two known cards. If the player should instead choose to not play, the will forfeit their initial bet.

A conservative player, one who will play only when the odds are strongly in their favour, may lose fewer hands but they will instead incur a relatively higher cost of lost buy-ins. Depending on the cost of the buy-in and the average odds of winning, the most profitable strategy will change but it will unlikely be the most conservative strategy.

In a lending organisation the equivalent role is played by the originations team. Every loan application that is processed, incurs a cost and so when an application is declined that cost is lost. A conservative scorecard policy will decline a large number of marginal applications choosing, effectively, to lose a small but known processing cost rather than risk a larger but unknown credit loss.  In so doing though, it also gives up the profit potential on those accounts. As with poker betting strategies, the ideal cut-off will change based on the level of processing costs and the average probability of default but will seldom be overly conservative.

A card player calculates their odds of victory from the known combinations of cards possible from a standard 54 card deck.  The player has the possibility of creating any five card combination made up from their two known cards and a further five random ones yet to be dealt, while each other player can create a five card combination made-up of any seven cards except for the two the player himself has.  With this knowledge, the odds that the two private cards will result in a winning hand can be estimated and, based on that estimate, make the decision whether to enter a bet and if so of what size; or whether to fold and lose the buy-in.

The methods used to calculate odds may vary, as do the sources of potential profits, but at a conceptual level the theory on which originations is based is similar to the theory which under-pins poker betting.

As each account is processed through a scorecard the odds of it eventually rolling into default are estimated. These odds are then used to make the decision whether to offer credit and, if so, to what extent.  Where the odds of a default are very low the lender will likely offer more credit – the equivalent of placing a larger starting bet – and vice versa.

Customer Management

The reason that card games like Texas Holdem are games of skill rather than just games of chance, is that the odds of a victory change during the course of a game and so the player is required to adapt their betting strategy as new information is revealed.  Increasing their exposure to risk as the odds grow better or retreating as the odds worsen.  The same is true of a lending organisation where customer management strategies seek to maximise organisational profit but changing exposure as new information is received.

Once the first round of betting has been completed and each player’s starting position has been determined, the dealer turns over three ‘community cards’.  These are cards that all players can see and can use, along with their two private cards, to create their best possible poker hand. A significant amount of new information is revealed when those three community cards are dealt. In time two further community cards will be revealed and it will be from any combination of those seven cards that a winning hand will be constructed. So, at this point, each player knows five of the seven cards they will have access to and three of the cards their opponents can use. The number of possible hands becomes smaller and so the odds that the players had will be a winner can be calculated more accurately. That is not to say the odds of a win will go up, just that the odds can be stated with more certainty.

At this stage of the game, therefore, the betting activity usually heats up as players with good hands increase their exposure through bigger bets. Players with weaker hands will try to limit their exposure by checking – that is not betting at all – or by placing the minimum bet possible. This strategy limits their potential loss but also limits their potential gain as the total size of the ‘pot’ is also kept down.

As each of the next two community cards is revealed this process repeats itself with players typically willing to place ever larger bets as the new information received allows them to calculate the odds with more certainty. Only once the final round of betting is complete are the cards revealed and a winner determined. Those players that bet until the final round but still lose will have lost significantly in this instance. However, if they continue to play the odds well they will expect to recuperate that loss – and more – over time.

The customer management team within a lending organisation works with similar principals. As an account begins to operate, new information is received which allows the lender to determine with ever more certainty the probability that an account will eventually default: with every payment that is received on time, the odds of an eventual default decrease; with every broken promise-to-pay, those odds increase; etc.

So the role of the customer management team is to design strategies that optimise the lender’s exposure to each customer based on the latest information received. Where risk appears to be dropping, exposure should be increased through limit increases, cross-selling of new products, reduced pricing, etc. while when the opposite occurs the exposure should be kept constant or even decreased through limit decreases, pre-delinquency strategies, foreclosure, etc.


As the betting activity heats up around them a player may decide that the odds no longer justify the cost required to stay in the game and, in these cases, the player will decide to fold – and accept a known small loss rather than continue betting and risk an even bigger eventual loss chasing an unlikely victory.

Collections has too many operational components to fit neatly into the poker metaphor but it can be most closely likened to this decision of whether or not to fold. Not every hand can be a winner and even hands that initially appeared to be strong can be shown to be weak when the latter community cards are revealed. A player who was dealt two hearts and who then saw two further hearts dealt in the first three community cards would have been in  a strong position with the odds that the fifth heart they need to create a strong ‘flush hand’ sitting at fifty percent. However, if when the next two cards are dealt neither is a heart, the probability of a winning hand will drop to close to zero.

