IO/PO Strip Effective Duration query

[Roshan Ramdas]

Hi David,

Need your guidance with regards to the below question from the end of GARPs Market Risk book.

Consider IO/PO strips based on original pass through MBS whose effective duration is 5 years. If the PO tranche has an effective duration of 20 years, what would most likely be the effective duration of the IO tranche ?

A. -25 years
B. -15 years
C. 0 years
D. 12.5 years

GARP's answer (5 - 20 = -15 years)

They have arrived at this answer by simply taking a diff b/w the overall pass through duration (5 years) & the PO strip duration (20 years).

In my mind the values of the IO and the PO securities need to also be taken into consideration as well i.e., it is the weighted average of the IO & PO strip duration's that equate to the duration of the pass through.

This question does not tell us what the value of the IO & PO strips are.

Options C & D can be ruled out as IO strips come with negative duration.

But why cannot option A (-25 years) be correct ??

Thank you

 

[David Harper CFA FRM]

Hi @Roshan Ramdas

I totally agree. I do not like this question, it depends a the notion that (effective) duration is preserved, which is clearly NOT true. Dollar duration is preserved (your mention of "weighted average" is really key!). Abstractly we'd parse the portfolio with a condition to preserve dollar duration (i.e., effective duration * price, where effective duration is the approximation of modified duration in an MBS) such that:

V(0)*D(0) = V(1)*D(1) + V(2)*D(2), in this two-tranche case:
V(MBS)*D(MBS) = V(po)*D(po) + V(io)*D(io), and
D(io) = [V(MBS)*D(MBS) - V(po)*D(po) ]/V(io), so for example if the value of the principle tranche is $70 and the value of the io tranche is $30 then:
D(io) = [100*5 - 70*20]/30 = -30 duration for the io. So, yes, -25 seems plausible!

I checked Veronesi and I can see how somebody would miss the importance of "weighted average" because his example at 8.4 on page 317 shows D(IO) = -21.19 and D(PO) = 17.21 which at first glance maybe looks a "mere difference" consistent with the mentioned original pass thru duration of 4.46.

But it's a weighted difference which is maybe an unfamiliar way to refer to the dollar duration:
V(MBS)*D(MBS) = V(po)*D(po) + V(io)*D(io) -->
634.76*4.46 = 423.98*17.21 + 210.78*(-21.19); i.e., I am getting the values from interest rate 5.00% row on table 8.7. If we applied the method implied by the question above, we would observe an original pass thru duration of 4.46 years and a PO duration of 17.212 years, then we would mistakenly conclude the IO durati0n is 4.46 - 17.212 = -12.752. But that's wrong as duration is not itself preserved, rather we would need:
D(io) = [V(MBS)*D(MBS) - V(po)*D(po) ]/V(io) = [(634.76*4.46) - (423.98*17.212)]/210.78 = -21.19 years. So, yes, I definitely do agree with you!

 

[Roshan Ramdas]

Hi David,

Apologies,.....I am just going through the focus review videos & am struggling with a few of the questions.

Query 1 is with respect to a simple illustration of the"Total Return Swap".

I have attached a screenshot of the question.

There is a line in the problem which states that the MTM value of the loan falls by 2%. I read the fall in MTM value as being a portfolio depreciation.

Going by the description of the Total Return Swap

The protection buyer pays (Interest + Portfolio Appreciation)
The protection buyer receives (Interest + Portfolio Depreciation + Spread)

Given that we are dealing with a 2% decline in MTM value (which to me is a depreciation),..should not the 2% be a part of what the protection buyer receives & not what he pays -

i.e.,
Helman pays = 300*(6.5%/2)
Helman receives = 300*(4.5%/2+2%)

Thank you

 

[Roshan Ramdas]

Hi @Roshan Ramdas

I totally agree. I do not like this question, it depends a the notion that (effective) duration is preserved, which is clearly NOT true. Dollar duration is preserved (your mention of "weighted average" is really key!). Abstractly we'd parse the portfolio with a condition to preserve dollar duration (i.e., effective duration * price, where effective duration is the approximation of modified duration in an MBS) such that:

V(0)*D(0) = V(1)*D(1) + V(2)*D(2), in this two-tranche case:
V(MBS)*D(MBS) = V(po)*D(po) + V(io)*D(io), and
D(io) = [V(MBS)*D(MBS) - V(po)*D(po) ]/V(io), so for example if the value of the principle tranche is $70 and the value of the io tranche is $30 then:
D(io) = [100*5 - 70*20]/30 = -30 duration for the io. So, yes, -25 seems plausible!

