I want to give a big thanks to pninen for starting this thread. Very good data analysis.

However, I want to point out that the data is not actually as bad as it seems. In economic theory terms, it shows that Prosper is not yet an efficient market. Basically, there are too many uninformed (newbie or otherwise) lenders who are willing to lend at unprofitable rates. However, as an earlier poster pointed out, a majority of the late loans are from borrowers with 3+ delinquencies, and if you just took out these numbers (i.e., didn't lend to these borrowers) the numbers would look substantially better. Thus, as a group of lenders, we aren't very good at picking out good risks from bad ones.

As an individual lender, however, it should be possible to make money exactly BECAUSE prosper is still an inefficient market. That is, since the market as a whole isn't good at finding good vs. bad credit risks, with research and discriminating lending practices you should be able to beat the market (i.e. the average Prosper portfolio). Now, it's still possible that as a whole the Prosper average is SO bad that beating it still provides a crappy return, but I believe that will change over time.

The situation is similar to the problem with skyrocketing Google Adwords rates. Basically, you have enough unsavvy Google advertisers who are willing to bid up Adwords to unprofitable levels because they think "I've GOT to be at the top of Google", even if it makes them lose money in the end. The smart advertisers are saying enough is enough and that it doesn't make sense to buy expensive, generic keywords and are learning to target their adwords purchases. Here at Prosper, you have lenders bidding down rates to levels that are too low, but at least they appear to be doing it indiscriminately, so it should still be possible to further segment borrowers to get a much better return than average.

Thus, the moral is that right now if you lend indiscriminately on Prosper you WILL lose money.

poof.. was off topic even for me..

lol

MMM

Agreed. Done it. Interest rate isn't pretty, but it's possible.

The straight line indicates an additional 2% in defaults each month. That projects a final default rate of 72%.

Perhaps you're asking what % of the dollars due are not paid back at that default rate? That's a bit more complicated...

Lets imagine we made 100 $1000 loans at 15%

each loan should pay back $34.67 each month, but if two borrowers drop out each month, the total payback would be only about $81,000 after 36 months.

If I'm wrong, someone correct me.

Not sure how to figure out the actual annual return rate on that.

The 1/15/2007 update.

(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-2007-01-15.gif)

See my earlier posts for explanation of methodology.

It's really interesting how flat the May curve is compared to all of the others.

Did lenders get really tight (relatively) when they saw the extended credit data for some of the crap they were funding?

It should come as no surprise to anyone here that holding the complete Prosper portfolio is a money-loser. Just take a look at some of the irrational exhuberance going on over there by lenders (no need for specific references, I hope).

What I'd really like to see is pninen's analysis with various bidding criteria applied to test out bidding strategies. THAT is a tool I'd be willing to pay money for!

May'06 is a very strange month. The all-grades data looks better than any other month, as you have observed, however this doesn't hold across the risk spectrum. The HRs from May are doing much better than HRs from other months, but the low-risk grades from May, especially A are doing very poorly. When I take one month's loans and then break it down further by grade, I end up with buckets that don't have very many loans in them, so the data is noisy, and it is difficult to draw useful conclusions. Nevertheless, it is very clear that May is strange.

That's a good hypothesis. However, lenders are not the only folks who affect the system. Prosper had a huge influx of new listings in late April'06 due to news story on ABC. This was memorable because it overloaded prosper's servers, to say nothing of lender's tactics at the time, which for many of us involved reading every listing. Could be that the unusual May'06 portfolio is driven by the characteristics of borrowers who watch ABC news, or how lenders responded to that surge of listings. However, the data doesn't answer "why" questions. Dunno.

The 2/1/07 update...
(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-2007-02-01.gif)

Data points are on the 1st and 15th of every month.

Looks like the curve for the first loans made almost a year ago are flattening out. Unfortunately, it is flattening out at 25%.

That is bad.

Yep.

We do expect these curves to be "curved". Even if we assume a constant "bad" rate (ie loans going "bad" at a constant rate for their entire life), these cumulative "bad" curves would not be straight lines. They would curve down. This happens for a simple reason. As you move to the right, some loans have already gone bad, so you have a declining population of loans left to go bad. So this declining population multiplied by the constant bad rate produces a slope that declines as time advances.

The first few curves do appear to be curving a little more than a constant default rate model would predict. Therefore, we may be observing a behavior where the default rates are higher in the early months. Where they end up is still open to question.

I've done a little work on this, and hope to write it up sometime soon. Getting around to writing the explanation is slower than doing the math.

