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Diversification and Setting Limits

01/8/08 posted by WealthBoy    

I would like to provide the Prosper community with some of my thoughts on building a profitable lending portfolio. Of course, what such article is complete without mention of diversification? Certainly anyone could tell you that diversifying your portfolio by spreading the risk over multiple investments is a good idea. But how many different loans should you invest in? At least 30!

Diversification

Why 30? A well-known statistical rule of thumb states that you should try to use a sample size of at least 30 in order to improve the accuracy of any analysis performed on normally distributed data. According to the central limit theorem, “as the sample size n increases, the distribution of the sample average approaches the normal distribution with a mean µ and variance ?2/n irrespective of the shape of the original distribution.” That means that even if data is not normally distributed, as the sample size increases the distribution will approximate that of the normal distribution.

It is very likely that the average return for unsecured loans is normally distributed, so the rule of 30 should apply well to peer-to-peer lending. Even if the average return isn’t normally distributed, the central limit theorem states, that the larger the sample size is the better it will approximate the normal distribution anyway. This means that the more loans in which you invest (with equal amounts per investment), the better your chances are in achieving the average expected return. Please note that I stated “average expected return” and not average interest rate. When I say average expected return, it means average interest rate - average net defaults - average fees.

Setting Limits

That brings me to the next topic of setting limits. It is very important to consider potential costs associated with your portfolio when placing bids. You should consider the probability of defaults and fees, as costs of maintaining the portfolio. When bidding on loans with lower debt grades (i.e. higher risk loans), you will need to set higher minimum rates in order to compensate for defaults and fees. Each bid placed should take these costs into consideration, as well as the desired total return on the portfolio. The “Expected Return” calculation on the Prosper bid page is an excellent tool in helping to decide at what interest rate to place your bids. (Editor’s Note: Another great tool is the Marketplace Performance Tool.)

Of course, each individual loan will ultimately either default or be fully repaid. Therefore, on an individual basis the actual cost of a loan default is much higher than the estimated cost. If a loan defaults, the cost will essentially be the original amount lent minus any principal and interest paid up until the time of default. However, if enough individual loans are made with similar estimated costs, the figures on the bidding page should provide a good estimate of the costs on the total portfolio.

Once you have placed your bids in accordance with your desired overall portfolio performance, you need to be patient and wait for the listings to close. If you’ve bid on a good listing, there should be plenty of other bidders on the loan and it should reach 100% funding. Often after a bid has reached 100% funding and it approaches the expiration, a bidding war takes place. I believe that the activity taking place is a result of the actions of two types of bidders:

  1. Those looking for a good deal (that matches their risk profile) that will close quickly.
  2. Those that were outbid and rebid to ensure that they win.

Do not become the latter! If you are outbid on a listing, do not be compelled to rebid. It is not a competition where you win a prize if you win the bid. If you were outbid, it was because the marketplace was willing to take on more risk than you. Besides, at the rapid pace that Prosper is growing, there will always be plenty of new listings to bid on.

It is of the utmost importance to be very patient when investing funds. You should draw the line and never cross it. You should expect to lose a lot of bids. You should also expect to do a lot of bidding before having a winning bid on a funded loan. I’ve found that only about 10% of my bids are being funded, which is just fine with me. As soon as I lose a bid, I look for another loan to bid on with the money returned to me. I think that all too often, lenders cross the line or even worse they never drew a line to begin with.

Prosper

If you properly diversify your portfolio and properly set your limits, you should be well on your way to building a profitable lending portfolio. I would recommend that you invest at least $1,500 and spreading it over 30 $50 loans. If you invest more than $1,500, investing in more than 30 $50 loans will make your results all the more predictable. If you invest considerably more (on the order of tens of thousands or more) it may not be as easy to keep your bids as low as $50. However, if you do keep your bids down to just $50, your results will be much more predictable. It will just take much longer for the large investment to eventually reach funded loans. All it takes is a little discipline and a lot of patience.

WealthBoy is a new Prosper lender (WealthBoy) and writes the personal finance blog WealthBoy. He performs financial and statistical analysis in his day-to-day job. He enjoys following the financial markets and seeking out new ways to invest. He is well versed in investing in mutual funds, stocks, and options and has found peer-to-peer lending to be another good method for investing. He also loves to watch Florida Football and Florida Men’s Basketball.


