# 146: The Magic Number On Lending Club

In previous SeekingAlpha articles, we analyzed the financial returns of Peer Lending, and the type of risks associated with this asset class. By far, the biggest risk is defaulting: the borrowers simply stopping to pay back a loan. The mantra in Peer Lending is that since an investor puts only small chunks of money, into many loans, that provides diversification and lowers this risk considerably. "Does it?" is the question we're trying to answer below.

As previously, our data analysis is based on Lending Club's historical data, which is available for anybody to peruse from the Lending Club website. As of January 2013, more than 230,000 loans have been issued. Unfortunately, most of them cannot be taken into account since they're too young to have been fully paid (or "reach maturity", in Bonds terms). If we restrict the dataset to loans that are old enough to have reached maturity, it leaves 17,558 36-months loans, issued between June 2007 and January 2011.

We can calculate the Return on Investment of a loan with the following formula:

where p is the sum of payments made to investors and c is the cost of the loan, or amount lent by investors. Both values are given by Lending Club's historical data, as "Total Payment to Investors" and "Amount Funded by Investors", although we have to discount the "Total Payment to Investors" by 1% to take into account the Service Fees kept by Lending Club.

When calculating the Return on Investment for multiple loans, we simply sum the payments and costs of all the loans' investments:

We will consider the returns between two loans to be independent of each other, which is reasonable since a) default from a man in Nevada who borrowed money to fix his car is unlikely to affect the probability of default from a woman in Florida who wanted to pay back her credit card, b) historical data (for instance from S&P Experian Consumer Credit Default indices) shows a close-to-zero beta, which means defaults on consumer credit defaults are not correlated with market conditions.

If returns are independent, returns will converge toward the total market average as the number of invested loans increases. If you want to show off at a cocktail party, you can even explain it's due to the Central Limit Theorem, and that the returns follow a normal distribution.

Considering the distribution is normal, the "Three Sigma Rule" tells us that almost all the outcomes (99.7% of them to be precise) are comprised between the average minus 3 times the standard deviation and the average plus 3 times the standard deviation.

We use a Monte-Carlo Method to calculate those numbers and measure how diversification reduces risks. The Monte-Carlo Method is just a fancy way of saying "repeat random trials a lot of times". We're first investing in a single loan at random, repeating the experiment 50,000 times to estimate the average return and standard deviation (or how much the results vary). Then we repeat the process by investing in 2 loans, 3 loans and so on â€¦

Investing in a single loan at random on Lending Club gives an average return of 5.75%, with a standard deviation of 24.35%. Therefore, in virtually all cases, our return for investing in a single loan would have been between -67.3% (5.75% - 3 * 24.35%) and 78.8% (5.75% + 3 * 24.35%). And the two words to characterize such an investment are: insanely risky!

But, as we increase the number of loans, the risk goes down precipitously:

Graph

Number of loans Average Return Standard Deviation Lower Bound Upper Bound
1 5.2033% 25.1532% -70.26% 80.7%
2 6.4844% 18.3609% -48.60% 61.6%
3 6.8782% 15.2617% -38.91% 52.7%
4 6.6811% 14.1559% -35.79% 49.1%
5 6.9942% 12.4705% -30.42% 44.4%
10 7.0534% 8.8711% -19.56% 33.7%
20 7.1361% 6.4418% -12.19% 26.5%
50 7.1726% 4.0416% -4.95% 19.3%
100 7.1784% 2.8620% -1.41% 15.8%
145 7.1700% 2.3919% -0.01% 14.3%
146 7.1597% 2.3790% 0.02% 14.3%
200 7.1815% 2.0266% 1.10% 13.3%
500 7.1782% 1.2646% 3.38% 11.0%

With 146 loans, the total returns is positive in (almost) all the cases. And that's our magic number. If one invest \$25 per loan, it means the minimum amount of money to be 'be sure' not loose money is \$3,650.

Returns sharply converge toward the average, which is 7.18% over the period. As a comparison, the average yearly return for 10-year T-bonds from 2007 until now is 5.3%. (source: Federal Reserve database), and is likely to be in sync with ETFs like IEF (iShares Barclays 7-10 Year Treasury Bonds)

Of course, past performance is never a guarantee of future results. And nothing proves the returns are independent, but we think that's a reasonable assumption. Since investing in 146 loans on Lending Club requires a very low amount of capital, Peer Lending seems to keeps in promises of affordable diversification and low-risk investment.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: I'm a co-founder of LendingRobot.com, a tool involved in the Peer Lending space.