### Author Topic: Help Understanding NAR, IRR when Reinvesting Principal and Interest  (Read 13000 times)

#### Deming

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• Posts: 39
##### Help Understanding NAR, IRR when Reinvesting Principal and Interest
« on: July 15, 2014, 06:23:48 PM »
I'm trying to understand LC NAR, IRR, and my account balance.

Suppose I have an account where I instantly reinvest all paid out principal and interest in new loans.  Assume my Adjusted Net Annualized Return (ANAR) is 17% with Average Age of Portfolio of 6 months.  Over the next 36 months, I continue this strategy of instantly buying new loans with paid out principal and interest until I finally reach an Average Age of Portfolio of 24 months with LC reporting ANAR of 7%.

QUESTIONS:
1. Since I am reinvesting the paid out principal and interest, will it take longer than 18 months to for the Avg Age to go from 6 to 24 months? Is there some rule of thumb for this?
2. Assuming instant reinvesting of principal and interest (no cash drag), would the IRR and ANAR be about the same?
3. Did I earn about 17% for the first 6 months PLUS a declining rate from 17% down to 7% for months 6 thru 36?
4. OR did I only earn about 7% annualized over the entire 36 months?

Thank you for sharing your expertise.

#### TonySaunders

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• Posts: 194
##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #1 on: July 15, 2014, 06:41:07 PM »
1. Yes. When you buy new notes the average age of your portfolio decreases. (I don't know the specific formula that LC uses in it's statistics.)
2. If you neglect the time that cash is idle in your account, then IRR and NAR ought to be about the same (ANAR will be slightly different, because it's "adjusted", of course). But that will never happen in practice. Cash is unavoidably idle while you wait for loans to be approved/funded (if nothing else).
3. No.
4. Yes.
« Last Edit: July 15, 2014, 06:43:17 PM by TonySaunders »

#### TonySaunders

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #2 on: July 15, 2014, 06:54:07 PM »
More accuracy regarding question 2 and 4:

You are basically right... but in this scenario you are reinvesting the interest you earn, so that the interest earns more interest. NAR doesn't account for this compounding interest, but IRR does.

So, you actually will earn MORE than the 7% reported by NAR.

In this scenario (we are neglecting the effect of idle cash on IRR) a 7% NAR at 36 months would be about the same as a 7.5% IRR at 36 months. (An original investment of \$1000 would be \$1225-ish after 36 months.)
« Last Edit: July 15, 2014, 07:19:34 PM by TonySaunders »

#### TonySaunders

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #3 on: July 15, 2014, 06:58:56 PM »
Hmmm... maybe someone should confirm that. I'm pretty sure though.

#### AnilG

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #4 on: July 15, 2014, 07:48:19 PM »
I doubt you can ever see the Avg age above 18 months for portfolio made of 36 month loans if you are reinvesting the monthly inflow from payments. Recall, every time you reinvest monthly payment, you get new loans that have age of zero. The arithmetic average of zero age loans and 36 month age loans is 18 months.

Simplified:

Average age = (0 + 36) / 2 = 18 months.

Complicated:

For every 36 loans you get approx one new loan every month. This doesn't take into consideration of reinvestment of monthly payment from loans purchased using reinvestment. It shows the maximum limit on average age. Actual average age will be somewhere between 0 and 27 months, most likely about 10 - 18 months.

Average Age = (1 * (0 + 1 + 2 + 3 .... + 35) + 36 * 36) / (36 + 35) = (35(36)/2 + 1296) /71 = (630 + 1296) / 71 = 27 months.

QUESTIONS:
1. Since I am reinvesting the paid out principal and interest, will it take longer than 18 months to for the Avg Age to go from 6 to 24 months? Is there some rule of thumb for this?
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#### Fred

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #5 on: July 16, 2014, 01:55:22 AM »
It is difficult to get IRR to match NAR (much less ANAR), because NAR takes into account late fees, charge offs, and recoveries from every periodic.

NAR formula:

To understand NAR behavior, it's probably best to construct a longitudinal analysis (i.e., throughout loan terms) using 2 loans, simulate some late payments, charge-offs & recoveries, and see how NAR changes on each period because of them.

Also, NAR is an "instantaneous" number (to borrow from Calculus class), not an average number for a period of time.  NAR changes every period.  I don't think we can use NAR to answer your questions 3 & 4.

Finally, when you start trading notes in FOLIOfn, your NAR and ANAR will be unreliable because LC uses OutstandingPrincipal, rather than PurchasePrice, for its PrincipalInvested values it the monthly statements.

#### Fred93

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #6 on: July 16, 2014, 02:33:39 AM »
It is difficult to get IRR to match NAR (much less ANAR), because NAR takes into account late fees, charge offs, and recoveries from every periodic.

It is impossible to get them to match.  NAR is a hack.  It contains no notion of time at all, so it can never properly account for the time value of money.

There is no value in even talking about how stupid it is, except that LC uses it, so people talk about it.  NAR is a hack.

Real men use IRR.

#### TonySaunders

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #7 on: July 16, 2014, 11:41:56 AM »
It is difficult to get IRR to match NAR (much less ANAR), because NAR takes into account late fees, charge offs, and recoveries from every periodic.