In this situation the player needs to make a difficult decision: they have invested in a hand that has turned out to be a ‘bad’ one and they can either accept the loss or invest further in an attempt to salvage something. If there is little betting pressure from the other players, they might choose to stay in the game by matching any final bets; figuring that because the total pot was large and the extra cost of participating small it was worth investing further in an unlikely win. Money already bet, after all, is a sunk cost. If the bets in the latest round are high however, they might choose to fold instead and keep what money they have left available for investment in a future, hopefully better hand.

As I said, the scope of collections goes well beyond this but certain key decisions a collections strategy manager must make relate closely to the question of whether or not to fold. Once an account has missed a payment and entered the collections processes the lender has two options: to invest further time and money in an attempt to collect some or all of the outstanding balance or to cut their losses and sell or even to write-off the debt.

In cases where there is strong long-term evidence that the account is a good one, the lender might decide – as a card player might when a strong hand is not helped by the fourth community card – to maintain or even increase their exposure by granting the customer some leeway in the form of a payment holiday, a re-aging of debt or even a temporary limit increase. On the other hand, in cases where the new information has forced a negative re-appraisal of the customer’s risk but the value owed by that customer is significant, it might still be preferable for the lender to invest a bit more in an attempt to make a recovery, even though they know that the odds are against them. This sort of an investment would come in the form of an intensive collections campaign or the paid involvement of specialist third party debt collectors.

As with a game of cards, the lender will not always get it exactly right and will over invest in some risky customers and under-invest in others; the goal is to get the investment right often enough in the long-term to ensure a profit overall.

It is also true that a lender who consistently shies away from investing in the collection of marginal debt – one that chooses too easily to write-off debt rather than to risk an investment in its recovery – may start to create a reputation for themselves that is punitive in the long-run. A lender that is seen as a ‘soft touch’ by the market will attract higher risk customers and will see a shift in portfolio risk towards the high-end as more and more customers decide to let their debt fall delinquent in the hopes of a painless write-off. Similarly a card player that folds in all situations except those where the odds are completely optimal, will soon be found out by their fellow players. Whenever they receive the perfect hand and bet accordingly, the rest of the table will likely fold and in so doing reduce the size of the ensuing pot which, although won, will be much smaller than it might otherwise have been. In extreme cases, this limiting of the wins gained from good hands may be so sever that the player is unable to cover the losses they have had to take in the games in which they folded.


The goal of credit risk strategy, like that of a poker betting strategy, is to end with the most money possible. To do this, calculated bets must be taken at various stages and with varying levels of data; risk must be re-evaluated continuously and at times it may become necessary to take a known loss rather than to risk ending up with an even greater, albeit uncertain, loss in the future.

So, in both scenarios, risk should not be avoided but should rather be converted into a series of numerical odds which can be used to inform investment strategies that seek to leverage off good odds and hedge against bad odds. In time, if accurate models are used consistently to inform logical strategies it is entirely possible to make a long-term profit.

Of course in their unique nuances both fields also vary quite extensively from each other, not least in the way money is earned and, most importantly, in the fact that financial services is not a zero sum game. However, I hope that where similarities do exist these have been helpful in understanding how the profit levers in a lending business fit together. For a more technical look at the same issue, you can read my articles on profit modelling in general and for credit cards and banks in particular.

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Probably the most common credit card business model is for customers to be charged a small annual fee in return for which they are able to make purchases using their card and to only pay for those purchases after some interest-free period – often up to 55 days.  At the end of this period, the customer can choose to pay the full amount outstanding (transactors) in which case no interest accrues or to pay down only a portion of the amount outstanding (revolvers) in which case interest charges do accrue.  Rather than charging its customer a usage fee, the card issuer also earns a secondary revenue stream by charging merchants a small commission on all purchases made in their stores by the issuer’s customers.

So, although credit cards are similar to other unsecured lending products in many ways, there enough important differences that are not catered for in the generic profit model for banks (described here and drawn here) to warrant an article specifically focusing on the credit card profit modelNote: In this article I will only look at the profit model from an issuer’s point of view, not from an acquirer’s.

* * * 

We started the banking profit model by saying that profit was equal to total revenue less bad debts, less capital holding costs and less fixed costs.  This remains largely true.  What changes is the way in which we arrive at the total revenue, the way in which we calculate the cost of interest and the addition of a two new costs – loyalty programmes and fraud.  Although in reality there may also be some small changes to the calculation of bad debts and to fixed costs, for the sake of simplicity, I am going to assume that these are calculated in the same way as in the previous models.



Unlike a traditional lender, a card issuer has the potential to earn revenue from two sources: interest from customers and commission from merchants.  The profit model must therefore be adjusted to cater for each of these revenue streams as well as annual fees. 

