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# Weighted average life (WAL), Choudhary Chapter 12

#### NNath

##### Active Member
Hi @David Harper CFA FRM , Under the Mortgage performance measure and weighted average life the PF (pool factor) refers to ‘pool factor’, which is assumed and is the repayment weighting adjustment to the notional value outstanding (O/S). What does that mean, how do we calculate from the O/S in table 12.1.

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#### David Harper CFA FRM

##### David Harper CFA FRM
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FYI, He accepted my LinkedIn invitation so I sent him the following message (cc @Nicole Manley )
Subject: Is it possible to get the spreadsheet that produced Table 12.1 in your book
Hello Mr. Choudhry,
I am a big fan. I teach the FRM, where your book "Structured Credit Products: Credit Derivatives & Synthetic Securitization, 2nd Edition" is assigned. We are trying to understand the Pool Factor calculations in Table 12.1. Is it possible to get a copy of the spreadsheet? Thank you! Cheers, David Harper

#### David Harper CFA FRM

##### David Harper CFA FRM
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Hi @NNath Moorad Choudhry was kind enough to reply to me (yay!). Here's what he said:

David Harper said the following: Hello Mr. Choudhry, I am a big fan. I teach the FRM, where your book "Structured Credit Products: Credit Derivatives & Synthetic Securitization, 2nd Edition" is assigned. We are trying to understand the Pool Factor calculations in Table 12.1. Is it possible to get a copy of the spreadsheet? Thank you! Cheers, David Harper

At 2:16 AM, Moorad Choudhry said the following: Hello David Thank you for the kind words, I appreciate it. I am glad the book is of value to you. Sadly, I don't have a copy of the book at home. Could you email me a scan of the page and I'll take a look? its mooradchoudhry@gmail.com Rgds Moorad

At 3:30 PM, David Harper said the following: Hi Moorad, Thank you! I access your book via my annual subscription to Safari books, here is the screenshot. I refer to Table 12-1 in Chapter 12: The page is broken up into two screenshots, please see these links: http://trtl.bz/choudhry-1 and http://trtl.bz/choudhry-2

At 4:27 PM, Moorad Choudhry said the following: Hello David The pool factor is simply an assumed number...one can use the CPR method whose formula is shown or simply say something like "we assume the notional will prepay by 0.05% every month". There is no fixed formula to it. The example in the table was from an RMBS transaction I worked on a long time ago, in 2004 I think....I don't have the spreadsheet itself, I only used the output so I could show an illustration of what the results look like. However you can easily produce one by using the CPR formula shown, just use an assumed SMM value. I hope this clarifies... Best Moorad

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#### NNath

##### Active Member
Hi @David Harper CFA FRM , Firstly, thanks, your diligence to the profession is admirable.

I look at your table in question 612.1 (page 12 of the question set) and the table 12-1 from the book and understand that from exam perspective, there no direct way (single formula instead of iteration) that the exam can query the calculation of WAL or can it? Just like WAC and WAM the question will have to give a table from which to calculate weighted average,

Also, on a separate note, I see the the formula for Single monthly mortality (SMM) and Absolute prepayment speed (APS) is exactly the same in table 12.2 i.e. Prepayments / Outstanding pool balance. This means they have same definition only the first one is for Mortgages and the other is for Auto loans?

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#### Delo

##### Active Member
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Is it fair to say
1. The difference between WAM and WAL is that WAL incoprporates "pre-payment" while WAM does not ?
2. WAM >= WAL

I am sorry I didn't get enough time to delve into this reading...

#### Mkaim

##### Well-Known Member
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Is it fair to say
1. The difference between WAM and WAL is that WAL incoprporates "pre-payment" while WAM does not ?
2. WAM >= WAL

I am sorry I didn't get enough time to delve into this reading...
Hi @Delo,

WAM = Weighted Average Maturity --> Sum of individual % loan weight (relative to pool outstanding balance) times it's remaining maturity
WAL = Weighted Average Life --> Sum of individual % payment relative to total scheduled payments times term. It's similar to duration but more appropriate for mortgage pools (MBS, RMBS, etc...)

