Author Topic: NAR doesn't make sense  (Read 3975 times)

mrwhizzard

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NAR doesn't make sense
« on: March 02, 2017, 05:18:05 PM »
So, I thought I at least had a rough understanding of how LC was computing NAR. However, today I see that even though my "Adjusted Account Value" is slightly below the value of the single ($5000) deposit I made about 18 months ago, the Adjusted NAR is (slightly) greater than 0:



What explains this? Is it taking into account some pending payment that hasn't shown up in the cash balance yet?
« Last Edit: March 02, 2017, 05:19:38 PM by mrwhizzard »

Paulie2083

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Re: NAR doesn't make sense
« Reply #1 on: March 03, 2017, 01:21:04 AM »
$4,999.47 + $14.52 available cash

mrwhizzard

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Re: NAR doesn't make sense
« Reply #2 on: March 03, 2017, 01:34:30 AM »
$4,999.47 + $14.52 available cash

I'm pretty sure the available cash is already included in the account value, based on the detailed breakdown.

SMWinnie

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Re: NAR doesn't make sense
« Reply #3 on: March 03, 2017, 07:47:31 AM »
Link to a nice explanation for why a time-weighted rate of return can be negative for a gain or positive for a loss.

The basic idea is that time-weighted rates of return abstract away from account size. Put another way, a time-weighted rate of return presumes that you had the same amount invested at all times. If, for instance, one has good returns on a relatively smaller amount of money and then bad returns on a larger amount of money, one might have a dollar loss with a positive rate of return.

OP (mrwhizzard) indicates a single deposit. If there were no withdrawals and no Folio purchases, then my guess is that: (1) OP's portfolio had modest gains; (2) OP reinvested the gains; and (3) OP's portfolio then suffered losses on the larger balance that more than offset the original gains.

Here's a quick, extreme hypothetical for illustration:
  • Invest $1000.
  • Portfolio doubles in first year.
  • Portfolio loses 55% in second year.
  • New balance is $900 for a 10% loss...
  • ...but the time-weighted rate of return is a little over 20%.
LC's discussion of their formula suggests a couple of other anomalies, but the formula basically looks sound. It accounts for the real cash flows, including LC's fees, and excludes accrued interest.

mrwhizzard

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Re: NAR doesn't make sense
« Reply #4 on: March 03, 2017, 10:40:10 AM »
Thanks for the links and example, they were informative.

Fred93

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Re: NAR doesn't make sense
« Reply #5 on: March 03, 2017, 12:05:31 PM »
Link to a nice explanation for why a time-weighted rate of return can be negative for a gain or positive for a loss.

But NAR is not a time-weighted return, so this explanation does not apply.

Fred93

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Re: NAR doesn't make sense
« Reply #6 on: March 03, 2017, 12:58:03 PM »
So, I thought I at least had a rough understanding of how LC was computing NAR. However, today I see that even though my "Adjusted Account Value" is slightly below the value of the single ($5000) deposit I made about 18 months ago, the Adjusted NAR is (slightly) greater than 0:



What explains this? Is it taking into account some pending payment that hasn't shown up in the cash balance yet?

If you look at the formula for ANAR...

you will see that the numerator is just a sum of various payments and the adjustment amount.  It looks complicated, but if you cancel the Pi that's shown twice in the numerator, you see it is just a sum.  It is intended to be all the payments that hit your account due to the loans (ie excluding deposits and withdrawals).  These are the payments that CHANGE your total account value.  If you had no deposits or withdrawals, then this sum should be equal to the difference between your present (adjusted) account value and original account deposit.

Your suggestion that there might be a timing difference, ie they might have calculated ANAR at a different time than they calculated the last adjusted account value is a good idea.  After all, they have never said WHEN they calculate ANAR.

Another possibility is that your account had some fee assessed of some obscure type which reduced its value by some small amount, and which was not used in the ANAR calculation.  This would be a bug in the ANAR calculation.  Things like this are quite a bit of work to reconcile.  You took the easy way out by looking at the final account value, whereas the ANAR calculation (at least per the docs) sums up all the payments one by one.  You could theoretically go back and look up every little payment one by one, pull them into a spreadsheet, and calculate ANAR yourself, and figure out which one they left out or whatever, but it would be a horrible pain in the ass.  After you complete the effort, you would have to beat LC over the head to get them to admit that its an error, for which they would give you a prize of zero.