IRR also accounts for these things. If you pay a fee (or whatever) then you no longer include that fee in the value of your account.

#### TonySaunders

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• Posts: 194
##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #8 on: July 16, 2014, 11:57:35 AM »
Also, NAR is an "instantaneous" number (to borrow from Calculus class), not an average number for a period of time.  NAR changes every period.  I don't think we can use NAR to answer your questions 3 & 4.

Yes. Well, kinda. It's an average of all the instantaneous values. In principle, it let's you say "I'm earning a rate of 8.5% at any particular time" even though your actual instantaneous rate might be up/down from minute to minute or month to month.

#### Deming

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• Posts: 39
##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #9 on: July 16, 2014, 01:26:27 PM »
Excellent information, thank you everyone.

Now I clearly understand:
1. My IRR and NAR (not exactly the same thing and NAR is a hack) will decrease as my avg portfolio age increases. IRR will be less than NAR.
2. By always reinvesting the principal and interest, the avg portfolio age will be less than the actual time which passes due to adding the new notes of zero months. The expected portfolio max avg age will be about 1/2 of the avg terms of the notes. So about 18 months for 36 month term notes.

So one way of estimating my expected long term NAR is to take the average term of my notes, divide by 2 and then use the LC chart https://www.lendingclub.com/info/statistics-performance.action and find the median point for that avg portfolio age with similar Weighted Avg Interest Rate.

For example, suppose I have all 36 month notes with Weighted Avg Interest Rate of 20%. So, after a long time, like maybe 5 years, my expected NAR would be around 9.4% as taken from the LC chart median value at 18 months. My IRR will be less than the 9.4%, but likely close to it.

Is that a reasonable approach to estimating my expected long term NAR (My IRR will be less than the NAR) ?

#### TonySaunders

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #10 on: July 16, 2014, 03:12:31 PM »
For example, suppose I have all 36 month notes with Weighted Avg Interest Rate of 20%. So, after a long time, like maybe 5 years, my expected NAR would be around 9.4% as taken from the LC chart median value at 18 months. My IRR will be less than the 9.4%, but likely close to it.

Is that a reasonable approach to estimating my expected long term NAR (My IRR will be less than the NAR) ?

Whether NAR is a reasonable metric is totally dependent what you are trying to measure. If you want to know what the long-term return on your investment will be then your current NAR is pretty much the completely wrong tool for the job. That's because it measures the rate you are getting right now on your active notes (with an average age of 18 months or whatever) and not the return you will eventually get on your notes after you've owned them for the full 36 month lifetime.

Hmm... I just went looking for rates of returns on mature notes. It seems like LC is rather fixated on NAR. Which is nice and everything, but as you clearly have learned, it will decrease significantly as notes age, and MOST of LC's notes are quite young (because LC is growing fast).

I guess you could look at the right edge of the NAR graph to get a better idea about the performance of a note after it's full 36 month lifetime. But THAT isn't particularly satisfying data.
« Last Edit: July 16, 2014, 03:14:14 PM by TonySaunders »

#### turing

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #11 on: July 16, 2014, 03:44:53 PM »
It is impossible to get them to match.  NAR is a hack.  It contains no notion of time at all, so it can never properly account for the time value of money.

There is no value in even talking about how stupid it is, except that LC uses it, so people talk about it.  NAR is a hack.

Real men use IRR.

I agree that NAR is not a good tool for measuring your actual return.  That begs the question, why does LC use NAR instead of IRR?

#### lascott

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #12 on: July 16, 2014, 03:46:27 PM »
I guess you could look at the right edge of the NAR graph to get a better idea about the performance of a note after it's full 36 month lifetime. But THAT isn't particularly satisfying data.
That is exactly what I was doing.
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#### Deming

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• Posts: 39
##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #13 on: July 16, 2014, 04:04:10 PM »
Quote
I guess you could look at the right edge of the NAR graph to get a better idea about the performance of a note after it's full 36 month lifetime. But THAT isn't particularly satisfying data.

So are 99% of all LC investors going to end up with a NAR in the range of about 5% to 10% (at right edge of graph) in the end?  IRR will be slightly less than that.

Does this mean that a strategy like "D-G Top Score" on InterestRadar predicting overall IRR of 13-15% is just a dream?

LC-Advisors offers a fund which has annualized returns of about 8% after accruing for future losses. I guess that is a pretty good return if all of us "do-it yourselfers" are only going to achieve 5-10% in the end anyway?

#### Fred

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##### Re: Help Understanding NAR, IRR when Reinvesting Principal and Interest
« Reply #14 on: July 16, 2014, 04:37:19 PM »
So are 99% of all LC investors going to end up with a NAR in the range of about 5% to 10% (at right edge of graph) in the end?

Accounts on the right edge of the chart are essentially idle accounts; i.e., no new investments.  Like several people already mentioned in this thread, new investments (even re-investment of payments received) keep your portfolio age low.

Furthermore, if you read LC 10-K, you'll notice that the charge-off rates during 2008-2009 were higher.

Perhaps those right-edge accounts gave up on LC, and are transferring their money to somewhere else.