From daily VAR to monthly VAR

[deriv108]

All else equal, how to calculate a monthly VAR if you are given a daily VAR?

 

[pimpineasy]

*t^0.5

 

[deriv108]

no compounding of return?
thanks. No compounding for VAR calculation.

 

[sk22]

yep thats correct.
daily = annual / sqrt( 250 )
daily = monthly / sqrt (22 or 21)
** key is you need to look at WORKING DAYS not just days! **
SK

 

[janakisri]

Sqrt(252)/Sqrt(12) ?

 

[pimpineasy]

janakisri Wrote:
——————————————————-
> Sqrt(252)/Sqrt(12) ?
thats what she said………………

 

[CFASniper]

I have seen this with a slight catch sometimes
If you are given a final VaR number you can scale it up or down with a square root of time factor. That’s straightforward
On the other hand, if you are given lets say annual return and SD numbers, in order to get a monthly VaR you need to divide return by 12 and SD by sqrt(12) and the use
portfolio value x (R - 1.65 x SD) for a monthly 95% VaR

 

[sk22]

pretty sure schweser said 250 days per year …i remember thinking hold on why isnt it 252 (12*21) - guess its bank holidays or something??
sqrt(12) for annual to monthly yea, but i was showing annual to daily and monthly to daily.

 

[SkipE99]

i nominate pmpeasy for the comment of the year

 

[pimpineasy]

thanks but i will settle for a pass…………………..crazy how much details these exams entail

 

[onelasttime]

CFASniper Wrote:
——————————————————-
> I have seen this with a slight catch sometimes
>
> If you are given a final VaR number you can scale
> it up or down with a square root of time factor.
> That’s straightforward
>
> On the other hand, if you are given lets say
> annual return and SD numbers, in order to get a
> monthly VaR you need to divide return by 12 and SD
> by sqrt(12) and the use
>
> portfolio value x (R - 1.65 x SD) for a monthly
> 95% VaR
I think if I remember is correctly, scaling a final VAR number directly ONLY applies if the EXPECTED Return is zero. A big assumption.
If you want to use the std dev and return, and calculate, monthly, annual, weekly VAR, you have to adjust both and the assumption of expected return equal to zero does not apply!
It is somewhere in the CFAI reading. Can’t remember it where, I read it like 2 months ago.
Edit: Found it book 5, page 236

 

[janakisri]

Just to clarify , CFASniper is correct , and onelasttime is also correct.
So to calc a monthly VAR from daily VAR, calc
monthly return = daily return * 252/12
monthly stdev = daily stdev * sqrt(252)/sqrt(12)
monthly VAR = monthly return - 1.65*monthly stdev.
This is more general and applicable even when mean return is not zero

 

[cookthebooks]

thanks for that, definitely clarified things

 

[onelasttime]

janakisri Wrote:
——————————————————-
> Just to clarify , CFASniper is correct , and
> onelasttime is also correct.
>
> So to calc a monthly VAR from daily VAR, calc
>
> monthly return = daily return * 252/12
> monthly stdev = daily stdev * sqrt(252)/sqrt(12)
>
> monthly VAR = monthly return - 1.65*monthly
> stdev.
>
> This is more general and applicable even when
> mean return is not zero
I think you meant to multiply by 250 not 252 and same with std dev x sqrt(250) (per cfai)

 

[SkipE99]

i would definitely get this concept down. this is exactly the tricky type of stuff that shows up

 

[bpdulog]

To get annual var from monthly var can we take monthly var multiplied by the square root of 12? Was this an only acceptable at L2 type of method?

 

[janakisri]

bpdu , it is ok only if mean exp. return is zero