### Author Topic: ROI and Loss calculation  (Read 14486 times)

#### brother7

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##### ROI and Loss calculation
« on: July 22, 2014, 02:22:09 AM »
For a single loan, how are the ROI and Loss calculated?

Run this LC filter:
Loan Status = Charged Off
Annual Income = 500000 to 500000

This results in exactly 1 loan: a \$35,000 loan that was charged off.
How is the Loss = 183.38%?
How is the ROI = -168.03% [EDIT: I figured it out using NSR Returns Formula, though I still don't understand it. If someone can explain it in plain English, that'd be great.]
Also, why is Completed = 0.00%? (Isn't a charged off loan completed?)
« Last Edit: July 22, 2014, 02:34:01 AM by brother7 »

#### rocco.g

• Jr. Member
• Posts: 53
##### Re: ROI and Loss calculation
« Reply #1 on: July 22, 2014, 12:19:36 PM »
The loss rate is a combination of forward looking math to support loss estimates and displaying results as a yearly ROI, not fixed.   The simplest example is a loan that makes 10% in the first 6 months.  This puts you on track to make a yearly ROI of 20%.  The same forwarding looking logic gets applied to losses.  So if you had a loan that defaults at 6 months which causes you to lose 90% of your investment, that puts you on track to lose 180% for the year.

The idea in both scenarios is that you are multiplying up your losses as well your gains in order to extrapolate an estimated ROI at a yearly rate.  Similarly if you had a 24 month loan that returned you 40% on your investment, it only has a yearly ROI of 20%.  This is an oversimplification, but at a high level it is what is occurring.

When looking at a single loan it might not make a lot of sense to do this, but that isn't what we are trying to do.  We want to come up with an estimated yearly ROI for a pool of loans, and this is when it starts to make more sense.  When a pool of loans are put together you dollar weight and time weight the yearly ROIs in order to come up with an estimated return for the entire portfolio.  This is when the loss rates of over 100% help.  In this pool of loans if you have a couple loans that charge off real early, that implies a high charge of rate and that you will have other loans charge off early and you need to capture that in your estimate.  The forward looking loss rate of over 100% gets averaged in and takes this into account creating a higher rate of loss for the entire portfolio from these early charge offs.

---

The completed flag in our system doesn't mean what you think it means.  It is an indication that a loan is older then its term.  So a 36 month loan originated over 36 months ago is completed.  It doesn't take into account anything else.  The use case for this feature is different then trying to find all loans that are in a certain state.  You should be able to filter on status to get all loans that are charged off and finished making payments if that is what you are trying to do.

#### Fred

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##### Re: ROI and Loss calculation
« Reply #2 on: July 22, 2014, 05:28:20 PM »
So if you had a loan that defaults at 6 months which causes you to lose 90% of your investment, that puts you on track to lose 180% for the year.

I do not think P2P investors can lose much more than 100% -- there should be better methods to get annualized numbers properly.

#### Randawl

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• Posts: 469
##### Re: ROI and Loss calculation
« Reply #3 on: July 22, 2014, 09:56:18 PM »
So if you had a loan that defaults at 6 months which causes you to lose 90% of your investment, that puts you on track to lose 180% for the year.

I do not think P2P investors can lose much more than 100% -- there should be better methods to get annualized numbers properly.

It is not saying that one is losing more than 100% in that particular scenario.  It is saying that the estimated yearly ROI in that scenario is -180%.

#### rocco.g

• Jr. Member
• Posts: 53
##### Re: ROI and Loss calculation
« Reply #4 on: July 22, 2014, 10:09:09 PM »
So if you had a loan that defaults at 6 months which causes you to lose 90% of your investment, that puts you on track to lose 180% for the year.

I do not think P2P investors can lose much more than 100% -- there should be better methods to get annualized numbers properly.

You are bolding half of a sentence after taking it out of context.  So yes, you are right, you can never lose more then 100%, and that sentence by itself is wrong.  But lets put the context back in and look at the very first sentence of my post which clearly says the loss rate is forward looking math to support loss estimates.  It doesn't say it is a real annualized return.  I never claimed it to be one.  I mention forward looking logic and estimates repeatedly throughout the post.

I was asked how are calculations work and to provide a simple explanation and I tried to do it.  I will try and re-clarify by saying that we are NOT calculating real annualized returns for single loans, or even groups of loans.  We are ESTIMATING annualized returns for groups of loans.  The 180% is showing you a subset of the estimation calculation that helps estimate future losses in other loans when used to in a group of loans the way the formula is designed to be used.

Saying "The simplest example is a loan that makes 10% in the first 6 months.  This puts you on track to make a yearly ROI of 20%." is equally as wrong out of context as the loss example.  Anybody who has done P2P lending for a year knows full well, that just because you made 10% in 6 months, doesn't mean you are on track to make 20% at the 12 month marker.  Some of those loans will default.  Everybody new to P2P lending learns that as their portfolio ages.  Including a 180% loss from one young loan with heavy losses helps drag down all those pristine notes you have that look like they will make 20% by helping to estimate the other defaults that will occur.

More then one person has disagreed with this approach, and that is fine.  But from my perspective, this formula has worked as a good estimation utility that generates ROIs that can be used to evaluate and compare different sets of loans with a reasonable level of confidence, which is exactly what it was designed to be. [it was also designed to have some good technical bonuses in implementation, but we are way past a simple explanation of the formula if I go into that]

#### Fred

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##### Re: ROI and Loss calculation
« Reply #5 on: July 23, 2014, 01:19:01 AM »
I happen to have a Ph.D. in Engineering, an MBA in Finance, and have been in quantitative finance for many years.  I have seen all kinds of financial equations and assumptions, but not the one you mentioned -- getting > 100% loss for what's considered long-only securities.