Total Revenue  = Fees + Interest Revenue + Commission Revenue

                                = Fees + (Revolving Balances x Interest Margin x Repayment Rate) + (Total Spend x Commission)

                                = (AF x CH) + (T x ATV) x ((RR x PR x i) + CR)

Where              AF = Annual Fee                                               CH = Number of Card Holders  

                           T = Number of Transactions                          PR = Repayment Rate

                           ATV = Average Transaction Value              i = Interest Rate

                           RR = Revolve Rate                                              CR = Commission Rate

Customers usually fall into one of two groups and so revenue strategies tend to conform to these same splits.  Revolvers are usually the more profitable of the two groups as they can generate revenue in both streams.  However, as balances increase and approach the limit the capacity to continue spending decreases.  Transactors, on the other hand, seldom carry a balance on which an issuer can earn interest but they have more freedom to spend.

Strategies aimed at each group should be carefully considered.  Balance transfers – or campaigns which encourage large, once-off purchases – create revolving balances and sometimes a large, once-off commission while generating little on-going commission income.  Strategies that encourage frequent usage don’t usually lead to increased revolving balances but do have a more consistent – and often growing – long-term impact on commission revenue..   

Variable Costs

There is also a significant difference between how card issuers and other lenders accrue variable costs. 

Firstly, unlike other loans, most credit cards have an interest free period during which the card issuer must cover the costs of the carrying the debt.

The high interest margin charged by card issuers aims to compensate them for this cost but it is important to model it separately as not all customers end up revolving and hence, not all customers pay that interest at a later stage.  In these cases, it is important for an issuer to understand whether the commission earnings alone are sufficient to compensate for these interest costs.

Secondly, most card issuers accrue costs for a customer loyalty programme.  It is common for card issuers to provide their customers with rewards for each Euro of spend they put on their cards.  The rate at which these rewards accrue varies by card issuer but is commonly related in some way to the commission that the issuer earns.  It is therefore possible to account for this by simply using a net commission rate.  However, since loyalty programmes are an important tool in many markets I prefer to keep it out as a specific profit lever.

Finally, credit card issuers also run the risk of incurring transactional fraud –  lost, stolen or counterfeited cards.  There are many cases in which the card issuer will need to carry the cost of fraudulent spend that has occurred on their cards.  This is not a cost common to other lenders, at least not after the application stage.

Variable Costs = (T x ATV) x ((CoC x IFP) + L + FR)

Where            T = Number of Transactions                         IFP = Interest Free Period Adjustment

                         ATV = Average Transaction Value             CoC = Cost of Capital

                         FR = Fraud Rate

Shorter interest free periods and cheaper loyalty programmes will result in lower costs but will also likely result in lower response rates to marketing efforts, lower card usage and higher attrition among existing customers.


The Credit Card Profit Model                   

Profit is simply what is left of revenue once all costs have been paid; in this case after variable costs, bad debt costs, capital holding costs and fixed costs have been paid.

I have decided to model revenue and variable costs as functions of total spend while modelling bad debt and capital costs as a function of total balances and total limits. 

The difference between the two arises from the interaction of the interest free period and the revolve rate over time.  When a customer first uses their card their spend increases and so does the commission earned and loyalty fees and interest costs accrued by the card issuer.  Once the interest free period ends and the payment falls due, some customers (transactors) will pay their full balance outstanding and thus have a zero balance while others will pay the minimum due (revolve) and thus create a balance equal to 100% less the minimum repayment percentage of that spend. 

Over time, total spend increase in both customer groups but balances only increase among the group of customers that are revolving.  It is these longer-term balances on which capital costs accrue and which are ultimately at risk of being written-off.  In reality, the interaction between spend and risk is not this ‘clean’ but this captures the essence of the situation.

Profit = Revenue – Variable Costs – Bad Debt – Capital Holding Costs – Fixed Costs

= (AF x CH) + (T x ATV) x ((RR x PR x i) + CR) – (T x ATV) x (L + (CoC x IFP)) – (TL x U x BR) – (TL x U x CoC +   TL x   (1 – U) x BHR x CoC) – FC

= (T x ATV) x (CR – L – (CoC x IFP) -FR) – (TL x U x BR) – ((TL x U x CoC) + (TL x (1 – U) x BHR x CoC)) – FC

Where        AF = Annual Fee                                               CH = Number of Card Holders          

                      T = Number of Transactions                         i = Interest Rate

                      ATV = Average Transaction Value               TL = Total Limits

                      RR = Revolve Rate                                                U = Av. Utilisation

                      PR = Repayment Rate                                          BR = Bad Rate

                      CR = Commission Rate                                        CoC = Cost of Capital

                      L = Loyalty Programme Costs                          BHR = Basel Holding Rate

                      IFP = Interest Free Period Adjustment        FC = Fixed Costs

                      FR = Fraud Rate


Visualising the Credit Card Profit Model  

Like with the banking profit model, it is also possible to create a visual profit model.  This model communicates the links between key ratios and teams in a user-friendly manner but does so at the cost of lost accuracy.

The key marketing and originations ratios remain unchanged but the model starts to diverge from the banking one when spend and balances are considered in the account management and fraud management stages.   

