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# Delta normal VAR

#### BartW

##### New Member
Hi David, Nicole,

I have question about the delta normal VAR in P1.T4. When I have a yearly expected return [E(r) year - z*(sigma year/ sqrt 250) *$] given in a question how should I translate this for e.g. to a daily expected return. I know it is somewhere in the BT material but I can't find it anymore. The square root rule doesn't t apply to this part (E(r)) in the formula of delta normal VAR. right? Looking forward to your explanation!! Kr, Bart Last edited: #### Nicole Seaman ##### Director of FRM Operations Staff member Subscriber Hi David, Nicole, I have question about the delta normal VAR in P1.T4. When I have a yearly expected return [E(r) year - z*(sigma year/ sqrt 250) *$] given in a question how should I translate this for e.g. to a daily expected return. I know it is somewhere in the BT material but I can't find it anymore.
The square root rule doesn't t apply to this part (E(r)) in the formula of delta normal VAR. right?

Kr,
Bart
Hello @BartW

Just in case David does not get to answer your question, I wanted to make sure that you are aware of our tags in the forum. These tags will bring up threads that should be helpful in answering your question. Because it is a few days before the exam, although David tries his best to answer all questions, it is not always possible. There are a lot of threads in the forum that discuss Delta Normal VaR. I hope this helps a bit! Nicole

#### BartW

##### New Member
Hi Nicole,

Thanks for the swift response I have read the threads but still couldn't find the answer. We have still a couple of days to go before the exam.

Thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi David, Nicole,
I have question about the delta normal VAR in P1.T4. When I have a yearly expected return [E(r) year - z*(sigma year/ sqrt 250) *\$] given in a question how should I translate this for e.g. to a daily expected return. I know it is somewhere in the BT material but I can't find it anymore.
The square root rule doesn't t apply to this part (E(r)) in the formula of delta normal VAR. right?

Kr,
Bart

HI @BartW The return scales linearly with time and the volatility scales with the square root of time (aka, variance scales linearly with time). Where Δt = t/T, in this case, Δ=1/250 is the scaling multiple. When computing absolute VaR (ie, when the VaR includes the effects of the return) we must treat the terms separately: return gets multiplied by Δt; and volatility gets multiplied by sqrt(Δt).

For example, assume annual µ = +10.0%, annual σ = 30.0% and α = 0.05 so that Z(.95) = 1.645 to reflect our want of a 95.0% confident one-day normal VaR. The absolute (%) VaR = -µ*Δt + σ*Z(α)*sqrt(Δt) = -0.10*(1/250) + 0.30*1.645*sqrt(1/250) = 3.0812%