I checked Veronesi and I can see how somebody would miss the importance of "weighted average" because his example at 8.4 on page 317 shows D(IO) = -21.19 and D(PO) = 17.21 which at first glance maybe looks a "mere difference" consistent with the mentioned original pass thru duration of 4.46.

But it's a weighted difference which is maybe an unfamiliar way to refer to the dollar duration:
V(MBS)*D(MBS) = V(po)*D(po) + V(io)*D(io) -->
634.76*4.46 = 423.98*17.21 + 210.78*(-21.19); i.e., I am getting the values from interest rate 5.00% row on table 8.7. If we applied the method implied by the question above, we would observe an original pass thru duration of 4.46 years and a PO duration of 17.212 years, then we would mistakenly conclude the IO durati0n is 4.46 - 17.212 = -12.752. But that's wrong as duration is not itself preserved, rather we would need:
D(io) = [V(MBS)*D(MBS) - V(po)*D(po) ]/V(io) = [(634.76*4.46) - (423.98*17.212)]/210.78 = -21.19 years. So, yes, I definitely do agree with you!

Thank you David,....I just hope that such questions do not turn up on the actual exam.

 

[Roshan Ramdas]

Hi David,

Query 2 with respect to the Credit Risk focus review video. I have attached a screenshot of the question. Please let me know if you are not able to view the s/shot on this or my earlier question and I will type it out.

This question tests us on the allocation of prepaid principal b/w different tranches.

This appears to be very much in line with the concept of "shifting interest", which is a form of credit enhancement. Here is the description from Adam B. Ashcraft on shifting interest - "Senior investors are also protected by the practice of shifting interest, which require that all principal payments be applied to senior notes over a specified period of time (usually the first 36 months) before being paid to mezzanine bondholders. During this time, known as the "lockout period", mezzanine bond-holders receive only the coupon on their notes."

The question in the screenshot comes with a "no lockout period" assumption. That to me implies that "shifting interest" is not being used. In a case where shifting interest is not used, cannot the prepaid principal be spread between tranches based on the size of the tranche ?

In the case of Junior Tranche A, 200/600*300 = $100

Once again, even if we were to assume that prepaid principal is to indeed be going to the senior tranches first,.....why are we not taking scheduled principal payments into consideration ? The solution simply gets us to assume that all of the prepaid principal is being used to pay off the senior tranche ($250 mn),....but I would expect some scheduled principal payments to be made to the senior tranche as well and in which case, the amount of prepaid principal routed to junior tranche A cannot simply be 300-250 ??

Thank you

 

[Roshan Ramdas]

Hi David,

Apologies,.....I am just going through the focus review videos & am struggling with a few of the questions.

Query 1 is with respect to a simple illustration of the"Total Return Swap".

I have attached a screenshot of the question.

There is a line in the problem which states that the MTM value of the loan falls by 2%. I read the fall in MTM value as being a portfolio depreciation.

Going by the description of the Total Return Swap

The protection buyer pays (Interest + Portfolio Appreciation)
The protection buyer receives (Interest + Portfolio Depreciation + Spread)

Given that we are dealing with a 2% decline in MTM value (which to me is a depreciation),..should not the 2% be a part of what the protection buyer receives & not what he pays -

i.e.,
Helman pays = 300*(6.5%/2)
Helman receives = 300*(4.5%/2+2%)

Thank you

Hi David,

Please ignore this query. Just found a link wherein you have already identified this as being a problem.

https://forum.bionicturtle.com/threads/frm-handbook-example-23-9-frm-exam-2008-q-3-31.4747/

Thank you