The first new ratio is the ‘usage rate’ which is similar to a ‘utilisation rate’ except that it looks at monthly spend rather than at carried balances.  This is done to capture information for transactors who may have a zero balance – and thus a zero balance – at each month end but who may nonetheless have been restricted by their limit at some stage during the month.

The next new ratio is the ‘fraud rate’.  The structure and work of a fraud function is often similar in design to that of a debt management team with analytical, strategic and operational roles.  I have simplified it here to a simple ratio of fraud: good spend as this is the most important from a business point-of-view, however if you are interested in more detail about the fraud function you can read this article or search in this category for others.

The third new ratio is the ‘commission rate’.  The commission rate earned by an issuer will vary by each merchant type and, even within merchant types, in many cases on a case-by-case basis depending on the relative power of each merchant.  Certain card brands will also attract different commission rates; usually coinciding with their various strategies.  So American Express and Diners Club who aim to attract wealthier transactors will charge higher commission rates to compensate for their lower revolve rates while Visa and MasterCard will charge lower rates but appeal to a broader target market more likely to revolve.

The final new ratio is the revolve rate which I have mentioned above.  This refers to the percentage of customers who pay the minimum balance – or less than their full balance – every month.  On these customers an issuer can earn both commission and interest but must also carry higher risk.  The ideal revolve rate will vary by market and depending on the issuers business objectives but should be higher when the issuer is aiming to build balances and lower when the issuer is looking to reduce risk.


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One of the business world’s most repeated truisms is that you get what you measure.  So it stands to reason that, if the goal of an organisation is to maximise profit, a unit’s contribution to that profit maximising effort should be the primary measure against which it is evaluated. 

Instead, it is common to find a wide range of diverse measures being used to evaluate and direct teams.  These measures are usually assigned using a traditional top-down budgeting approach.  The CEO might start the budgeting process by aiming to deliver a specific return on equity to shareholders.  Then, together with the other directors, she might identify a number of strategies that they believe will deliver that return.  Those strategies are then broken down into goals to be achieved by each of the business units that make up the organisation.  For example, the marketing team’s goal might be to generate new loan applications.  Similarly, the product team’s goal might be to increase the average revenue-per-account.  These goals are converted into specific measures and success is defined by the team’s ability to meet and exceed those measures.

This approach seems logical but it has several important weaknesses.  In this case, the marketing team might offer loans to potential customers at a reduced interest rate in order to increase demand.  As logical – and rewarding – a move as this might be from their point-of-view, it would also be in direct conflict with the product team’s goal of increasing the average revenue-per-account.  Alternatively, a change in the prevailing market conditions might reverse the need for market share growth.

Profit Model Analytics offers a solution by improving goal alignment in two ways: it co-ordinates the activities of disparate teams with each other and with their environments.

Firstly, consider the interaction between teams.  Individual profit levers seldom reinforce one another.  In fact, the improvement of one profit lever is often only possible at the detriment of another.  So, when teams are given goals based on individual profit levers, conflict is the norm.  For as long as the full impact of a strategy is divided across two or more teams some of those teams will remain overly conservative and the others overly aggressive.

However, the profit model looks beyond a team’s narrow area of interest and considers the impact that a strategy will have on the broader organisation.  It elevates the interaction of profit levers, or the profit model, above the performance of any individual profit lever.  Thus, it forces teams to share goals and co-ordinate their activities across reporting structures.

In the scenario above, the marketing team would now be incentivised to follow a different and more profitable strategy than simply increasing the number of new applications received.  A profit model would show that the number of applications a bank receives is a cost driver, not a revenue driver.  In fact, revenue is only derived from loans that are turned into good customers and this is a factor of the bank’s approval rate, the rate at which customers’ take-up approved loans, the customers’ attrition rate and the inherent risk of the target market.  In order to maximise profit therefore, the marketing team might decide to concentrate its efforts on appealing to a lower risk population whose members are more likely to be approved for loans or on encouraging customers who have been approved to take-up their loans.  Neither of these strategies would have a negative impact on the other teams.  In fact, if the marketing team chose to focus its efforts on reducing the rate at which customers left the bank, both the marketing team and the product team could benefit.

Secondly, consider the interaction between a team and its changing environment.  Goals set using the top-down process usually change in gradual steps – coming into being after one summit meeting and remaining in force until the next such meeting.  The environment, however, is more dynamic.  This can lead to confusion and conflict as team goals diverge from – and are emphasised at the expense of – organisational goals.  Fortunately the single, widely-held goal of profit optimisation not only reduces inter-team conflict, it also increases goal consistency and goal relevance over time. 

