Rethinking Historical Default Rates When Applied to Small Value P2P Loan Portfolios

Historical default rates can be difficult to apply to small value P2P loan portfolios.  The first thing to remember is that, much like stock market returns, historical default rates do not necessarily predict future default rates.  The next major problem with analyzing risk in small P2P loan portfolios is that a small number of loans does not meet the threshold for statistical significance.  In other words, if you have one loan with a historical default rate of 5%, you can’t directly apply that rate to your loan.  A 5% historical default rate might lead you to expect 5 out of 100 such loans to default, but what whole number is 5% of 1?  If you estimate high, 5% of 1 is 1 meaning that your loan will be expected to default.  If you estimate low, 5% of 1 is 0 meaning that your loan will not be expected to default.  Realistically, a 5% historical default rate means that you might expect a 5% probability of default.  Practically, a small number of loans means that you have a 5% probability of total (or significant) loss.

A conservative approach (perhaps too conservative) is to round default rates upwards to your loan value to portfolio value percentage.  If you had 10 loans for example, then each loan would be worth 10% of your portfolio, assuming that they were all for the same amount.  If your loans had a historical default rate of 5%, you would round that up to 10%.  So you would assume that 1 loan would default in the first year, one in the second, and one in the third.  The method becomes more accurate as you have more and more loans, since the error from rounding goes down.  With 100 loans, you would assume 5 loans default the first year(5% of 100), 5 default the second year (5% of the 95 loans left, rounded up) and 5 default the third year (5% of the 90 loans left, rounded up).

This method tends to favor riskier loans, which have higher historical default rates because there will be more rounding error for low risk loans in small portfolios.  Assume you wanted to choose between 5 loans with a 1% default rate and 5 loans with a 5% default rate.  Since each rate would be rounded up to 20% (1/5 loans), the low risk loans get skewed further than the higher risk loans.  It’s not until you have enough loans that your loan value to portfolio value is between the default rates of the two options that accuracy returns.  Typically by that point you have a sufficient number of loans that statistical significance returns as well and the higher returns of the higher risk loans tend to win out again.  So for small and large portfolios, riskier loans seem to be the best option predicted by this method.

My basic conclusion from this analysis is that the risk of having a small value P2P loan portfolio makes the differences in historical default rates seem less discriminate.  With similar risk, the highest possible return is desired so loans paying the highest interest rate should be chosen.  Larger value portfolios are able to compensate the higher risk of default with diversification in many loans with higher interest rate returns.  Depending on the interest rates and assumed default rates, this too often makes higher risk loans the most profitable.

To make more sense out of how historical default rates might affect loan performance, I ran a monte carlo analysis on a select set of hypothetical loans.  The results are shown in P2P Lending Default Considerations (Part 2).