### Author Topic: NAR doesn't make sense  (Read 4986 times)

#### Fred93

• Hero Member
• Posts: 2221
##### Re: NAR doesn't make sense
« Reply #15 on: March 08, 2017, 01:55:02 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 revised this response to be more clear/correct/directly responsive to the above...

The denominator is not simply your account balance, but is instead a SUM of each month's account balances, and thus has a factor of N hidden in it.

If the denominator had been written as the average balance x N, then the N would have been explicit.  The N is still in there, its just hidden.

So now the inside part is a kind of monthly return, which they turn into an annual return by raising 1+r to the 12th power.

You could create a similar sort of return formula where you took the N out of the denominator and put it in the exponent, as you describe, but that is not what they chose to do.

« Last Edit: March 09, 2017, 11:18:45 PM by Fred93 »

#### Emmanuel

• Full Member
• Posts: 157
##### Re: NAR doesn't make sense
« Reply #16 on: March 09, 2017, 07:18:41 PM »
Here's a blog post we wrote a while ago to (try to) explain NAR:

http://blog.lendingrobot.com/research/comparing-expected-return-and-net-annualized-return/

• Full Member
• Posts: 202
##### Re: NAR doesn't make sense
« Reply #17 on: March 10, 2017, 12:10:44 AM »
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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%.

You explained this much better than I did, and WAIR is indeed weighted as you suggest. I suppose what I should have stated is that the summation of payments,less adjustments, used in ANAR calculation is essentially weighted already since all interest payments in the numerator are based on interest % of the principal amount in the denominator (e.g., actual note purchases).

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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.

Most investors are interested in the return of their portfolio overall, not just a subset of the notes that don't default. There may of course be value in looking at the notes that don't default to analytical or predictive purposes, but a true return can't be fully calculated until completely after-the-fact. I am not really that concerned a subset of notes that don't default, because that gives me no insight into whether or not LC was a good investment or not. I once heard this analogy about inflation: If you exclude from an index all the items that are increasing in price, then you have no inflation. Likewise, my portfolio returns on LC are incredible this past year, but only if you don't look at the notes that have defaulted (or will default).

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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.

On this point, I completely agree. LC could do a better job in their ANAR making some sort of approximation to account for losses on notes that are in the current status. After all, this shouldn't be that difficult to do given that they have all the historical data and can see and model the trend line and can likely extrapolate the curve. In theory, they could do a similar thing to what is being done in customized loss rates. My guess is that if customized loss rates included an estimated write down for notes in current status that returns look a lot less rosy than what is on the ANAR in the first 12 months. This might be a good thing, however, as investors would have more realistic expectations.
« Last Edit: March 10, 2017, 12:16:04 AM by SLCPaladin »