It actually looks like the most recent set of data is defaulting at a slightly faster rate than in the previous months. Granted, that there is not a lot of data (only 2 sets of payments), but this is not a good indicator. One would hope that lenders would get better at picking loans... Or, do you think that it is borrowers are becoming better at scamming?

I am really glad that I read this entire set of posts before I put a lot of money into prosper. It really makes me rethink my strategies, and recalculate my expected rate of return...

I think the moral of the story, is to stay "C" or better (with a few exceptions), and to stay away from anyone with more than 3 current DQ's. Sounds simple enough... Lets just hope it works.

Interesting. I look forward to this write-up.

I think you also must remember that new lenders are constantly coming in, with the older lenders slowing down, so I don't think these graphs are good indicators of lenders getting better or worse at picking loans. It'll be interesting to see the December loan data, as the Money Magazine article came out in late November mentioning prosper.

But, the post Scorex loans seem to be performing significantly better, I'm looking and they look around 4% better at the same age, give or take. Maybe Pninen can give us the some more exact numbers, say around month 3 or so. It looks to me, after month 3 on the chart, most are around 8%, whereas the pre-scorex was around 10. So, maybe that indicates the post scorex loans will flatten out around 20% (granted, not much better, but better nonetheless).

Thanks for tracking all this, Pninen!

It is sobering to see how good mere numbers are at predicting things.

2/15/07 update...
(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-2007-02-15.gif)
See my earlier posts in this thread for info on methodology.

Wow. The May '06 loans are about to be better than June, July, and August.

Very interesting and helpful data. Thanks!

What if ONLY HR's are taken out of that chart? Does it look just as bad? I think that HR's are really messing up that chart, not to mention that most of the listings are HR's as well. I'm wondering which credit grade has the most number of loans out for each month. Also, if you take out high, over 20%, DTI originations for each month, how does the chart look? There are just so many variables to play with.


Would be intesting to see all the months originations separated by credit grades. That would be more an apple to apple comparison. So say somebody who lends only to AA could see the progression as months pass by, or someone who lends to B etc etc. Overall it just looks really bad due to the HR's. I think if HR's, D's and E's are taken out as well as any high DTI borrowers(in any credit grade) it doesn't look this tragic at all.

You can look this stuff up on the performance page.

DTI is almost meaningless. I published a chart with DTI<20% separated out awhile back. Some months DTI<20% curve is higher than tha DTI>20% curve and some months it is lower. Very weak information content in DTI. Prosper erred when they gave DTI such a prominent place in their presentation.

I posted charts broken out by credit grade earlier in this thread. NJD also published some statistical analysis broken out by credit grade in another thread.

The 03/01/07 update.
(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-2007-03-01.gif)

See earlier posts for explanation of methodology.

We now have enough data to begin to look at the shape of these cumulative late curves and think about what this means for the evolution of the prosper portfolio. In the following chart, I have shifted each month's graph to the left so that the curves have a common origin. The horizontal axis is now days since the beginning of the origination month. The curves have very similar shape. Not identical, but nicely clustered.

(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-model1-2007-03-01.gif)

To this data I have added four dashed curves which represent models of loan behavior. The simplest model is represented by the green curves. This is the "constant bad rate" model. In each time interval, a certain (constant) fraction of the still-surviving loans "go bad". Once bad they stay bad. (The mathematicians among you will recognize that the shape of the resulting cumulative bad curve is a negative exponential. ) I've drawn two green curves. One matched to the worst month and one matched to the best month. If this model reasonably fits our data, then one might expect all the months would evolve roughly between the two green curves.

There's a problem. The data looks like it curves downward more than the green curves. The green model is a very simple model. It only has one "knob" I can turn to match it to the data. I can move the curve up and down, but I can't make it curve more to fit the data better. This gives us a hint that the loans in the Prosper portfolio may be experiencing a bad rate that is higher at the beginning of the loan, and then goes down during the first few months. To fit this sort of data we need a model with more knobs.

The blue curves represent just such a model. It has three knobs: A high initial bad rate, a time constant over which the bad rate comes down, and an eventual lower bad rate. As you might expect with three knobs I can make the blue curves fit the data much better. Of course there is a moral hazard here. With enough knobs I can make curves that look like they fit any data, even if the model really tells us nothing about the nature of the underlying objects. That's why we start simple and only add complexity if the simple model seems to not work well enough. That's the situation we're in.

