VaR of bond portfolio

Discussion on Value-at-Risk Models
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TRAXX
Posts: 5
Joined: Wed Jul 18, 2012 10:35 pm

VaR of bond portfolio

Postby TRAXX » Thu Jul 19, 2012 10:32 am

Dear Professor,
I have got some strange exercise from polish version of CFA exam (exam is called 'investment adviser') and I want to know what do you think about it.
In exercise there is bond portfolio with 1 mln PLN value and duration 4,8 years (each bond has time to maturity longer than 2,5 years). Risk free rate equals 5%. There is 0,05 probability that RFR will raise to 5,5% and the question is about portfolio VaR value at 0,95 confidence level.

The official answer is 229 000 PLN.



1 000 000 PLN x 1,05^4,8 = 1 263 888,13
change%W= -MD x W x change%YTM.
change%W= -4,8/1,05 x (0,055-0,05) = 0,022857
Value from Gaussian distribution for 0,95 probability level is 1,65

1,65 x 0,022857 x 1 263 888,13 x 4,8 = 228 800 = 229 000 PLN

What do you think about this reasoning on VaR at polish version of CFA exam? Thank you in advance

Best regards
TRAXX
Last edited by TRAXX on Thu Jul 19, 2012 10:07 pm, edited 2 times in total.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: VaR of bond portfolio

Postby coalexander » Thu Jul 19, 2012 10:50 am

Given the information in the question this is the reasoning I would use:

1. The change in bond value for a given change in yield of +0.5% is - Modified Duration * 0.5%, to a first order approximation. Given the data, this is -2.2857%, as you calculated.

2. The rest of the arguments in your post seem strange. The correct argument (given the data) is this:
a) There is a 5% chance that the rate will rise by 0.5%, in which case we know the portfolio makes a loss of -2.2857% of its current value.
b) Thus, by definition of VaR, the 95% VaR is 2.2857% of its current value.
c) Its current value is 1 million, so the required VaR is 228,570.

If the answer is multiple choice and 229,000 is the closest to this figure, then select 229,000 as the correct value.

Cheers, Carol

TRAXX
Posts: 5
Joined: Wed Jul 18, 2012 10:35 pm

Re: VaR of bond portfolio

Postby TRAXX » Thu Jul 19, 2012 12:08 pm

Thank you very much for the answer, but i dont understand one thing. Why 2,2857% from 1 mln is 228 570?
I calculated 1 000 000 x 0,022857 = 22 857
Thank you in advance
Best regards

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: VaR of bond portfolio

Postby coalexander » Thu Jul 19, 2012 1:33 pm

oops! Yes, sorry, I put an extra zero.


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