Another possibility is inconsistent rounding.  The basic LC accounting does this nice thing where they record every payment out to many decimal places, to be fair for all the very small payments.  However, not every LC programmer understands or appreciates how that works.  (The folio pages, for example, don't let you see many things past the 2nd decimal place.)  Could be that the guy who wrote the ANAR calculation code was similarly decimal-appreciation-challenged.

Because your net return is very close to zero, it only takes a small offset of some kind to create the discrepancy you see.  This could easily be the result of some obscure rounding error.

mrwhizzard

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Re: NAR doesn't make sense
« Reply #7 on: March 03, 2017, 02:28:54 PM »
You could theoretically go back and look up every little payment one by one, pull them into a spreadsheet, and calculate ANAR yourself, and figure out which one they left out or whatever, but it would be a horrible pain in the ass.

Yes, I briefly considered that, and then decided that posting here was a better use of my time. :D But you did encourage me to send a note to LC support and ask them to explain the discrepancy. I'm sure that will be even less productive, but I figure that's kind of their job.

SMWinnie

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Re: NAR doesn't make sense
« Reply #8 on: March 03, 2017, 04:26:28 PM »
(*snip*)
If you look at the formula for ANAR...you will see that the numerator is just a sum of various payments and the adjustment amount.  It looks complicated, but if you cancel the Pi that's shown twice in the numerator, you see it is just a sum.
Thanks for the correction. Let me pick apart LC's ANAR formula and see if I have this right.

The inner term of the ANAR starts with a numerator of (all payments to the account minus fees, writeoffs and note status adjustments). The denominator is (running total of the N various monthly principal amounts).

Numerator/denominator isn't evaluated for each period and geometrically linked, so it's not a time-weighted return. The running total of principal weights makes the inner term a type of average monthly gain.

Then that gets annualized by [(1 + "avg monthly gain" inner term)^12] - 1.

Does that sound about right?

Edward Reid

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Re: NAR doesn't make sense
« Reply #9 on: March 04, 2017, 11:07:44 PM »
I don't understand the formula entirely. Oh, I can read it, the trouble is it doesn't all make sense. However it appears to me that the ANAR is a most-recent-month figure. The Adjusted Account Value is the result of all gains and losses over the history of the account, adjusted for the status of notes. Thus there's no reason they should be even closely correlated.

The "to the twelfth power" tells me that this is a single-month calculation. Raising it to the twelfth power is to annualize it.

And I assume the sums are "over all active notes in the account". (It cannot include paid-off or charged-off loans, since the principal on these is zero and would result in a divide by zero.)

I don't understand the "Principal[]/Principal[]" inside the sum in the numerator.

Then the Note Status Adjustment Amount (NSAA) is only a single value -- it's not inside the sum -- and so is not a per-note adjustment. And yet it has a subscript -- it's the NSAA for the N-th note. This seems lot a (rather large) bit of hand-waving, since it's obviously in fact an adjustment for each note status.

So what I make of the formula is:
  • Sum all credits and debits for the account, excluding deposits and withdrawals.
  • Subtract a separately calculated status adjustment amount.
  • Divide by the total principal in the account, resulting in a monthly rate of return.
  • Annualize.
(Describing it this way also avoids the issue of notes with zero principal.)

I see no indication that past months feed into the ANAR at all. And as others have noted, we don't know when the ANAR is calculated -- or for that matter, what month is used for the calculation, even whether it's a calendar month, the past 30 days, the last full month since the account was opened, or something else. (Someone who has watched their ANAR daily could probably answer this.)

We all notice large swings in the ANAR depending on what has happened in the past month, which fits with it being a single-month calculation.

OTOH, the anomalies I noted above make me distrust the formula. If I were told to code that formula -- and I'm retired from over 40 years of programming -- I would press for answers related to the points above. I would say what's the sum over -- if it's all notes in the account, then I have a divide by zero. I would say why do you have P[]/P[] inside the sum. I would say where is this "Note Status Adjustment Amount" coming from and why is it subscripted when it's not inside the sum. That's a mighty lot of questions for a little formula.

