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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.