Odds provide a useful frame for considering that important business question: where to set the score cut-off.
The basic business logic is to set the cut-off at the score where marginal profitability equals zero – i.e. if you moved the cut-off any lower you would be losing money on each additional applicant so approved, whereas if you set the cut-off higher you would be leaving money on the table. Easy to say, but not so easy to do, because the concept of marginal costs is a movable feast depending on accounting treatments and assumptions about fixed and variable costs, as well as the context within the current business strategy.
But anyway, the odds allow one to frame the question in an easy-to-grasp way: how many goods does it take to offset one bad? If the answer is 15, it means that your tipping point is at 15:1 odds, which can be converted to the score as per previous post. This would then be the cut-off. This post assumes a simple automatic accept/decline score, ignoring ‘refer’ bands and contested decisions and overrides etc.
To arrive at “15″ would involve a full revenue/cost modelling through the product cycle (lifetime customer value?), for 15 goods versus 1 bad. Naturally the “cost” that dominates here is the credit loss of principal (LGD) for the default.
Don’t pay any attention to the example value “15″ used above – it’s going to make a lot of difference what product is involved, secured vs unsecured, limits, etc.
3 comments
2 May, 2008 at 10:18 am
Andrew
Clive,
It also does not allow for risk-based pricing. It has always interested me on how you set the bands and cut-off when you are pricing for risk. Perhaps you can over that at some stage?
2 May, 2008 at 10:33 pm
Clive
Some suggestions offerred on no great authority:
The revenue/cost model would have a parameter input for the interest rate charged: as one cranks this parameter upwards (e.g. 12%-14%-16%) the model naturally reports better and better profits on the good accounts (but by the same token becomes a less attractive proposition in the market). For this illustration let’s say just 3 interest rates offerings are envisaged (12%, 14%, 16%).
Start with the parameters for premium customers i.e. the best interest rate the product can offer (12%). Figure the break-even on this basis, which will require fairly good odds (say, 32:1) because the profit per good customer is at the low end and so one needs more goods (at least 32) to offset one bad. Whatever score 32:1 translates to (say, a score of 600) is then the cut-off for the best rate (12%), and any customer whose score is over 600 is offered 12% and hopefully this is also a good marketing proposition for them.
Those who fall not far below 600 would be a loss on average @12%, but running the model with the assumption of 14% interest would naturally boost the revenue side and require fewer goods (say, only 16), to offset the one bad. This means that down to 16:1 (score=580) you can still do profitable business @14%. So, in the intermediate score band 580-600 you could offer 14% but not 12%. Whether this is a good proposition in the market depends on the customer’s options. If another bank’s scorecard puts them in the premier band, they’ll place their business there. If all scorecards worked equally well, the customer should find themselves generally rejected or offerred less than premier rates, so your offering would then be competitive to that customer.
Continuing likewise, your profit model predicts that @16% interest, you are making so much surplus from the goods that it takes only 8 of them to offset one bad. 8:1 odds means a score of 560, so applicants scoring in the range 560-580 could be offered 16% and be expected to be profitable business on average. Naturally down here the pricing signals are strong and the bank would need to feel confident of the assumptions and models being used in extending credit to applicants who presumably are marginal prospects.
As before, all the figures quoted are fictional, but hopefully the concept makes sense. The scores are based on 5001:1 and PDO=20.
A subtle point is the value of a good scorecard. A scorecard that discriminates well should enable the bank to price accurately and competitively in the market and thereby to gain share, and profitably so. An institution with a weak scorecard should find themselves struggling in all three tiers (if they followed a similar plan). This segues to the more complicated consideration of the actions and behaviours of one’s competitors.
Hope these comments are helpful and generate some contributions from those with more experience on these points.
5 May, 2008 at 12:22 am
Marginal vs Average profitability and TTD « ozrisk.net
[...] II, Credit Risk, Default Analytics by Clive Tags: average, cut-off, marginal, scorecard, TTD The previous post discussed setting of scorecard cut-off by the criterion of marginal profit, which translates to [...]