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The previous post discussed setting of scorecard cut-off by the criterion of marginal profit, which translates to marginal PD. But what about average profitability (or average PD) as a measure for a portfolio or as a criterion for arriving at a cut-off?
The general issue of marginal vs average cost, revenue & profitability is a familiar one in business economics and won’t be revisited here.
However, the particular feature of the debate that is relevant to setting a scorecard cut-off is the set of assumptions made about the TTD (through-the-door) population.
A cut-off is by its nature a marginal issue. If the cut-off is at (say) odds of 15:1 then we know that the only accepts will be those with PD of 1/16 or better. But what will the average PD of all the accepts be? That will depend on the distribution of the TTD – proportionately how many applicants there are in each risk band. Obviously the average PD of the accepts will be better than 1/16, but how much better will depend on a calculation based on the shape of the TTD distribution. A typical assumption is that future TTD will be like past TTD for similar products, but this assumption can sometimes turn out to be quite wrong. The drivers of TTD are a complex mix of marketing, the competitiveness of the product, actions taken by competitors, and the economic climate. In plain English, you might have an excellent scorecard, but if lousy applicants walk through the door, it will be hard to do good business.
Nevertheless, it is natural for the business to ask questions about average profitability (equivalently, average PD) because that characterises the overall returns on the portfolio. Also note that besides the shape of the TTD distribution, a big parameter assumption is the volume of TTD. Volumes are important for diluting the ‘fixed cost’ aspects of the business costings.
So the business will probably want to target a certain average PD. The cut-off decision, though, is strictly a marginal one, which has only an indirect effect on the average, mediated by the TTD assumptions. Modellers should communicate these levels of uncertainty to the business as it is all too easy for a computer printout to look infallible.
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.