Simulation Results

To get a better handle on the effect of historical default rates on P2P loan portfolios, I performed a monte carlo simulation on portfolios lending $100, $500, $1000, $2000, and $5000.  Since I assumed that the money was spread across investments of $25 each, those dollar amounts correlate to 4, 20, 40, 80, and 200 loans respectively.  For each test case, I simulated investing in all A1, C1, E1, or G1 loans (using Lending Club grading terminology) as well as an equal mix of those 4 grades, which I called Div for diversified.  I used the following historical yearly default and corresponding loan interest rates (again from Lending Club’s site):

Since loans on Lending Club have 36 month terms, I calculated payments across each of these months, accounting for the appropriate probability of default. Using 36 months is more accurate that defaults/year since borrowers can default at any time and although month 1 and month 12 are both in year 1, the difference of those two default scenarios is significant. The overall results wouldn’t have meant much for one instance of each test case, so I instead ran each case 1000 times.  The results show the total value of all of the payments made.

Let me explain the $100 results as an example and then present the others for you to analyze.

$100 Investment

For this small investment amount, you can see that most cases of each portfolio had the same result, which is why you see prominent bands around the max expected returns for $112 $118 $121 $124  and $129.  We would expect the number of cases at the maximum to decrease as more money is invested, though the minimum result would also be expected to rise.  To read this graph, assume that you had $100 to invest.  If you invested in all A1 loans, using the historical default rates and corresponding loan interest rate, the total payments received would be one of the dark blue dots.  Had you invested in C1 loans, you’d be a pink dot, and so on.  The other dots of the same color (other than the one that is “you”) can be thought of as other people who also invested in the same number and grades of loans.  Remember that this simulation gives hypothetical returns using historical default rates and the payments you receive could be worse.  It’s just a matter of probability.  Now that we’ve looked at the $100 investment results, you can probably guess how the rest will look and analyze them yourself.  Here they are:

$500 Investment

$1000 Investment

$2000 Investment

$5000 Investment

General Conclusions;
As more money is invested, the likelihood of getting the full expected return declines, as the occurrence of default becomes more prevalent.  Investing $1000 or more always (at least in these simulations) resulted in a profit, whereas investing smaller amount sometimes resulted in a loss.  The average return of the riskiest (All G1) portfolio was always the highest.

The results of these simulations indicate two things to me:
1) Investing more money seems to be safer
2) If you do invest more money (in as many loans as possible) the higher returns of riskier grade loans seem worth it.  This is likely due to the fact that while the individual loans do carry more risk, the fact that you’re diversifying by investing in so many of them tends to moderate the risk.