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14 Responses


Dean | January 8th, 2008 at 6:49 pm

Yes. Usually a sample of size thirty yields a distibution that can be considered Normal (Gaussian). How this relates to being a proper number for sufficient diversification, I fail to see. If I recollect correctly, with fewer than 30 observations the distribution is better fit by Student-T, but why being nearly Gaussian the appropriate standard?


WealthBoy | January 8th, 2008 at 10:35 pm

Thanks very much for your comment Dean. I was thinking more in terms of trying staying within 2 standard deviations of the population mean with a 95% confidence interval. Even with a t-distribution, you need at least 12 degrees of freedom if you want to be within 2.2 standard deviations and maintain a 95% confidence interval. All this talk about samples, t-tests, Gaussian distributions makes me want to take a look at some of the actual numbers! Stay tuned…


Peer Lend | January 8th, 2008 at 11:55 pm

Yes, I think it would be wise of you to look at the actual numbers. I looked at yours, which you linked to, and you have 20 loans, not a single one of which has yet aged enough to make its first payment. I’m not pointing that out as any sort of ad hominem attack - on the contrary, welcome to Prosper and I wish you much luck here - but if, as you say, you haven’t looked at the actual (and readily available) marketplace data, and since, clearly, given the youth of your portfolio, you aren’t speaking from personal experience - well, what, exactly, *are* you doing?

I’ll also add, at the risk of appearing to be “picking” on you, that you’ve committed the “average interest rate - average defaults - average fees = expected return” sin. Prosper loans are for 3 year terms and are fully amortized over same. That means you have to account not only for declining principal balances over the term (as payments come in, the interest rate remains constant, but the balance upon which you make that interest rate declines), but that you have to constantly factor for reinvestment into new loans in order to maintain some (ranged) return over time.


WealthBoy | January 9th, 2008 at 1:11 pm

Don’t get me wrong, I’ve done plenty of analysis of the marketplace data. I wouldn’t have just jumped in and started bidding on loans without having done so. I do indeed have a very young portfolio, and I’m still trying to expand it.

However, given my criteria for what I deem to be loans with appropriate rates in regard to the risk, it is taking some time to build. I’ve planned on starting off with 50 $50 loans for a total initial investment of $2,500.

I also understand amortization and the declining balance as payments are made. I felt it was a bit too much detail to get into for the article. :) If I average an interest rate of around 15%, I should make about $85 in cash flow per month barring any defaults and late payments. That would give me enough cash to fund a new loan every 18 days. It also means that I would have to have more than 1.7 defaults per month (3.4% of the total portfolio) before I start making a negative return.

When I said I wanted to look at some of the actual numbers, I meant I wanted to perform some regression analysis for the the different credit grades and other criteria to try to develop some regression formulas for total return. Total return being the annualized return for interest paid on amortized principal, less fees and net defaults. I think taking a look at median values instead of mean values may be a good idea too, to see whether or not the data is skewed.


NewHorizon | January 9th, 2008 at 2:25 pm

“If I average an interest rate of around 15%…”

Your initial ROI expectation is roughly in line with the expectations of most other lenders when they’re new. It’ll be interesting to touch base with you again in a year.

…if I can remember to do it. :)


RateLadder | January 9th, 2008 at 2:33 pm

@NewHorizon

15% was referring to average interest rate, not ROI.

@WealthBoy

What is your expected ROI?


NewHorizon | January 9th, 2008 at 3:46 pm

Then I should have quoted “barring defaults and late payments” instead. ;)


WealthBoy | January 9th, 2008 at 4:50 pm

RateLadder, thanks for pointing out that I did say interest rate. My expected ROI is around 11% and as of right now my average interest rate is around 18% on 23 loans. I used a lower interest rate in my prior comment, because I wanted to be conservative in estimating my cash flow. I still don’t know exactly where my average interest rate will land once I’ve established the other 27 loans.


Tom | January 10th, 2008 at 9:17 pm

Matt wrote a good article about diversification. He found that 70% of lenders have less than 20 loans.

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