Diversification of Online Lending portfolios is an important consideration in order to minimize risk of defaults and improve returns. Both LendingClub and Prosper discuss diversification on their websites. They both clearly state that diversification is a key component to a successful Online Lending investment strategy. Prosper states that investors with at least 150 notes have over a 97% chance of making a 7%+ return. LendingClub states that 99%+ of investors with at least 100 notes have experienced a positive return. We think it’s great that both of the originators are open and upfront with investors about this fact; otherwise those without much knowledge of lending or consumer credit could make some bad investment decisions.

We wanted to understand how portfolios differ based on the number of notes they include, so we simulated the default rate distribution for a portfolio of **Prosper** notes from the 2012 vintage, assuming the same investment amount per note and that all notes were originated on the same day (this is done to simplify the analysis). We used our early default rate definition, which defines any note that missed at least 1 payment as “bad”. We do this because the notes are not fully seasoned, so this takes into consideration early default behavior, which is a high indication of later charge offs.

The objective of the analysis is to understand how the variability of the expected default rate changes as the number of notes in the portfolio increases. For instance, a portfolio of just one note will either have a 0% or 100% default rate; a portfolio of two notes will either have a 0%, 50% or 100% default rate, and so on. In order to do this, we randomly constructed 10,000 portfolios made up of 5, 10, 25, 50, 100, 150, 200, 300, 500, 750 and 1000 notes using the technique of Monte Carlo simulation.

When such a large number of simulations are run, the average default rate for each population will converge to the overall mean (for this population it is ~12.9%), but what changes is the variability. In other words, the average default rate might be 12.9% for a portfolio with 5 notes, but the likelihood that any given portfolio actually has that rate is quite low. By increasing the number of notes in a portfolio, the investor decreases the variability – making a predictable default rate (and return) more likely.

**Simulated Portfolios in Detail**

The below graph shows the change in default rate distribution and variability (std dev) for each portfolio simulation. The average is always around 12.9%, but in the portfolios with fewer notes, the standard deviation is quite high. This can also be observed by looking at the extreme values (max and min). As the number of loans increases, the standard deviation and maximum default rate decrease.

From our analysis, the minimum number of notes that an investor should hold in a portfolio is around 200 (which aligns with the general “consensus” from other articles that have been written). At this portfolio size, the variability is low enough to ensure a positive return assuming an average interest rate of around 20%. Anything below 200 makes the predictability of the default rate less certain. Additionally, there is clear benefit from further diversification, as the standard deviation continues to decline.

For more details on the analysis, see the below default rate distributions, generated for each portfolio simulation set, showing how the distribution tightens around the mean as the number of notes increases.

In Conclusion

Many factors affect the return of any given portfolio – especially the credit grade distribution (and, therefore, the interest rates), as well as the filter/model/strategy used to select investments. However, an easy factor to control is the number of notes in the portfolio. Based on our analysis, if an investor cannot invest in at least 200 notes, the resulting portfolio may be too volatile to be predictable, and the likelihood of a very low (or negative) return becomes higher.