Can you tell me more about this forward looking math to support loss estimates?  And what is the path from this "math" to the final loss estimates?
« Last Edit: July 23, 2014, 01:33:05 AM by Fred »

#### Fred

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##### Re: ROI and Loss calculation
« Reply #6 on: July 23, 2014, 01:58:06 AM »
It is not saying that one is losing more than 100% in that particular scenario.  It is saying that the estimated yearly ROI in that scenario is -180%.

It does say Loss = 183% on the page -- see below.

The "Total Loss" for this \$35,000 loan is \$30,256.20.  Simple math seems to say that the loss is about 86%.  This is nowhere near the 183% loss (or -168% ROI) mentioned in NSR.

Or, perhaps I am missing some important details here?

#### rocco.g

• Jr. Member
• Posts: 53
##### Re: ROI and Loss calculation
« Reply #7 on: July 23, 2014, 04:53:53 AM »
I think the detail that is missing is that I can't fit exact definitions of what our formula generates into the header column.  The column headers "Loss" and "ROI" are the best descriptions that fit in the small space we have for the header, and they are pretty good descriptions for what those fields are.

The numbers that show up there do not always equate to the text book definition of the one word header.  I tried to explain what they mean in some weird scenarios, such as when a number over 100% shows up in the Loss column.  It seems like you are ignoring the explanation of the data and saying that the one word header must exactly describe the data, even after I post a message saying it doesn't in all scenarios.

It is a real loss estimate for most usage scenarios, so I am ok leaving the word Loss there.  But in some scenarios it is over 100% because the loss occurs extremely quickly and skews the calculation at which point the number means there is large loss in a very short time frame (with the larger the number being the faster the loss occurred), and that needs to be captured in order to balance out other young loans that are performing well.  Extrapolating to yearly returns from young loans causes stuff like this to happen.

But again, I have to reiterate, the formula is not meant to be used on extremely small set of loans.  The number for any single loan is not meant to be used by itself, that is not what our tool is designed for.   Any estimated numbers that are generated can have weird results if there is not enough meaningful data to normalize the results.

#### brother7

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##### Re: ROI and Loss calculation
« Reply #8 on: July 23, 2014, 05:22:01 AM »
Any estimated numbers that are generated can have weird results if there is not enough meaningful data to normalize the results.
What do you think is the minimum number of loans that would normalize the results?
Can you refer me to a publication or website that might explain more in-depth the formula that you used? Is this a home-grown formula or it is widely used in the world of finance?

Thanks for sharing your knowledge regarding the formulas and methodology behind the numbers. I don't completely understand the logic but I'm getting there.

#### rocco.g

• Jr. Member
• Posts: 53
##### Re: ROI and Loss calculation
« Reply #9 on: July 23, 2014, 07:41:05 PM »
What do you think is the minimum number of loans that would normalize the results?

I don't think there is a simple answer where I can say "800 notes and your are good".  Since it isn't just a quantity of notes, but it also has to do with what notes you are looking at.  For example, if you query for all the notes released in the past 6 months, it is all very young notes.  Having a whole bunch of young notes will be better better then a few young notes, but both scenarios really lack enough history that any type of extrapolation isn't going to be very helpful.   You really want the same thing you would want on any system when looking at ROI, regardless if it is including estimates, or only using known numbers.  You need sets of loans (probably in the hundreds) that have at least enough similarity and age that the return is a meaningful representation of growing that grouping.

As for the formula, it is home grown.  The base for the formula started with the description of the formula that Prosper uses.  I like the formula they use and feel it is a better representation of ROI then the formula Lending Club posts.  The formula was then tweaked to support estimates.  So sorry, no literature, but the basis is what Prosper describes, so it isn't something I made up completely.

#### splat313

• Newbie
• Posts: 2
##### Re: ROI and Loss calculation
« Reply #10 on: August 07, 2014, 10:03:55 PM »
Hello,

I'm also attempting to understand how NSR calculates ROI.  In the formula given at https://www.nickelsteamroller.com/#!/stats/roi , what do L0 and Ln represent?

I appreciate any help, thanks!

#### brother7

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##### Re: ROI and Loss calculation
« Reply #11 on: August 07, 2014, 11:01:27 PM »
In the formula given at https://www.nickelsteamroller.com/#!/stats/roi , what do L0 and Ln represent?
The summation from L0 to Ln means to calculate for each loan from 0 to n, then add them.

#### Rob L

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• Posts: 2124
##### Re: ROI and Loss calculation
« Reply #12 on: January 27, 2016, 12:10:49 PM »
But again, I have to reiterate, the formula is not meant to be used on extremely small set of loans.  The number for any single loan is not meant to be used by itself, that is not what our tool is designed for.   Any estimated numbers that are generated can have weird results if there is not enough meaningful data to normalize the results.

Just a word of caution for others on a very old topic. The >100% Loss and < -100% ROI does not only show up when analyzing a small number of loans. I was interested in charge offs of 36 month loans issued between 1/1/2015 and 6/30/2015 and chose that subset for LC back test. The total loan count was about 121k, of which 1,323 were charged off. The charged off loan ROI was shown as -340% and the Loss 353%. Fortunately the NSR analysis provides all the individual numbers needed for me to calculate ROI and Loss any way I want. However, if one analyses loans over a short period of time (maybe less than a couple of years or so, I dunno) the NSR method of computing ROI and Loss appears to result in numbers that are not what one might expect.