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The Grameen Bank has (rightly I think) been recognized for promoting bottom-up development in poor countries. One thing they do is make small microloans available to entrepreneurs without collateral (thus, traditional lenders would typically not lend to them, either due to lack of collateral, or the risk of their business and the cost of administering small loans). They have been lauded for getting repayment rates of well over 95%, and have reported some as high as 99%. Let’s take these data to be completely accurate.

If you are a bank, would achieving a 100% loan repayment rate be desirable? In unicorn world it would be. In other words, if it was costless to monitor and administer loans, then a bank sure would have an interest in getting every single dollar it lent out back. But in a world where it is costly to monitor loan performance and it is costly to collect on delinquent loans, the optimal rate of repayment is less than 100%. How much less? Well, that depends on the marginal benefits of efforts to collect another $1 of delinquent loans and the marginal costs of doing so. The costs are straightforward – they are the computing, secretarial, collection agency and other resources used to go after debtors. But what are the benefits? There are actually two, not one. The obvious benefit is to getting a $1 of loan money back. The second benefit is a prevention mechanism – by the bank going after delinquent customers today, it may reduce the chances of loans going delinquent in the future (via a variety of mechanisms). Just how large a deterrent effect is needed will vary by country, by customer, by loan and over time. Taken together, you will see that it is often rational for firms to expend a lot more than a $1 worth of resources today to collect the next dollar of delinquent loans. But that too also should remind you that they will stop collecting loans well before the last dollar of unpaid loans has come back to them.

So just pointing to high repayment rates does not tell a complete story of how well a bank is running its business. After all, if you make extremely risky loans, you may have low repayment rates and still be more profitable than a bank making safer loans with a high repayment rate. An interesting question is to ask what does an optimal equilibrium distribution of repayment rates by risk look like? I suspect it is neither linear nor uniform, but a little math probably could yield an answer. Any takers?

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