Edward

Fred93

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Re: NAR doesn't make sense
« Reply #10 on: March 05, 2017, 12:20:41 AM »
I don't understand the formula entirely. Oh, I can read it, the trouble is it doesn't all make sense.

The guys who wrote this aren't good at writing formulas.  Takes a bit of work to figure out what they meant.  You failed.

Quote
And I assume the sums are "over all active notes in the account". (It cannot include paid-off or charged-off loans, since the principal on these is zero and would result in a divide by zero.)

No, it includes all notes, including the ones paid off.

Quote
I don't understand the "Principal[]/Principal[]" inside the sum in the numerator.

Its quaint.  I presume they wrote it that way to make a subexpression look a certain way.

Quote
Then the Note Status Adjustment Amount (NSAA) is only a single value -- it's not inside the sum -- and so is not a per-note adjustment. And yet it has a subscript -- it's the NSAA for the N-th note. This seems lot a (rather large) bit of hand-waving, since it's obviously in fact an adjustment for each note status.

No.   The index (ie the subscript) that goes from 1 to N is over MONTHS, not loans.  The numbers such as interest are all the interest received in that month from all your notes.  There are implied sums over notes not shown.  There is only one adjustment factor, not one for each month.  That's why it is outside the sum-over-months.

I don't know their precise definition of months.  Nobody does.  ANAR updates much more often than monthly.  It changes every day, so there is a bit of a mystery there.  I suspect that the last month is just calculated using everything received so far in the month.  Once you have looked at this stuff for awhile, you realize they never do anything sophisticated, so they've almost surely done something simple.  You will notice that there's actually nothing magic about months in the formula.  In the numerator, when you sum over the months, that's just summing over everything received over all time.  In the denominator, summing over months just gets you a sort of weighted principal amount.  In that case, details of the definition of a month just change the weighting slightly.

Quote
If I were told to code that formula -- and I'm retired from over 40 years of programming -- I would press for answers related to the points above.

The guy who wrote the code probably did ask a lot of questions.  Maybe he even got answers.  Some of them were probably even correct answers.  Its just that nobody took the answers and used them to improve the documentation.  A lot of LC's documentation has difficulties such as this.  The documentation for the API and the fields in the various CSV files suffers from similar horrors.  There are many totally undocumented fields.  You get used to it.

SLCPaladin

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Re: NAR doesn't make sense
« Reply #11 on: March 06, 2017, 11:32:48 AM »
ANAR and adjusted account value have always been a little bit of a mystery, but this thread has helped me understand it better. The more I think about it, the more I think it makes sense, and I also think the formula is the truest approximation that can be given. I don't think there is any contradiction with the $5k initial deposit, an adjusted account value of approximately $5k, and an ANAR of .17%. Here is how I see it:

1) An investor makes a deposit into LC.
2) LC funds are used to select notes to invest in.
3) Each note has its own interest rate; the sum of all interest rates is the weighted average.
4) The actual return can only be known in retrospect and after all loans have either been paid off or charged off.
5) In the interim, one way (is it the best?) to approximate the return given the uncertainty of future payments is to sum all payments and adjustments as a percentage of principal and then annualize it.
6) The adjusted account value is an extrapolated amount based partly on your current payments and partly from loss assumptions from LC platform based on the trailing 9 months.

The ANAR and adjusted account value are kind of just projections, but they have some validity because it uses historical 9-month loss assumptions. But it is still fairly uncertain, and your exact loss rates will not match the LC platform as a whole. Mathematically, the fact that you had an initial deposit of $5k and an adjusted account value of roughly $5k doesn't mean that ANAR should be 0%.

Here is another way to think about it: take the sum of all your payments to-date, less adjustments (charge-offs and service fees), and apply some adjustment amount to take into account future charge-offs. This will give you a monthly return. Annualize it and then apply it to your note principal for the remaining life of your note amount and you will get some other number (i.e., adjusted account amount). This other number, when compounded at an .17% for the time period of your weighted note terms, just happens to be astonishingly close to your initial investment amount. This isn't evidence that the formula is overestimating anything at all or being misleading, it's just dealing with uncertainty in the way it was designed.

