FRM Fun 12. Find the mistake in a published LVaR question

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM, Jul 18, 2012.

  1. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    This is a circulating question on liquidity-adjusted value at risk (LVaR) that several members have submitted over the years (image source: a member posted elsewhere in the general forum):


    At least one mistake has been confirmed!

    Question: what is the correct 95% LVaR answer (hint: it is not given as an option)?
  2. ShaktiRathore

    ShaktiRathore Well-Known Member

    The Liquidity Adjusted VaR is,
    LVaR=VaR+Liquidity cost
    LVaR=VaR+(mean of spread+1.96*volatality of spread)*V; there should be plus instead of minus sign in the formula above
    Another Mistake above seems that mean and volatility of spread are taken in USD and when multiplied by V gives USD^2 as unit which is not valid. Hence we first need to convert mean and volatility to % terms before calculating LVaR.Instead of taking mean and volatlity as .1USD and .3USD they should be corrected to .1% and .3% accordingly.
    Thereby after correction,
    LVaR=1 million+.5*(.1%+.588%)*1million
    LVaR=1 million+.5*(.688%)*1million
    LVaR=1 million+.344%*1million
    LVaR=1 million+3440
  3. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    Hi ShaktiRathore,

    Thank you, I agree that question should instead read "spread of 0.1% with spread volatility of 0.3%." The answer appears to treat the spread as %; and, also, if the spread is really USD, it is hard to know how to treat (surely that cannot be the spread on the whole position). So, IMO, I agree this counts as one mistake.

    I also agree that another mistake, which follows Culp, is to employ the +mean - volatility (i.e., +.1 - .3). This cannot be correct because it implies an increase in mean will lower the cost of illiquidity. This is an old error from Culp due to computing VaR = mean - volatility * spread and this error is why I prefer Dowd's:
    • VaR = -mean + volatility*sigma; this format seems to be more robust to pilot error because then LC is always a natural addition:
    • LVaR = -mean + volatility*sigma + LC; i.e., +LC increases a positive VaR
    Finally, I think the third error is to use 1.96. This has been much discussed on this forum. My view is that the spread deviate should also be 1.645 per a one-tailed critical value: we are not interested in the other tail, only the adverse tail where the spread moves against us.


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