When times are good, the marketing team might be encouraged to increase market share by targeting slightly riskier populations.  However, risky growth becomes unprofitable as soon as the market experiences a downturn.  It is easy to see how a conflict between the interests of the team and the interests of the organisation could have arisen if they were measured against a static goal based on the growth in the number of new accounts while the environment changed around them.  Profit, on the other hand, is a fluid goal.  In this case, as soon changes in the environment make a conservative strategy more profitable, the marketing team could adapt quickly by, for example, abandoning their initial growth goal in favour of a risk-minimisation goal.  Although the goal remains the same – to maximise profit – the optimal means of achieving it will vary just as surely as a mountaineer attempting to summit Everest might need to adjust their route to compensate for changes in the prevailing weather conditions.

One simple way to visualise the profit model is as a pyramid.  Each layer of the profit model pyramid expresses the layer above it in finer detail.  So, on top of the pyramid is profit which is the result of all the activities of an organisation.  Profit can, most simply, be broken into revenue, variable costs and fixed costs and so the next layer down is made-up by these major profit levers.  Each of these profit levers is, in turn, made-up of more detailed profit levers and so on.



Regardless of the budgeting process employed, each team is likely to be given one overriding goal.  The success of each team is then measured by their ability to meet a pre-set target that is represented by a measurable metric that resides somewhere in the pyramid.  The further down the pyramid that a measurable metric resides, the more likely a goal based on it is to be counter productive across teams and to become variable over time.

Returning to the example of the marketing team, they might be measured on the number of new applications (level three), the number of active accounts (level two) or profit (level one).  A marketing team with the ‘level three’ goal of increasing the number of new applications will be in continual conflict with a risk team measured on the opposite and competing ‘level three’ goal of minimising the number of accounts in default.  There will be less conflict if both teams are measured on ‘level two’ goals – such as number of active and up-to-date accounts and accounts in default as a percentage of all account balances – but the conflict will only be resolved entirely when both teams are measured according to the ‘level one’ goal of profit.  The unified goal of profit optimisation will alter the relationship between these two teams from adversarial to cooperative.

Making profit the unifying goal of all teams does not mean that all teams are evaluated on the overall performance of an organisation, however.  The usual rules about effective goal setting still apply and such a broad-stroke approach would make it difficult for team members to identify the link between their efforts and the fruits thereof.  Rather, it means that each team should be evaluated on its ability to maximise profit by implementing projects that positively impact those parts of the profit model over which they exert some control.

To do this, the organisation must follow a simple three step process.  The first step is to reach agreement on the make-up of its profit model.  Teams should agree on which profit levers to include in the profit model as well as the way in which those levers interact.  The second step is to identify which teams impact which profit levers.  Most teams will have a primary impact for a small number of profit levers and a secondary impact on a few more.  (Note: A profit lever with no identified ‘owner’ points towards a weakness in organisational structure, as does a profit lever with too many owners)  The third step, once the breadth of a team’s potential impact has been established, is to ensure that every project implemented by a team includes processes to monitor and aggregate the performance of all of the profit levers under its influence.

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An earlier article in this category constructed the profit model as an equation.  However, in certain circumstances, it is also possible to use a diagram to achieve the same goal.    

A diagrammatic profit model is a useful communications tool when the intended audience is non-technical and may feel uneasy with equations.  On the down side, although a diagram can highlight the interactions between profit models it can’t easily show the size of each interaction.  This means that it doesn’t facilitate accurate calculations in the same way that an equation would.    

In practice, therefore, the two formats compliment each other.  As a piece of analysis progresses though its life-cycle, the dominant format of the profit model will change.  

Usually, an analyst’s first step would be to draw a draft profit model in diagrammatic form.  This helps the analyst to identify the key profit levers and the interactions between them.  In this format it is easy to manipulate the profit levers and to understand their relationships.  

The next step would be to translate that draft model into a series of equations and to populate those equations with actual data from the business.  These equations will be calculated and the results interpreted in order to determine the optimal strategy for the situation in question.    

Once the analyst is sure of their answer, they will need to communicate their findings and the logic behind them to a broader audience.  At this stage, the equations will be put back into a diagram.  This should contain enough information for the majority of the audience members.  In cases where more detail is required, the analysts would answer those questions by referring back to the equations.   


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Credit risk analytics is a technical discipline and the temptation to recruit analysts purely on the strength of their technical expertise is often overwhelming.  However, ‘accurate analytics’ is not always the same as ‘value-creating analytics’.   Accurate analysis must be combined with sound business strategies before real value is created.  So, if your’s is an organisations wanting to implement the next generation of value-creating analytical techniques – profit model analytics, test-and-learn analytics, etc. – it is important to hire analysts that posses technical skills as well as a deep understanding of the business environment. 


The best way to identify candidates with this mix of abilities is to make case studies an integral part of the recruiting process – particularly case studies based on the profit model.  Case studies should form part of a larger three-pronged recruitment strategy which should determine the candidate’s compatibility with the organisation’s culture, the candidate’s technical ability and the candidate’s business understanding. 


