This is a story about charge-off rates. What are they and how does a lender decide whether to charge-off a loan?
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What is a charge-off?
A charge-off occurs when a lender writes off the loan usually based on a lengthy default.
Hypothesis: One might expect that the charge off rate is negatively correlated with average income, at least when controlling for loan amount and/or grade.
Surprisingly, this is NOT true
This shows that charge-offs occur more frequently for recipients with larger average income, within individual grades. Lenders use grades to rate a loan recipient on their likelihood to default. Additionally, charge-offs occur more frequently for recipients with larger average income even when holding loan amount constant. Loan amounts were grouped in bins of $5,000
This tends to answer the question in general, namely that charge off rates are positively correlated with average income. Nevertheless, it begs the question of whether this is true of simply a summary statistic (e.g. average annual income) or if it is generally true of the entire distribution.
For instance, it is possible the charge-off averages are pulled upward by outliers. It would be helpful to remove some of the binning, so that we get a more complete picture.
Because we are still taking an average income, the data is still grouped (or binned), albeit to a lesser degree. The size of the circle represents the number of records (i.e. loan recipients) that that data point encompasses.
This chart shows that there is a positively correlated band of (blue) non-charged off loans. The average annual income of these loan holders increase fairly linearly, grouping by loan amount. There is also a very small amount of variance within this set of loan holders, which tends to indicate that loan holders who do not get charged off do not recieve loans outside their abilities to pay it back given their annual income. Alternatively, loan holders that do get their loans charged off have greater variance in regard to their annual income.
Conclusion: The data militates against our original hypothesis. Although charged off loans tend to be simply more variant than their ostensibly more risk-averse counterparts, on average, they also have higher incomes. It should be noted that there can be multiple explanations for this, including the possibility that creditors tend to charge off loans of greater amount, which is positively correlated with income.