Now when matching curves to this portfolio performance we'd really have a much easier time if we had data points over on the right side of the graph. Unfortunately we have no such data points. What I am forced to do is take a simple model, match it to how much the data seems to be bending downward over on the left side of the chart, and use that to extrapolate where we might end up when we get over to the right side of the chart. To quote Elizabeth May "Credit Scoring for Risk Managers" pg 135 "It is important to have seasoned loans in your data if you want to estimate lifetime default probabilities...". Right Liz. We get it. We just don't have the data yet, so we're doing the best we can.

Here are the bad rates that produced the dashed curves in the cumulative chart above.

(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-model2-2007-03-01.gif)

As described above, the green model is based on a constant or "flat" bad rate, and the blue model is based on a bad rate that slides down during the first few months.

Based on nothing more than observing how well these various models seem to fit the data we have so far, it does seem likely that we are experiencing loan behavior where the bad rate is higher in the first few months and then comes down. I don't want to go too far beyond that. We'll learn how far it comes down when we get more data.

Meanwhile, if you're wondering how to apply this to models of return... The various formulas such as R = I - D or R = (1+I)(1-D)-1 presume a constant default rate. If the default rate is not constant vs time, these formulas aren't quite up to the task. However, you can get quite far with some hand-waving. You can see where the cumulative bad rate ends up for the blue model, and you can see that produces the same number of bad loans as a constant bad rate of about 15%/year. The defaults in the blue model are front-loaded, which is worse for the lender, which means the effect on the lender will be similar to a constant default rate which was a bit higher, maybe 17%. The old Experian numbers predicted about 8% for the all-prosper portfolio, so we're still in the neighborhood of 2x worse than Experian.

From time to time someone posts a comment in this thread which goes something like "Hey, but things aren't all that bad. Those curves include all loans, and I only bid on the good loans so I'll do better." Yes. We certainly hope so. But even tho the all-prosper portfolio has different performance than your portfolio, I think it is useful to track. I'm doing this to learn about the behavior of Prosper loans. As a practical example of that, once you see how bad the all-prosper portfolio is, you realize that you have to do better than average to keep from losing money. It thus provides a kind of landmark which shows us that we need to be selective.

Lendingstats.com indicates about 6.2% 1 month late or worse with respect to the # of current loans. Your data appears to be about 2x that.

No.

Well first I should point out that in the charts above you will not find a ratio of all late loans to all current loans, which is I suspect the sort of thing you are reading from lendingstats. I think you are likely comparing apples and oranges.

The curves how how lates evolve OVER TIME. You can't see that on the lendingstats web site.

I don't think its very illuminating to look at the total fraction of a portfolio that is late. The problem is that to understand the meaning of such a number you have to know the age distribution of loans in the portfolio. (Loans to bad over time.) A lot of people throw such numbers around and confuse themselves.

Go back and read my posts from the beginning of this thread where I explain my methodology.

Thanks, pninen. Another great contribution to our knowledge base.

The blue model seems consistent with the heterogeneity of the portfolio- it is made of many different credit grades, with many HRs going bad quickly and some AA-B going bad slowly. This gives a reasonable theory to support the math- looking at total bad rates we would see a high early rate with the rate coming down over time as the proportion of HR loans to total comes down.

Good point. After reviewing post #1, I see where you are coming from. If you are so inclined, an update by credit grade would be helpful. Or perhaps a summary excluding the now-known bad actors, (nc and hr). That might be somewhat less horrifying.

Thanks,
Ray

I love the forecast charts, much fun. Thank you Pninen!

After looking at the blue lines a bit, I realized that the top line is clearly forecasted off of 1 of the first 2 months of Prosper lending. Those 2 months without extra lending data had (as can be expected) more defaults than other months.

By rough eyeballing it, it seems the top blue line would be around 37-38% after 3 years if it were based on August loans rather than April.

thanks again for the analysis, pninen...

Whoa! Good thought. I think you might be right. If so this argues for a slightly different model and/or conclusion. I'll let that rattle around in my head for awhile.

Thanks, Pninen!

A new chart of shattered dreams, delivered fresh every two weeks. (IMG:http://www.brilliantisland.com/images/yay.gif)

Very interesting data, thanks again, Pninen.
Am I correct in my understanding that the blue curve is representing a portfolio that sees no re-investment?

Considering that the re-invested portion of the portfolio reverts back to the original high-default-rate portion of the slope...the true slope of a "whole portfolio" would remain slighly higher than the blue curve, correct?

3/15 update coming soon, yay. :)

-arebelspy

Last posting the curves flat out a little. Can't wait to see the next one.