You actual, after-the-fact return will of course be different than what you see here, but this can't be known until all notes have run their full course, and at that point it's a very simple calculation. This is just an interim approximation. The easiest way to see how fickle the ANAR is and adjusted account amount is to tweak it yourself:

« Last Edit: March 06, 2017, 11:55:32 AM by SLCPaladin »

mrwhizzard

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Re: NAR doesn't make sense
« Reply #12 on: March 06, 2017, 02:44:27 PM »
The ANAR and adjusted account value are kind of just projections, but they have some validity because it uses historical 9-month loss assumptions. But it is still fairly uncertain, and your exact loss rates will not match the LC platform as a whole. Mathematically, the fact that you had an initial deposit of $5k and an adjusted account value of roughly $5k doesn't mean that ANAR should be 0%.

The adjustment that turns your account value into an adjusted account value, and your NAR into an ANAR, should be the exact same adjustment. If it's possible for these two calculations to get out of sync, I think they're doing it wrong.

mrwhizzard

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Re: NAR doesn't make sense
« Reply #13 on: March 06, 2017, 05:17:14 PM »
Interestingly, I now see the exact opposite: adjusted account value shows a (slight) gain, but ANAR now shows a (slight) loss:


Edward Reid

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Re: NAR doesn't make sense
« Reply #14 on: March 08, 2017, 12:54:08 PM »
The index (ie the subscript) that goes from 1 to N is over MONTHS, not loans.

I don't care if I convince you, but for the sake of anyone reading this for information, your discussion makes no sense. If the index were over months, the annualization would consist of raising to the power 12/N rather than just 12.

I think it makes sense, and I also think the formula is the truest approximation that can be given.

I don't know if it makes sense to call any estimate "truest" in general. Different investors need different estimates, and all must recognize that the number is only an estimate, not truth.

Generally I agree with your list. Comments:

Quote
3) Each note has its own interest rate; the sum of all interest rates is the weighted average.

Perhaps you meant this, but the WAIR is weighted (as the name suggests) by the principal amount. I assume that it's weighted by the outstanding principal of the note, which makes sense, but I haven't found an explicit statement to that effect on LC. For example, if you have a note with $100 outstanding at 12% and a note with $300 outstanding at 14%, your WAIR is 13.5%.

Quote
4) The actual return can only be known in retrospect and after all loans have either been paid off or charged off.

This can be true for a subset of your notes. You can know the final return on some notes without waiting for all loans in your account to run their course.

Quote
The ANAR and adjusted account value are kind of just projections

No "kind of" about it. They are just projections. (I'm assuming that by "just" you mean "only", not "equitable".)

Quote
they have some validity because it uses historical 9-month loss assumptions.

True, though I don't know why they limit it to nine months. Some loans fail more than nine months out.

Quote
Here is another way to think about it: take the sum of all your payments to-date, less adjustments (charge-offs and service fees), and apply some adjustment amount to take into account future charge-offs. This will give you a monthly return.

That will give you a total return, not a monthly return. You could still annualize it, but the power you need for that would be 12/N rather than 12, where N is the number of months. And this would be a lot less meaningful, since loans perform much better early on, and since most investors add notes along the way, and since most of us look at that number for prediction. The adjustment is based on recent data to give better predictions.

Quote
The easiest way to see how fickle the ANAR is and adjusted account amount is to tweak it yourself:

That's a good tool. I have two issues with it.

First, the defaults they give you are based on nine-month projections. Enough loans fail more than nine months out to make the defaults significantly over-optimistic.

Second, they do not discount loans in current status at all, and do not even allow you to enter a custom loss estimate for current status. Some loans in current status do charge off within nine months. Since most investors have far more notes in current status than any other status -- at the moment, 95% of my notes are current -- the lack of a discount for current status makes a big difference.

The adjustment that turns your account value into an adjusted account value, and your NAR into an ANAR, should be the exact same adjustment. If it's possible for these two calculations to get out of sync, I think they're doing it wrong.

I'm not sure I'd call it "wrong", simply because we have to realize that both results are estimates and therefore an exact comparison is also only an estimate. I agree that it appears there's either a difference in the way they are computed or that they are not synchronized. The blog page New Adjusted Return Metric implies that the same adjustment is being applied.

Edward