CFA confusing VaR calculation method

[richboy4865]

Information from question given: Portfolio value $150, annual return 12%, annual return volatility 25%, calculate VaR using 3 standard deviation.

my answer is = 150( 12%-3*25%)= 94.5

but solution given is 150*3*25%

it is very confusing, when we should include the annual return of 12% to calculate VaR?

Anyone know this? thank you

 

[David Harper CFA FRM]

Hi @richboy4865 This is much already discussed in forum (search "relative" and/or/versus "absolute" VaR). The assumptions here is that the arithmetic returns are normal; aka, normal VaR. Either is okay:

• absolute VaR (aka, aVaR or just VaR) = -μ + σ*Z; in this case, -12% + 25%*3 = 63.0% or $94.50 is best (your answer is the best default) because it is the worst expected loss relative to the initial position
• relative VaR (aka, rVaR) = σ*Z; in this case, 25%*3 = $112.50 is the worst expected loss relative to the future expected value. The position is expected to grow from $150 to $150*1.12 = $168 and the rVaR of $112.50 implies the worst expected future position (with 99.87% confidence) is $168 - $112.50 = $55.00 which is $94.50 (the aVaR) below the initial 150: 150 - 94.50 = $55.50. Both aVaR and rVaR indicate the worst expected future position of $55.00, so they are consistent.

Ultimately a good question must be specific. It is a flawed question (imprecise at a minimum) to provide the annual return then not use it. Otherwise, your answer is the best. Hope that's helpful,