Hi ajsa,
Sure, this alternative approach only recently finds an introduction in the FRM with Dowd's Liquidity VaR.
We typically (following Jorion) use the "arithmetic" approach;
i.e., absolute returns VaR (%) = -mean + (volatility * deviate)
where the "cutoff return" r* = mean - volatilty * deviate
instead under Dowd's "geometric" approach (i.e., log returns are normal --> prices are lognormal):
r* = LN (today's price/yesterday's price)
r* = LN(P2) - LN(P1)
LN(P2) = r* + LN(P1)
EXP(LN(P2)) = EXP(r* + LN(P1))
today's price P2 = EXP(r*) * P1
P1 - P2 = P1 - EXP(r*) * P1
(P1 - P2) = P1*(1 - EXP(r*))
source: Dowd page 62
and if today's price P2 = cutoff value (i.e., loss that corresponds to VaR) = P2*,
then VaR = P1 - P2* = P1 * (1 - EXP(r*))
where r* = mean - volatility * deviate, so that
VaR = P1 - P2* = P1 * (1 - EXP(mean - volatility * deviate))
or % "absolute" lognormal VaR = 1 - EXP(mean - volatility * deviate)
e.g., 10% mean return and 20% volatility = 1 - EXP(10% - 20% * deviate) = 20.5% @ 95% confidence
compare to "arithmetic" of -10% + (20 * 1.645) = 22.9%
Hope that helps, David
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