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Hi David,

In the textbook you have mentioned two formulas to calculate Liquidity VaR.
You have added the liquidity component either to lognormal VaR or to geometric VaR.

Please advice what is the recommended method.. Should we use lognormal VaR or geometric VaR?


Deepak Chitnis

Active Member
Hi @gargi.adhikari, I dont think David had mentioned two formulas there. I think there is only on formula with lognormal var. But I think you should use lognormal var when returns or mean is lognormally distributed or if the return or mean are normally dustributed we expected to use geomatric var. I think @David Harper CFA FRM can elaborate more. Hope that helps.
Thank you:)

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @Kavita.bhangdia

Neither method is recommended, sorry! But please note that with respect to VaR, we can use two approaches which really speaks to our assumption about returns and the implied price distribution:
  1. if discrete period (aka, arithmetic or simple) returns are normal, we have "arithmetic VaR" or "normal VaR:" VaR = -σ + µ*α
  2. if continuous returns (aka, continuously compounded, or Dowd calls this "geometric" which I think can be confusing to some) are normal, we have "lognormal VaR"
Liquidity adjusted VaR (LVaR) refers to an increase in VaR due to the liquidity component, which is the topic of Dowd's liquidity risk. Examwise, the most relevant is the (simpler) constant spread which adds 0.5*spread; this (adding 1/2 spread) applies to either VaR above.

I will note that GARP's 2016 practice exam contains fully two questions, both of which apply the constant spread to an arithmetic/normal VaR; i.e., the simplest approach you can take. For example, P2.19:
19. A trader observes a quote for Stock DUY, and the midpoint of its current best bid and best ask prices is CAD 45. DUY has an estimated daily return volatility of 0.38% and average bid-ask spread of CAD 0.14. Using the constant spread approach on a 20,000 share position and assuming the returns of DUY are normally distributed, what is closest to the estimated liquidity-adjusted, 1-day 95% VaR?
a. CAD 1,600
b. CAD 5,600
c. CAD 6,600
d. CAD 7,600
The key here, imo, is to notice the absence of "lognormal." The FRM favors keeping it simple: don't assume lognormal unless you see the word "lognormal." Although I might send them feedback because notice:
  • The question strictly means: "assuming the arithmetic returns of DUY are normally distributed" but
  • this question does not intend "assuming the geometric returns of DUY are normally distributed" which would imply a lognormal VaR (i.e., lognormal price distribution, same as GBM in BSM). The key (to this question) is that we do not see the word lognormal. I hope that helps!
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