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

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

  1. 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. 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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