The first two prongs of the strategy are achieved using traditional recruitment techniques.  Each organisation’s culture is different and so those parts of the recruitment strategy designed to test for cultural compatibility will vary from organisation to organisation.  Usually though, competency based interviews and one-on-one discussions with existing team members will suffice.  The candidate’s technical abilities can be determined by a thorough analysis of their resume and, potentially, a series of mathematical tests.  These steps are vital and case studies should be a compliment to them, not a replacement.


Profit model case studies, then, are designed to test the candidate’s ability to apply analytical techniques and business insights to solve a problem.  Because technical competency is proven separately, the design of these case studies should emphasise the logic of the profit model above mathematical complexity.  The standard profit model case study follows a simple template.  The case will always start with a brief introduction to a business scenario which, to put candidates at ease and to emphasise the fact that the case is not testing for pre-existing banking knowledge, should ideally not be banking related.  Some common scenarios include selling second-hand golf balls, operating a passenger ferry and delivering pizzas.


The first questions should be kept general and should test a candidate’s breadth of thinking and their ability to work with ambiguous and/ or limited information.  A candidate must be able to identify key profit levers in the business and come up with logical ways to measure and manage those profit levers.  The candidate should also be able to estimate reasonable values for one or two of these measures in an environment of limited information.


Consider a case that deals with a business selling second-hand golf balls.  The candidate would be asked to identify those ratios which they would measure to determine the desirability of such a business.  What they are actually being asked to do is to identify the key profit levers in the business – number of balls, price of balls, cost of retrievals, etc.   Once they have identified these profit levers, the candidate should suggest a logical way to estimate, for example, the number of golf balls in a particular water hazard – a function of the age of the course, the number of players, the likelihood of hitting a ball in that hazard, etc.  At this stage it is common for a strong candidate to already be showing signs of a logical thought-process.  However, it is the numerical questions that follow that most clearly differentiate candidates. 


These questions test for two critical abilities: the ability to construct an equation and the ability to manipulate an equation.  An equation is a numerical representation of a logical thought.  In this case, the equation being constructed is a profit model.  Candidates should be provided with the values for key profit levers which they should then use to determine the current level of profitability for the pertinent business. 


Continuing the example, a candidate could be asked to calculate the profitability of the second-hand golf ball business assuming there are 5 000 balls in a particular dam on the local golf course which can be sold for a dollar each but, in order to be allowed to retrieve the balls, there is an obligation to pay a royalty to the club of 5% of total sales and to pay a diver a fixed cost of five hundred dollars per retrieval.


There are two approaches a candidate can take to solve this problem.  The first approach is to construct an equation.  In this case profit is equal to revenue (sales price multiplied by the number of balls sold) minus variable costs (the cost of the royalty) and fixed costs (the cost of the dive).  Populating and solving this equation quickly reveals the answer.  The second approach – reminiscent of accounting formats – is to calculate each component separately before combining them at the end.  There is nothing expressly wrong with this approach and most candidates will still get the correct answer.  However, candidates who think and work in equations will almost always do much better in the more difficult questions that follow.


The second set of numerical questions should oblige the manipulation of equations.  These questions provide the most insight into a candidate’s ability to visualise a business problem in terms of a dynamic numerical relationship between various profit levers – i.e. to visualise a profit model.  In these questions one of the factors in the original equation should be adjusted and the candidate asked to calculate the implications of that change.  A candidate might, for example, be told that the royalty is set to increase and be asked to calculate the maximum level this royalty could reach before the business made a loss or they might be told that prices are dropping and be similarly asked to calculate the break-even selling price.  By seeing business problems as a series of dynamic numerical relationships which can be represented and analysed using equations, strong candidates prove themselves comfortable with the concept of profit levers and profit models even though they may be unfamiliar with those specific terms.

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The goal of every business is to make a profit and so, by extension, the goal of every strategy should be to move that business towards optimal profitability.  To this end, all strategists should first identify those actions which a business undertakes in its day-to-day operations that enable to it make a profit.  These actions are called profit levers.  As with mechanical levers, an adjustment made to a profit lever will result in a change in profit.  

Although it is possible for profit levers to reinforce one another, it is more common for them to compete.  One can therefore not optimise total profit by optimising each profit lever in isolation.  To do so, one must take into account the nature of interactions between profit levers.  A lending business is no different.  One can not evaluate the risk of a loan portfolio without taking into account the interest rate charged; one can not adjust the bad-debt collection strategies without considering the impact they have on customer service strategies and one can not build a new scorecard without knowing the cost of business it will turn away.  


The relationships between each of a business’ individual profit levers can be mathematically – or graphically – represented in a profit model.  The profit model for almost any business can be started as a function of sales revenue less all variable and fixed costs.  A bank is simply another form of business – one that makes its profit by borrowing a large lump sum of money at a low rate of interest, breaking it into multiple smaller sums and lending those sums on to its customers at a higher rate of interest.  So, although terminology might change when one considers a banking example, the concepts remain identical.    


