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.