Scheduled payments don't incorporate prepayments.

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#### Delo

##### Active Member
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Thanks Mkaim, but "Scheduled payments don't incorporate prepayments. for WAL" is sounding contradictory to what i saw in notes.
See Page 11, David's Questions PDF

#### Mkaim

##### Well-Known Member
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Thanks Mkaim, but "Scheduled payments don't incorporate prepayments. for WAL" is sounding contradictory to what i saw in notes.
See Page 11, David's Questions PDF
View attachment 642
Hi @Delo,

For the purpose of the exam then, you should assume it incorporates prepayments. While I worked in pricing for several years, I've seen WALs both with and without any prepayment assumptions. When a new agency MBS was issued, the WAL for the pool didn't always include prepayment assumptions. You can enter an MBS in a pricing engine and get back a WAL figure even without entering any prepayment assumptions as it will do what I mentioned above.

#### David Harper CFA FRM

##### David Harper CFA FRM
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I agree with @Mkaim

There is firstly the easy question: 2. Is WAM >= WAL? The answer is yes, unless the bond is a bullet; in any amortizing bond or MBS, the WAL must be less than WAM due to (any) principal repayment.

Second, weighted average life (WAL) is new to FRM 2016 (due to Choudry), it never appeared before. And, you can see the above (incl correspondence with Choudhry himself), I personally do not think it is even defined in the assignment (hint: I wouldn't worry too much about it this year); all we get is the summation of t*PF(s). However, we can assume, based on Choudrhy's answer (if not the actual text), that he defines it to include both scheduled and unscheduled principal prepayments. (because he implies it includes the effect of the CRP assumption; at least in my models, CPR informs prepayment exclusively in addition to scheduled/amortizing prepayments). In short, I infer that Choudhry's WAL includes all estimated prepayments.

Nevertheless, it makes sense to me Mkaim has seen it both ways. Take the wikipedia definition https://en.wikipedia.org/wiki/Weighted-average_life. The WAL of 17.97 years for a 30-year amortizing loan given a rate of 4% is assuming only scheduled prepayments. In the models I've done for MBS, the model includes scheduled principal plus unscheduled principal (this latter informed by PSA assumption) such that you could compute a WAL for either. And the WAL (scheduled + estimated, unscheduled) < WAL (scheduled only) < WAM. I hope that helps, thanks. Good luck tomorrow!

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#### Mkaim

##### Well-Known Member
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I agree with @Mkaim

There is firstly the easy question: 2. Is WAM >= WAL? The answer is yes, unless the bond is a bullet; in any amortizing bond or MBS, the WAL must be less than WAM due to (any) principal repayment.

Second, weighted average life (WAL) is new to FRM 2016 (due to Choudry), it never appeared before. And, you can see the above (incl correspondence with Choudhry himself), I personally do not think it is even defined in the assignment (hint: I wouldn't worry too much about it this year); all we get is the summation of t*PF(s). However, we can assume, based on Choudrhy's answer (if not the actual text), that he defines it to include both scheduled and unscheduled principal prepayments. (because he implies it includes the effect of the CRP assumption; at least in my models, CPR informs prepayment exclusively in addition to scheduled/amortizing prepayments). In short, I infer that Choudhry's WAL includes all estimated prepayments.

Nevertheless, it makes sense to me Mkaim has seen it both ways. Take the wikipedia definition https://en.wikipedia.org/wiki/Weighted-average_life. The WAL of 17.97 years for a 30-year amortizing loan given a rate of 4% is assuming only scheduled prepayments. In the models I've done for MBS, the model includes scheduled principal plus unscheduled principal (this latter informed by PSA assumption) such that you could compute a WAL for either. And the WAL (scheduled + estimated, unscheduled) < WAL (scheduled only) < WAM. I hope that helps, thanks. Good luck tomorrow!
Thanks @David Harper CFA FRM ,

Thanks for clarifying and thanks for all the help. Gotta go check into the hotel where the exam is being offered. Good luck for the exam today (India) @Delo