A bank typically earns revenue from fees and interest on outstanding balances, pays variable costs that include the cost of holding capital and the cost of bad debt as well as the various fixed costs associated with the provision of banking services.  The same simplified profit model can therefore be expresses for a bank as a function of total fee and interest revenue less bad debt write-offs, capital holding costs and the fixed costs associated with operations.  


Profit = Revenue – Bad Debt – Capital Holding Costs – Fixed Costs  


Terms such as ‘revenue’ and ‘bad debt’ are too nebulous to direct specific actions and so further deconstruction is required.  Revenue is a function of total outstanding loan balances, the ratio of customers repaying their loans to those in default and the interest rate charged.  In a similar way, it is possible to further simplify the total outstanding loan balances as a relationship between total loan balances offered to customers and the average rate at which those available balances are actually utilised by customers.  


Revenue = (Loan Balances Offered x Utilisation Rate) x Repayment Rate x Interest Rate  


Repeating this process for each of the other factors brings us to a point where we have a basic profit model for a bank – or at least for its lending operations.  


Profit = (L*U*(1-BR))*i – (L*U*BR) – (L*U*CoC + L*(1 – U)*BHR*CoC) – FC  


Where: L          = Loan Balances Offered            U          = Utilisation Rate  

            BR        = Bad Rate                                i           = Interest Rate  

            CoC      = Cost of Capital                        BHR     = Basel Holding Rate  

            FC        = Fixed Costs  


This profit model is, however, not yet complete.  We can see the directional impact that an increase in loan balances will have on each profit lever – an increase in revenue, bad debt write-offs and capital holding costs – but not by how much each factor will increase; let alone their combined impact.  This framework must still be customised from three sources – financial information, an analysis of existing data and test-and-learn analytics.  


Financial data is usually readily available and easy to access.  In this example, it should be possible to quickly determine the interest rate charged by the bank and the interest rate it pays its funders.  With a little more effort – and a reliable data warehouse – it should also be possible to analyse the bank’s historical data and calculate from that the total loan balances offered, the average utilisation rate and the average bad rate for this product.  So, even without sophisticated analytical capabilities, an organisation should be able to populate an ‘as-is’ view of the profit model template for each of its major products.    


Returning to our example, it should be easy enough to find the figures needed to determine that the product in question is generating nearly three million Euro in profit  


Assuming:                    L          = €100,000,000                         U          = 75%  

                                    BR        = 2%                                       i           = 17%  

                                    CoC      = 10%                                       BHR     = 20%  

                                    FC        = €300,000  


Profit = (100,000,000*75%*98%*17%) – (100,000,000*75%*2%) -(100,000,000*75%) *10%) – (100,000,000*25%*20%*10.5%) – 300,000 = 2,695,000  


Knowing the ‘as-is’ view is important to a business but not as important as having a tool to evaluate and compare the outcome of potential future actions.  This simple model can be used to determine the impact that a new strategy will have on profitability but only if we assume that all the other factors remain unchanged.  For example, increasing the interest rate by a percentage point will increase in profit by three-quarters of a million Euro.    


Although this assumption (ceteris paribus) is common in economics, it does not present a true reflection of reality.  We know that an increase in interest rates is likely to have a consequential impact on, among others, the utilisation rate and the risk of the portfolio.  Thus, using the profit model becomes more complex when the impact of a change is considered.  


What is likely to happen if a bank offers all its customers a 10% increase in available balance?  This is not a question that can be answered without an understanding of how the model performs in a changing environment.  The performance of the model in a changing environment is known as ‘marginal performance’ and can only be calculated using a forward-looking analytical technique.  Test-and-learn analytics is a technique that gathers real-time marginal performance data in a series of small and controlled experiments.  The results of these experiments can then be used to populate the profit model which can, in turn, be used to extrapolate the likely impact the new strategy will have when rolled-out on a large-scale.    


In our example it was easy to use historical data to calculate that, on average, seventy-five percent of the available loan balance is utilised. But this fact does not necessarily extend to say that seventy-five percent of any increased balance will also be utilised.  In fact, it is likely that the marginal utilisation will be significantly lower than that.  A test must therefore be constructed to determine, in a controlled environment, the marginal utilisation rate.    


A test of this sort would start with the random selection of group of customers to be tested.  Some of these customers will be contacted and reminded of their existing available balances while the others will be contacted and offered a further 10% in available balances.  By monitoring the relative performance of these two groups it would be possible to calculate both the marginal utilisation (what portion of the new balance was taken up) and marginal risk (what portion of the new balances ended in default).  The only ‘new’ cost in this scenario would be those costs directly linked to the campaign.  


