FRM Fun 13: Absolute versus relative VaR versus UL

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM CIPM, Jul 19, 2012.

  1. FRM Fun 13 (this is a P2 FRM question but P1 candidates are welcome to try)

    Today's question isn't really fun, but it has been asked literally dozens of times in various guise since I started the forum. A "star" goes to the most helpful answer.

    Despite its weaknesses, value-at-risk (VaR) is the most prominent risk measure in the FRM curriculum. Because VaR, as a worst expected loss, associates with a time horizon (and a confidence level), the "drift" of an exposure factors into the worst expected loss. For example, if my I expect my portfolio to gain by +$2 over the month, but its worst expected loss is $10, I can either include or exclude the expected gain in a VaR number. In an equities portfolio, drift is the positive return we expect over time.

    Several authors reflect this distinction--i.e., to include or exclude the drift-- by specifying an "absolute VaR" or a "relative VaR."

    Two questions (both are FRM P2 although UL makes an appearance in P1) :
    1. What is the relationship among relative VaR, absolute VaR and unexpected loss (UL)?
    2. Under the Basel method, the three big risk buckets are market, credit, and operational risk.
      What is the presumed (i.e., default or assumed) VaR for each risk bucket; e.g., are they each absolute VaRs? are they each relative VaRs? Put another way, can we identify a conclusive set of presumed VaRs for:
    • Credit risk
    • Market risk
    • Operational risk
  2. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    David,

    I'm just throwing this out there - or thinking out loud - but would it be an idea to, e.g. put in parenthesis whether the question pertains to P1 or P2, and if one question contains multiple sub-questions (like here), write P1 on q1 and P2 on q2?

    The reason I ask is twofold:
    1) if you are a candidate for part 1, you don't really need to be stressed out by scratching your head over a P2 question (unless you really want to and see it as a challenge).

    2) Should a P2 candidate or FRM holder maybe give P1 candidates a "grace period" of a day or two before answering?

    My reasoning here is that a P2 candidate is obviously more likely to know the answer, but importantly, by showing willingness to participate even for P1 questions the candidate might already be quite active on the forum.

    Just thinking it might deter a P1 candidate to give it a shot if he/she knows that an FRM holder or P2 candidate will provide an answer first. In other words, I'm thinking a P1 candidate might give a great answer if given the opportunity, and then a day or two later P2 candidates can weigh in with additional information, add to the answer, clarify certain things and so forth.

    The downside is of course that one runs the risk of having P2 candidates who are not yet comfortable with P2 material not participate as actively...
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  3. ShaktiRathore

    ShaktiRathore Well-Known Member

    Yeah Aleksander is right in this regard.Lets give chance to all. May be some people might come out with better answers than us. Seeing a lot of wise people visiting the forum. Nice to see such conceptual Questions.
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  4. Aleks, thank you, yes excellent suggestion to distinguish between P1 and P2! Edited above and I will do so going forward, cheers,
  5. ShaktiRathore

    ShaktiRathore Well-Known Member

    Absolute VaR is nothing but VaR calculated as we normally do with respect to a mean of zero as the maximum loss that can occur at a certain confidence level(CL) over a specific period of time.Relative VaR is given by at 95% CL as 1.645*volatility*Value of Portfolio. Whereas Absolute VaR will take into consideration the overall Loss including the gain from the positions that can be expected for a Given CL.For e.g. Suppose relative VaR is -12. Then as David highlighted that if there is +2 expected gain in portfolio position then the maximum loss that can occur over a period is -12+2=-10 is absolute VaR.
    Unexpected Loss is the loss that can occur beyond the expected loss due to uncertain events. This losses are out of the blue losses that can jeopardize the finance of the institution and banks always set aside some capital for facing these losses.
    As far as I know all the three VaRs are absolute VaRs. The credit VaR is calculated at 99.9% CL using Internal Ratings Based Approach wherein ratings are internally generated for Bonds and debt using complex models and then risk weights are assigned according to rating and VaR is finally arrived through summation of products of Risk weights and corresponding outstanding debt,
    Market VaR at 99% CL for 1 year (250 days) using Internal Models Approach wherein all the portfolio market positions are combined into one portfolio and the total risk is given by portfolio volatility(takes into account diversification of asset classes)
    and finally operational VaR at 99.9% CL over a year using Advanced measurement Approach uses a combination of LDA approaches.Here separate distributions of frequency of losses(poisson distribution) and lognormal distribution of severity of losses. The combined distribution of above will give us the operational VaR. All the three VaRs are assumed over a period and have conclusive VaRs that are drawn. Backtesting can be employed to test the models that are employed in VaRs calculations.
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  6. nilay14

    nilay14 New Member

    Hi david,
    I have gone through above question and I am agree with the explanation given by ShaktiRathore. but
    when I visited http://www.bionicturtle.com/forum/threads/relative-var-tracking-error.8/ link it created confusion for absolute and relative VaR concept
    please go through below excerpt from your thread...

    Relative versus Absolute VaR
    For our purposes (the exam), relative VaR refers to VaR relative to the expected value of the portfolio. Absolute VaR refers to VaR relative to zero. So, if you start today with portfolio value of $100, expected annual return of 10% and (annualized) standard deviation (of returns) of 10%, the one-year 95% RELATIVE VAR = ($100)(10%)(-1.645) = -$16.45. The one-year 95% ABSOLUTE VAR = ($100)[(-1.645)(10%)+10%] = -$6.45. See the difference? At the end of the year, we expect the portfolio to grow to $110. But $16.45 is "at risk." Relative VaR is the full $16.45 and Absolute VaR, giving credit to the gains that theoretically relate to the risk, speaks to loss versus initial value. Another way to view it: either way, our 1-year 95% VaR (note how i am careful to qualify the VaR with both a time horizon and a confidence level, because there is a different VaR for different combinations of time & confidence) says the risk is a final value of $93.55. The difference is whether we count the loss relative to where we started ($100) or where we expect to end ($110).

    Which one is correct?
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  7. ShaktiRathore

    ShaktiRathore Well-Known Member

    Hi Nilay,

    Yes I wrongly in hurry interchanged Absolute and Relative Vars definitions was really hurried up to finish this long answer. Sorry for the mistake. But i have made the changes above.
    thanks
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  8. nilay14

    nilay14 New Member

    Hi Shakti,

    No need to sorry... that mistake cleared my doubt. I was having misconception regarding Absolute and Relative VaR. Thanks for the correct ans.
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  9. Just wanted to close the loop on question 2 (since I'm linking to this thread):

    Under Basel II advanced approaches (IRB for credit risk, IMA for market risk and AMA for operational risk), the defaults are:
    • Credit risk capital charge is relative CVaR since it is a charge for UL which excludes EL (in credit, EL is an ongoing expense that Basel expects to be expensed by provisions. If, however, there is a gap, capital must first address the gap)
    • Market risk capital charge can be argued as either, IMO, because the drift is uniquely positive: maybe better is Absolute VaR where the drift is assumed to be zero; or, if you like, relative VaR where the drift is omitted.
    • Operational risk capital is absolute OpVaR because, unlike credit, otherwise coverage of EL is not presumed (i.e., it is not ordinary practice to expense OpRisk EL):

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