The math related to investment diversification

Increasing diversity reduces the risk of a big loss compared to portfolio size, but it also reduces the chances of none or small losses. It merely makes the probability of loss closer to the average across the investment universe.

IMHO the optimum strategy is to do a certain amount of DD dependent on your time and interest and weed out a proportion of opportunities which do not appeal, but otherwise go for maximum diversification.

An influencer here is time. You need diversification to reduce potential of big loss but you also have to offset it against your time? I personally am spending possibly too much time monitoring 6/7 sites picking the good loans, trying to manage some risk by selling before term end all to try and improve rates as this is harder than it used to be. Yes I am probably averaging 11% after some losses BUT I could just bung the money across 3 sites with no real work and get 7/8% especially if you then start taking into consideration less tax as earning less interest etc etc.

I won't because unfortunately I am a little addicted and love it, but for some busy people it is getting tougher to get good rates without riskier loans, time for some could be a factor.

I tackled some of the maths on P2P loan diversification recently.
To keep it simple the lending model is a loan that returns 10% interest in a single end of year repayment, and has a 5% bad debt rate with no recoveries. When invested in an infinite number of such loans the expected return is +4.5%, but we are concerned with what happens when the investment is spread over a much smaller numbers of equal sized loans.

Outcomes with 1 loan:
Outcome        No defaults        One default
Probability            95%                5%
Return                +10%             -100%
 
Outcomes with 2 loans:
Outcome        No defaults        One default        Two defaults
Probability         90.25%              9.5%                 0.25%
 Return               +10%               -45%                -100%
 
Outcomes with 3 loans:
Outcome        No defaults        One default        Two defaults        Three defaults
Probability         85.74%             13.54%               0.71%                0.01%
Return              +10%                -27%                  -63%                -100%
 
This is called a binomial distribution. Inspection of these figures shows that by spreading the investment over a number of loans the probability of a total loss is rapidly reduced, but that the probability of making a more modest loss is increasing. This trend continues until with 10 loans the probability of a small loss is a staggering 40%. As the number of loans is increased further the probability of loss falls and rises in steadily decreasing waves. However it is not until there are more than 98 loans is the probability of loss always less than our original 5%.

This shows that modest diversification, whilst hugely reducing the chance of a total loss, has the (perhaps) unexpected effect of increasing the likelihood of making an overall small loss. I suspect that this effect is why many who dabble in P2P lending without adequate diversification come away with a bad experience.

nellerdk newbiealert - diversification is a key aspect to managing risk in P2P lending.  As noted above, it doesn't reduce your overall risk, but it can reduce the volatility of your outcomes, and provide you with a better risk-adjusted return (Sharpe ratio) for your portfolio.

As your upside is capped in lending (the best you can do is get your interest and capital back) the outcomes are skewed, and so the best way to optimise returns is to manage your downside risks (you can spend lots of time loan picking for the "best ones"; the sole purpose of that activity is to avoid the "worse ones", not to try to identify "home runs").

Enabling easy diversification is a core feature of our service at BondMason, and one of the reasons we set up the platform in the first place (please excuse the mention) - with Autobid clients can choose a minimum of 50-100+ positions. This takes an average of 4 weeks to get fully allocated, but doesn't require any effort from our clients, and all loans are hand curated by the team.  

Whilst clients end up with different portfolios, their performance over a 12 months period tends to be close to the average performance (more so for those with 100+ positions) - demonstrating the value of diversification.  In time we intend to implement a 200+ loan option, which we feel will enable even better (more consistent) outcomes.

But you do need to be patient during the initial allocation phase...

Very interesting analysis. As the number of loans gets large the distribution of the portfolios value approaches the normal distribution due to one of the most remarkable results in statistics called the Central Limit Theorem (https://en.wikipedia.org/wiki/Central_limit_theorem). Because this distribution is defined by the mean and standard deviation you can simply calculate the the mean and standard deviation of the portfolios value. One of the things with this analysis is it is assuming defaults are independent and uncorrelated. If you want to model correlated defaults you have to use something called a copula.

The 0 5% promise must be coming by the same transport as money from Switzerland on another platform as its been so long.