Diversification and Risks of Loss: the Important Numbers

Warning: This article is for informational purposes only. Back-tested results are NEVER a guarantee of future performance. Underwriting on the various Peer Lending platforms can change over time, which may cause the performance profiles of the platforms to change.

In January of 2014, we did an analysis about how many loans one needed in a portfolio to be fairly confident of earning a positive return. It is time for an update, along with a small tweak to the original methodology. Again, we investigate loans from Lending Club, but the same principle could easily apply to Prosper or Funding Circle.

We conduct our analysis on loans that reached maturity and have a completed status. Of over 1 millions loans issued by Lending Club, 103,685 loans meet our filtering criteria and are included in this analysis. This is almost six times as many loans used for analysis compared to our predecessor article.

Similar to before, we use Return on Investment as our measuring stick. This means that we only care about initial amounts funded and total amounts paid out by loans with no regard to length of investment.

To make the analysis more applicable to investing in Peer Lending, we take the following approach:

1) We standardize loans to be of the same dollar amount Most investors will have (near) similar amounts invested in each of their notes for diversification purposes. We emulate this by adjusting the loan amounts of originated loans to be equal. In turn, we also adjust the total payments received by the loan to match the standardized loan size. This removes the effect of, for instance, the return of a \$40,000 loan having four times the weight of a loan that was only for \$10,000.

2) We net out relevant fees (1% of each monthly payment for Lending Club fees) Fees are real and have a noticeable effect on returns, especially when compounding over several years. They must be accounted for so we net them out of the returns.

3) We assume that an investor will deploy all of his/her cash within one month and then starts winding down his/her portfolio. We weight the probability of starting investing in a certain month by the number of loans issued in that month One oversimplification in our predecessor article was that we assumed an equal probability of having any loan in the analysis pool. That approach meant that if you had a loan issued in January 2008, you had an equal probability of owning a loan issued in July 2010. This assumption of equal probability is not reflective of how actual investors participate in Peer Lending. Normally, all initial cash is deployed quickly to reduce cash drag. It seems rather unlikely that if you started investing in 2008, you would hold some idle cash ready to just deploy in 2010. It is much more likely that you deployed all of your cash in January 2008 and happened to pick up a few loans in July 2010 from reinvesting any payments received in June 2010. This means that your probability of having July 2010 loans should be significantly less than January 2008 loans. We simplify the probabilistic calculations by assuming no reinvestment of monthly payments and the winding down of portfolios after initial cash deployment. To determine which month an investor is likely to deploy their cash in, we base the probability on the number of loans issued in a certain month. The effect of this is that the oldest months (when loan origination numbers were small) have a lower probability of being the starting month, and thus a smaller effect on the analysis. We think this is desirable because the underwriting back then was the furthest from what it is today (e.g. interest rate changes). Also, more investors entered the Peer Lending space as it matured, thus it makes sense to make it more probable for our hypothetical investor to start later. So in a simple attempt to stay relevant given that our analysis uses historical data, we put more weight on newer months and less on older months.

For each portfolio size, we use Monte Carlo methods with 100,000 trials to generate the following table. The lower bound corresponds to the performance of portfolios in the 2.5th percentile while the upper bound corresponds to portfolio performance at the 97.5th percentile. Returns are rounded and net Lending Club fees:

Portfolio Size Average Return (%) Standard Deviation (%) Lower Bound (%) Upper Bound (%)
1 7.44 25.50 -77.28 31.94
5 7.69 11.38 -20.04 22.62
10 7.67 8.14 -11.10 19.92
50 7.69 3.94 -0.66 14.66
60 7.67 3.66 -0.12 14.21
62 7.66 3.63 -0.08 14.07
63 7.67 3.60 0.05 14.10
70 7.68 3.47 0.33 13.88
80 7.68 3.30 0.70 13.54
90 7.68 3.15 1.11 13.25
100 7.69 3.03 1.32 13.07
150 7.65 2.69 2.04 12.35
200 7.66 2.49 2.51 11.97
250 7.68 2.35 2.88 11.73
500 7.69 2.09 3.72 11.10

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We can see that from a portfolio size of 62 to 63, the lowest 2.5 percent of portfolios crosses the 0 mark, meaning that even they are breaking even or barely making a positive return. The general takeaway is the same as before; diversification is important to guard against any single bad note having too much of an impact on your total performance. Investors tend towards risk adversity so it’s worth trading marginal increases to returns in exchange for greater perceived gains in safety. In comparison to the January 2014 article, the portfolio size at which this crossing into positive territory has changed from 146 to 63. Part of this reduction in portfolio size is due to slight methodology alterations, but delving deeper into the data also shows that a significant portion of it can be attributed to better performance of loans issued between 2011 and 2013 in comparison to loans issued earlier. And what if we want to be even more confident of the minimum number of notes needed to be in positive return territory? We repeat our analysis from above and instead have our upper and lower bounds capture 98% of theoretical portfolios rather than 95%:

Portfolio Size Average Return (%) Standard Deviation (%) Lower Bound (%) Upper Bound (%)
1 7.76 24.74 -87.67 39.47
5 7.63 11.40 -26.69 25.06
10 7.58 8.15 -15.63 21.73
50 7.63 3.95 -3.09 15.76
60 7.66 3.67 -2.21 15.40
70 7.65 3.47 -1.88 14.80
80 7.71 3.26 -1.31 14.57
90 7.67 3.16 -0.79 14.26
100 7.70 3.03 -0.75 14.05
150 7.68 2.68 -0.11 13.27
200 7.67 2.51 0.37 12.81
250 7.66 2.37 0.44 12.43
500 7.67 2.08 0.67 11.70

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With our more stringent bounds, we see that our portfolio size that crosses the 0 mark is somewhere between 150 and 200 notes. So what does this mean for you as a Peer Lending investor? That the importance of diversification cannot be overstated. While market and industry conditions change over time, for better or for worse, diversification will always be at work protecting your investments from downside risk.


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