The 3/15/2007 update...
(IMG:http://img.villagephotos.com/p/2006-6/1187065/prosperlate-2007-03-15.gif)

Data points are added on the 1st and 15th of each month. See earlier posts for explanation of methodology.

December is the best out of the gate performer thus far

i had a vision that 112233 will be a smart ass on days ending in "Y"...

Thank you for all of the analysis, very interesting.

Something I would love to see, though it would be harder to do, would be the same statistics by loan category. That is, look at the listings, and put them into buckets, like:

1. Debt consolidation
2. Fund one or two person business
3. Borrow to lend on prosper
4. Home improvement
5. Real estate investing / flipping

etc. We could probably come up with 10 categories that would capture 80% of the listings. Then, I'd like to see the same late / default statistics by category. This would give us an idea of which loans are more likely to succeed (from a lender's perspective) than others.

I have my suspicions, and flipping through the listings for late and defaulted loans, I can get some data. I would bet that the consolidation loans where the person has $5-20K of high-rate credit card debt are among the most likely to default, because they have a spending problem. I'd also guess that a lot of the "seed money for startup business" are also late because a lot of the business ideas are not very good.

What do you think?

LBYM

"No doc" or "low doc" loans do NOT account for 80% of mortgages nationwide. Maybe for certain lenders in certain areas, maybe those that specialize in "alt-A" lending. And maybe during certain periods of the housing "bubble" lending standards were looser.

But there are a LOT of loans for little $100-200K properties in the midwest, the "conforming" mortgages, that are the good old fashioned full-doc 20% down payment variety.

I would not make a generalization about the mortgage lending industry just based on one source.

LBYM

Just saw this - I have a Nodoc loan and yes they DO check. They pulled my credit report from all 3 bureaus (and I have excellent credit). I refinanced so that included my previous mortgage. In fact, when my HELOC was showing as a 2nd mortgage I had to get my previous bank to fax a letter to me stating it was closed and there was no balance on it before I could close. I also put down 20%. The appraisal was VERY conservative too. And I'm not late ;)

I don't have any "sources" but I would suspect the majority of lates are or will be ARMs, especially in areas where the housing market is going to hell and they have no way to sell to get out from under.

It looks like it's not unprecedented.

Sep '06 went down from 1/15/07 - 2/1/07

Mar '06 went down from 10/1/06 - 10/15/06

I think I'll just consider Prosper to be a "sucker's charity" until proven otherwise. When I compare this to Kiva and ask,"Will I get my money back?" I would say their pictures are "hotter" than Prosper's pics. <_<

How about a graph at each credit grade for every combination of extended credit data? :lol:

How much are we paying pninen? ;)

Very useful tools indeed. Can anyone see a difference related to 2Mils CP's which
go back to atleast Nov06. One day the lines will probably have to correct for the
implosion of the 2Mil group.

I wonder if Pninen has 36 colors to keep this chart around for 36 months without confusion :)

Wonderful thanks

Do you have a webpage where you keep this or just this thread? Great to watch this metric over time. You are going to run out of colors eventually though!! ;)

May 06 was a relatively good month, but wow Jun 06, bad month, looks like a 45 degree angle past 2 months. I was hoping these would level off after about a year... (all those who WILL default, HAVE defaulted by a certain time frame) but thus far it doesnt seem to be the general pattern but more data/time necessary to make firm conclusions. Also who knows what type of people (quality level) of borrowers found Prosper in the first few months when it was less publicized.

I hope December 06 is a trend and not a blip. Might be the start of some more rigorous screening (or maybe 2M paying off all its DQ loans messing with the data??)

Just here.

Someone archiving for if/when the board loses data in a crash?

-arebelspy

I actually like the debt consolidation more than most of the other categories, reason being of your categories, this is the only one of the 5 that does not increase the total debt load... (IN THEORY!) If they just go and re-use the credit cards my theory is shot

But funding a new business (to me very high risk), home improvement (just more debt), and real estate investing (that was so 2005, but seriously - more debt) are in some ways more risky

BUt I do agree its all about the behaviour. An AA or A borrower who is doing a home improvement is a good bet, whereas a D I'd never even consider.

Borrow to lend on prosper seems to me a foolish escapade :) Even the AAs are getting around 7-8%, its hard to turn a profit on that money - if you can get 5% on a 100% backed CD, you'd need to return 12-13% on Prosper, if you borrow 7-8%, and that does not pay for the risk... so unless its for altruistic reasons you need to get a low lower rate than 7-8% to borrow to lend on prosper...IMO

We are ok... unless pninen's computer crashes :) he is the source data, what is lost on a message board can always be reposted.