Inverse floater's VAR

[ajsa]

Hi David,

A portfolio manager invests $100 million in a 5-year inverse floater paying 18%-2*LIBOR. The modified duration of a 6% 5-year bond is 4.5 year. What is the 95% VaR of the inverse floater if the yield volatility is 0.66%?
a) $3.0M
b) $5.9M
c) $8.9M
d) cannot be determined

my calculation:
3*4.5*0.0066*1.65*100M = 14.7M
but i cannot find an answer... could you please help?

Thank you!!

 

[David Harper CFA FRM]

Hi ajsa,

The hard part is getting 3 * 4.5, but I agree the inverse floater has duration 13.50
therefore VaR = 0.66% yield volatility * (3 * 4.5 duration) * 1.65 (we have to assume normality?) * 100 = $14.65

i get the same answer as you!
(let me know if you find something that contradicts....i'd love to see it, otherwise, frankly, I will assume we are correct )

David

 

[hsuwang]

Hello David,

Can you please explain the logic behind getting the duration for the inverse floater? (3 * 4.5) I can't recall seeing this in the past..

Thank you.

 

[David Harper CFA FRM]

Hi Jack,

This may help: http://forum.bionicturtle.com/viewthread/1727/
(or this: http://forum.bionicturtle.com/viewthread/1562/)

I input the above example (ie., 18% - 2*LIBOR) into my XLS:
http://sheet.zoho.com/corporate/1978922/btzoho/111809-inversefloat
(to the right, cash flows...)

The exercise is in the FRM handbook (p 188). The key is to ensure dollar durations are equal, in this case:
$33.33 MM inverse @ 18% - 2* LIBOR = Long $100 MM fixed @ 4% - Long $66.67 MM floating rate @ LIBOR
Dollar duration: $33.33 * 13.5 = 100 * 4.5 - 0
i.e., floater has zero duration

However, none of this was assigned in 2009; you should not be tested on inverse floater duration!
(you do not recall for good reason, it was not assigned)

David

 

[ajsa]

Hi David,

I have some question about the convention of the inverse floater? Is it $33.33M or $100M? I thought it was $100M and the fixed was $300M.

If it is $33.33M, should the VaR calculation be: 3*4.5*0.0066*1.65*33.33M instead?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

Right, I was lazy in my XLS, although it doesn't matter on the 13.5 duration. To match my understanding of the question, I should have input:
$100 MM inverse @ 18% - 2* LIBOR = Long $300 MM fixed @ 4% - $200 MM floating rate @ LIBOR
....but it's still 13.5 duration for the inverse (I knew that becase of doing these problems, if the rate is -2x, the duration leverage is 3X; if -3x, duration leverage is 4X, etc)

So i think the question implies:
$100 floating = $300 fixed "collateral" funded with $200 floating rate note, or

Rather than:
$33 floating = $100 fixed funded with $67 floating rate note

simply b/c it reads "A portfolio manager invests $100 million in a 5-year inverse floater"

...i guess it's possible the question is looking for a "cannot be determined" because it doensn't provide the leverage, but i hesitate to pursue unsourced questions further frankly...sometimes they are just imprecise

...does it not even give you an answer, why don't you have an answer?

thanks, David

 

[David Harper CFA FRM]

I re-uploaded the XLS. This matches my (mere) interpretation of the problem:

http://sheet.zoho.com/public/btzoho/111809-inversefloat-v2

i.e., $100 reverse floater = $300 fixed bond funded by $200 floating rate note
e.g., at 8%
fixed bond pays = 300*6% = 18
floater pays 200* 8% = 16
reverser floater pays 100*(18% - 2*8%) = 100*2% = 2

fixed bonds "decomposes" into floater + inverse floater: 18 = 16+2
or, floater is "receive" $18 on fixed but pay $16 on funded floater = leaving $2 on inverse floater (2% on $100 invested)

David

 

[liordp]

is inverse floater is part of aims 2010 ?

 

[David Harper CFA FRM]

No, to my knowledge it's not "directly" in the AIMs ... see my note from last year (and, based on what i heard, it was not asked in the exam. So, we were correct to exclude).
However, the FRM famously (notoriously?) asks questions that apply building block concepts, or "in between" concepts. I think this is a fine application practice question, in that regard: it combines ideas that arguably link to AIMs - David