Benchmark VaR

Discussion on Value-at-Risk Models
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pedram
Posts: 5
Joined: Thu May 10, 2012 7:40 am

Benchmark VaR

Postby pedram » Thu May 10, 2012 9:41 am

Hi dear professor

I got a little confused in IV.1.8.1 regarding benchmark VaR. since I am going to compare portfolio VaR with a benchmark index, I need to compute BVaR. So I got VaR= 466 $ for portfolio and BVaR= 229 $. In last paragraph of section IV.1.8.1 you mentioned " when a portfolio is expected to outperformed a benchmark then the risk of the portfolio reduced if it is measured by benchmark VaR,but not if it is measured by the tracking error" . I couldn't understand how can I use this expression in my interpretation of result?
what would be my interpretation of VaR and BVaR that I calculated?
is it correct if I say that my portfolio is outperforming benchmark index because its VaR is higher than BVaR?

Thanks in advance
Pedram

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

Re: Benchmark VaR

Postby coalexander » Thu May 10, 2012 10:11 am

There are many performance metrics (eg Sharpe ratio, Sortino ratio, Omega etc) but lets just use the expected return for this example.

That means, as I understand your question, it is:

Suppose VaR > BVaR. Then is the expected active return positive?

The answer is no. If a portfolio tracks a benchmark fairly well, the active returns will be small, so their risk will be small. Hence BVaR can be much less than VaR. But at the same time as tracking fairly well the portfolio could still under-perform the benchmark just a little bit, so expected active return is small and negative. This will add a little bit to BVaR, but it could still be less than VaR.

Cheers, Carol

pedram
Posts: 5
Joined: Thu May 10, 2012 7:40 am

Re: Benchmark VaR

Postby pedram » Thu May 10, 2012 12:46 pm

Thanks for your response. I appreciate it.
my expected active return or the average of all active return is -0.000181. Hence my portfolio is tracking benchmark fairly well because of small amount of active return and also under-performing the benchmark by 229 $( BVaR) because of negative amount of active return. Do I compass correctly?
what should be our scale to decide about the smallness of active return? ( can we say less than our confidence level 5%? )

Excuse me if I am annoying you. I know you are busy. This will be my last question. so sorry .

In section IV.1.5.1 Normal linear formula, we have Mean in VaR formula, but in case study IV.1.9.4, looking at CD solution, you ignored Mean in Normal Linear VaR.
I thought that because of assumption of normality distribution you assume mean=0 . But I am not sure.
What would be better , use mean or ignore it in normal linear method?

Sorry again.
Thanks for your fabulous book series.
Pedram

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

Re: Benchmark VaR

Postby coalexander » Thu May 10, 2012 6:08 pm

Hi

When you say "and also under-performing the benchmark by 229 $( BVaR) " I don;t think that statement is correct at all.

Can you also explain what is to be "less than our confidence level of 5%"?

Regarding your last question, the mean that you state of -0.000181 is certainly small enough to be ignored, it will have very little effect on the VaR.

Hope this helps, Carol

pedram
Posts: 5
Joined: Thu May 10, 2012 7:40 am

Re: Benchmark VaR

Postby pedram » Thu May 10, 2012 7:07 pm

Helps a lot.
wow. I think I got it now. BVaR gauge the amount of under-performing portfolio relative to benchmark. Therefore we can conclude : the most likely amount that our portfolio may under-perform relative to its benchmark is lest's say 229$.

by "less than our confidence level of 5%" I meant that how can I decide whether my expected relative return is small. should it be based on a special amount such as significance level( Alpha) ? ( My mistake I wrote confidence level instead of significance level. )

pedram
Posts: 5
Joined: Thu May 10, 2012 7:40 am

Re: Benchmark VaR

Postby pedram » Fri May 18, 2012 3:22 am

Hi again dear Professor

I am still waiting.
Is my interpretation right?

Regards
Pedram

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

Re: Benchmark VaR

Postby coalexander » Fri May 18, 2012 9:29 am

BVaR is simply the VaR of active returns. A 5% 1-day BVaR of $500, say, means that you are 95% confident that you will lose no more than $500 more than the benchmark, if you hold the portfolio for 1-day without rebalancing,

Cheers, Carol

pedram
Posts: 5
Joined: Thu May 10, 2012 7:40 am

Re: Benchmark VaR

Postby pedram » Sat May 19, 2012 6:02 am

Very helpful
Thanks a lot.

Regards
Pedram


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