Posts Tagged ‘risk profitability models’

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.

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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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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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