An individual loan charges off with a probability of approximately 0.2 and you can treat a portfolio of N loans as a binomial random variable. The expected number of charge-offs will be 0.2*N. The standard deviation in the charge-offs of your portfolio will be SQRT( N*0.2*0.8 ) . So, the mean number of bad loans grows linearly with your portfolio, but the standard deviation will only grow with the square root of N. As your portfolio grows you will get more predictable numbers of charge-offs.

In terms of charge-off rates, a random sample of N loans will be expected to (95% of the time) to have a mean charge-off rate between:

N: CI

25: (4%, 36%)

50: (9%, 31%)

100: (12%, 28%)

200: (14%, 26%)

400: (16%, 24%)

800: (17%, 23%)

If you feel your strategy can eliminate some of the bad loan choices, you may need fewer loans in your portfolio to overcome the variance. For what it's worth. Once you get above 1000 loans the benefit of diversifications really drops.

The benefits of diversification above 800 notes are shown below:

The table at the top of the graphic provides data for all completed LC loans (courtesy of NSR). Avgerage interest rate and ROI are shown for informational purposes only and were not used to generate the graph.

The data from Bryce's post shows two sigma confidence intervals for a 20% average default rate (approximately Grade D loans) where the number of notes varies from 25 to 800. In the case of 800 notes the lower and upper two sigma confidence intervals are 17.2% and 22.8% respectively (5.6% apart). Taking Bryce's table a bit further:

N: CI

800: (17.2%, 22.8%)

1250: (17.7%, 22.3%)

2500: (18.4%, 21.6%)

5000: (18.9%, 21.1%)

At 5000 notes the CI's are only 2.2% apart; an improvement of 5.6% - 2.2% = 3.4%. The coloured graph above shows this improvement beyond 800 notes for each loan grade as a function of the number of notes starting at 1250. Obviously improvements per note added continue to fall per the sqrt of deviation but seem to me to be significant. If you think you have a great set of filters or a great model you might want to ask yourself it's edge will overcome bad luck if too few notes are purchased. Guess I don't believe in over diversification, but there are practical limitations as to how many loans one can buy directly from the retail platform. The 2pm PT release just came and went with only 8 D&E loans combined. It is Sunday afternoon.

Bryce & Fred; where's the party?