Profit = (L*MU*(1-MBR))*i – (L*MU*MBR) – (L*MU*CoC + L*(1 – MU)*BHR*CoC) – FC  



L          = Loan Balances Offered            = €10,000,000  

MU       = Marginal Utilisation Rate          = 30%  

MBR     = Marginal Bad Rate                  = 35%  

FC        = Fixed Costs                            = €15,000  


Returning to the profit model it is now possible to calculate that this strategy, because it leads to a lower marginal utilisation and a higher marginal risk, actually leads to a decrease in overall profitability.  In this format a profit model becomes a truly useful tool.  

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The goal of every business is to make a profit and so, by extension, the goal of every strategy should be to move that business towards optimal profitability.  To this end, all strategists should first identify those actions which a business undertakes in its day-to-day operations that enable to it make a profit.  These actions are called profit levers.  As with mechanical levers, an adjustment made to a profit lever will result in a change in profit.  Profit levers are not limited to the sales process, however.  Profit is the difference between the money that comes into a business and the money that goes out of it and so, while some profit levers affect the ‘money in’ side of the business, others affect the ‘money out’ side and every business is an amalgamation of several such profit levers.


Although it is possible for profit levers to reinforce one another, it is more common for them to compete.  One can therefore not optimise total profit by optimising each profit lever in isolation.  To do so, one must take into account the nature of interactions between profit levers.  A discount that increases sales volumes does so at a cost to gross margin and a new target market that is more responsive to an offer may also be more risky.  In each case, maximum profit is achieved only when the correct balance for each profit lever is found.


The relationships between each of a business’ profit levers can be mathematically – or visually – represented in a profit model.  The first step in building a profit model is to deconstruct a business into its most basic profit components.  The profit model for almost any business can be begun as a function of sales revenue less all variable and fixed costs. 


Profit = Revenue – Variable Costs – Fixed Costs


The simplicity of this equation is what makes it broadly applicable but it is also what limits its usefulness.  To be useful, each of these components must first be further broken down into their more detailed constituent parts.  For example, it is clear from the equation that an increase in revenue will lead to an increase in profit.  However, ‘an increase in revenue’ is too nebulous a term to inform a specific course of action.  The ‘revenue’ component must therefore be broken further into its component parts.  In this case, revenue is equal to the number of units sold multiplied by the selling price of each unit, so revenue can be affected by adjusting one of these profit levers – by changing the selling price, etc.  The other components must also be broken down until each fragment of the equation is a fully formed profit lever.


Profit = No. Units Sold (Sales Price) – No. Units Sold (Cost per Unit) – Fixed Costs


At this stage though, the profit model is only a template that shows the directional impact that an adjustment to one profit lever might have but not the size of that impact. Without knowing the size of any one impact, it is also not possible to know the likely combined impact of those adjustments.  For example, by adding a new feature to its product – and therefore increasing the cost per unit – a company might be able to increase the number of units it sells.  The profit model shows us that an increase in the number of units sold will lead to an increase in revenue but it also shows us that an increase in the cost per unit will lead to an increase in variable costs.  What the model can’t do, therefore, is tell us if that increase in revenue will be sufficient to cover the increase in costs.  Before it can do this, the model needs to be populated with organisation-specific information.


Customising a profit model is a two stage process. The first stage is used to describe the organisation’s current situation and the second stage to describe the likely impact of a new strategy.  Describing the current situation should be a relatively simple process as most of the data needed is usually readily available from historical databases and published financial reports.  A good understanding of the status quo is important but profit models are most valuable when they are used as forward-looking tools.  For example, it is good to know the current profitability of a business but it is so much more valuable to be able to estimate how that profitability will be changed by a new strategy that, for example, discounts the selling price of goods or one that increases fixed production costs but lowers unit costs. 


Building such a forward-looking profit model requires an understanding of two important concepts – marginal performance and test-and-learn analytics.  It is important to differentiate between performance on average and performance at the margin or, in other words, to differentiate between performance in a stable environment and performance in that same environment once a change has occurred.  Because new strategies always change the existing environment, their success is determined by marginal performance.  A company that sells one thousand items at one price might sell two thousand if it drops it price by fifty percent; or it might still just sell one thousand.  Before it launches a campaign to offer discounted prices it vital to know which of these new environments is most likely.


Historical data sources only show average performance.  To correctly account for marginal performance, therefore, it is imperative to have access to forward-looking analytical tools that can calculate the change a strategy will have on its environment.  It is clearly not possible to know the future impact of a strategy before it is implemented so test-and-learn analytics is not, strictly speaking, a forward-looking technique.  Rather, it is a technique that gathers real-time marginal performance data in a series of small and controlled experiments.  The results of these experiments are used to populate the profit model which can then be used to extrapolate the likely impact of the strategy where it to be rolled-out on a large scale.  Rather than offering a fifty percent discount on all items, for example, the firm could randomly offer a few different discount rates to small groups of customers, measure the marginal performance of each of the groups, populate the profit model accordingly, identify the most profitable strategy and then offer that discount rate when the campaign is officially launched.  All major decisions can therefore be made using profit models populated with real marginal data.



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