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

[David Harper CFA FRM]

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)?

 

[ShaktiRathore]

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=1million+.5*(.1%+1.96*(.3)%)*1million
LVaR=1 million+.5*(.1%+.588%)*1million
LVaR=1 million+.5*(.688%)*1million
LVaR=1 million+.344%*1million
LVaR=1 million+3440
LVaR=1003440

 

[David Harper CFA FRM]

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.

Thanks!