EWMA methods in VaR method

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Julia Cains
Posts: 10
Joined: Tue Aug 09, 2011 7:37 am

EWMA methods in VaR method

Postby Julia Cains » Wed Aug 29, 2012 7:12 am

Dear Carol madam,

I have one hypothetical portfolio consisting of some equity, bonds and Forex transactions. I am trying to arrive at VaR estimate using Historical, Monte Carlo simulation and VaR-Covar method. While the Historical and Monte Carlo are giving me estimates in the range of 10 to 12 million, the VaR-covar method is giving me VaR estimate of about 1 million.

I have identified the risk factors and applied the EWMA to the returns in case of Var-covar method.

However considering the significant difference in the VaR estimates, am I supposed to apply EWMA in case of historical and Monte Carlo simulation methods also or is it that EWMA is applicable for Var-covar method only? Kindly guide.

With warmest regards

Julia

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

Re: EWMA methods in VaR method

Postby coalexander » Wed Aug 29, 2012 10:54 am

Hi Julia,

With such a difference as you have, my guess is that you have an error, perhaps in time scaling?

To check the problem, first use what I call the normal linear VaR model (you call it VaR-Covar method) without EWMA covariance matrix, just using standard covariance matrix derived from same data period as you use for historical [and I suppose you also use same data to get Covar matrix in Monte Carlo method?]

Your result should be similar to historical VaR, and theoretically identical to the MC VaR! The MC VaR results will differ from the normal linear VaR ONLY because of MC sampling error. Repeating the sims for MC method will give you different results, that range around the Normal linear VaR result. The latter is the exact result. You do not need MC when you use normal linear VaR model assumption, it only introduces a sampling error.

When you have corrected your results with standard covariance matrix so that you get very similar results to MC VaRs, only then add the EWMA refinement. If you results change hugely, then the problem is in the code for the EWMA.

EWMA can also be applied to historical simulation -- see 'filtered Historical simulation' section in Chapter 5 (I think).

No need to do MC VaR at all anyway, for reasons given above, unless you depart from normal assumption.

Thanks for the kind comments about my new job. I am very excited!

Cheers, Carol

Julia Cains
Posts: 10
Joined: Tue Aug 09, 2011 7:37 am

Re: EWMA methods in VaR method

Postby Julia Cains » Thu Aug 30, 2012 8:48 am

Dear Carol madam,

Thanks a lot for your great help and sincerely apologize for replying bit late. I will definitely go through your suggestions. Madam, even we are also excited and too happy when we refer to your books, your discussion forum. It's like revisiting the college days and we are your students. This feeling encourages us to refer and study all your material. This bond between you and we all as students is something we love a lot.

Thanks again madam

Regards

Julia

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

Re: EWMA methods in VaR method

Postby coalexander » Thu Aug 30, 2012 6:46 pm

Dear Julia

Many thanks for your appreciation - and you are most welcome!

Carol


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