Value at Risk CFA Mock Question
- Thread starter whystudy
- Start date
- Thread starter
- #3
heer Wrote:
——————————————————-
> My understanding is:
>
> Value at risk will decrease when you move from
> daily to monthly as variability reduces when a
> longer time period is considered.
that’s exactly what I though, however CFA states that it increases because the MAGNITUDE of the losses would be greater as the time increases. So essentially what they ar esaying is that in any given day a stock can increase/decrease 10%, however on a monthly basis it’s more common to see 20%-40% change. Don’t know why the answer is that, it’s beyond me!
it’s in one free sample exam
——————————————————-
> My understanding is:
>
> Value at risk will decrease when you move from
> daily to monthly as variability reduces when a
> longer time period is considered.
that’s exactly what I though, however CFA states that it increases because the MAGNITUDE of the losses would be greater as the time increases. So essentially what they ar esaying is that in any given day a stock can increase/decrease 10%, however on a monthly basis it’s more common to see 20%-40% change. Don’t know why the answer is that, it’s beyond me!
it’s in one free sample exam
- Thread starter
- #5
heer Wrote:
——————————————————-
> ahh
I may have got it wrong and still didn’t
> learn
you are right, cause anyone with a mathematical sense would realise that N (sample set) decreases from daily to monthly, meaning volatility or VAR/SD would decrease or be less.
so i am lost, can someone shed some light
——————————————————-
> ahh
I may have got it wrong and still didn’t> learn
you are right, cause anyone with a mathematical sense would realise that N (sample set) decreases from daily to monthly, meaning volatility or VAR/SD would decrease or be less.
so i am lost, can someone shed some light
SanFranMatt
New member
- Jun 18, 2026
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VAR is estimating the minimum expected loss (or maximum expected loss, depending on how you look at it). You can lose more in a month than you can lose in a day, so VAR would increase when you go from daily to monthly.
markdirtbags
New member
- Jun 18, 2026
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How about you do the calculations?
- Thread starter
- #8
SanFranMatt Wrote:
——————————————————-
> VAR is estimating the minimum expected loss (or
> maximum expected loss, depending on how you look
> at it). You can lose more in a month than you can
> lose in a day, so VAR would increase when you go
> from daily to monthly.
That’s not exactly true; it can also be viewed from a different way. if the market is highly volatile for an example, the monthly return of the stock can be like 10%, you lose on the first half and recover on the second half, however, any given day the return can be more than 20%.
——————————————————-
> VAR is estimating the minimum expected loss (or
> maximum expected loss, depending on how you look
> at it). You can lose more in a month than you can
> lose in a day, so VAR would increase when you go
> from daily to monthly.
That’s not exactly true; it can also be viewed from a different way. if the market is highly volatile for an example, the monthly return of the stock can be like 10%, you lose on the first half and recover on the second half, however, any given day the return can be more than 20%.
markdirtbags
New member
- Jun 18, 2026
- 0
- 0
whystudy Wrote:
——————————————————-
> SanFranMatt Wrote:
> ————————————————–
> —–
> > VAR is estimating the minimum expected loss (or
> > maximum expected loss, depending on how you
> look
> > at it). You can lose more in a month than you
> can
> > lose in a day, so VAR would increase when you
> go
> > from daily to monthly.
>
>
> That’s not exactly true; it can also be viewed
> from a different way. if the market is highly
> volatile for an example, the monthly return of the
> stock can be like 10%, you lose on the first half
> and recover on the second half, however, any given
> day the return can be more than 20%.
Just do the calculation. Same portfolio.
$100million
20% return
10% SD
5% level.
Then do one day against one month.
Which one is bigger? Not that hard; you are overthinking it.
——————————————————-
> SanFranMatt Wrote:
> ————————————————–
> —–
> > VAR is estimating the minimum expected loss (or
> > maximum expected loss, depending on how you
> look
> > at it). You can lose more in a month than you
> can
> > lose in a day, so VAR would increase when you
> go
> > from daily to monthly.
>
>
> That’s not exactly true; it can also be viewed
> from a different way. if the market is highly
> volatile for an example, the monthly return of the
> stock can be like 10%, you lose on the first half
> and recover on the second half, however, any given
> day the return can be more than 20%.
Just do the calculation. Same portfolio.
$100million
20% return
10% SD
5% level.
Then do one day against one month.
Which one is bigger? Not that hard; you are overthinking it.
- Thread starter
- #10
mark@dirtbags Wrote:
——————————————————-
> whystudy Wrote:
> ————————————————–
> —–
> > SanFranMatt Wrote:
> >
> ————————————————–
>
> > —–
> > > VAR is estimating the minimum expected loss
> (or
> > > maximum expected loss, depending on how you
> > look
> > > at it). You can lose more in a month than
> you
> > can
> > > lose in a day, so VAR would increase when you
> > go
> > > from daily to monthly.
> >
> >
> > That’s not exactly true; it can also be viewed
> > from a different way. if the market is highly
> > volatile for an example, the monthly return of
> the
> > stock can be like 10%, you lose on the first
> half
> > and recover on the second half, however, any
> given
> > day the return can be more than 20%.
>
>
> Just do the calculation. Same portfolio.
>
> $100million
> 20% return
> 10% SD
> 5% level.
>
> Then do one day against one month.
>
> Which one is bigger? Not that hard; you are
> overthinking it.
I don’t think that’s overthinking it at all. Maybe you can answer this question first. would Variance, standard deviation increases or decrease moving from daily to monthly
——————————————————-
> whystudy Wrote:
> ————————————————–
> —–
> > SanFranMatt Wrote:
> >
> ————————————————–
>
> > —–
> > > VAR is estimating the minimum expected loss
> (or
> > > maximum expected loss, depending on how you
> > look
> > > at it). You can lose more in a month than
> you
> > can
> > > lose in a day, so VAR would increase when you
> > go
> > > from daily to monthly.
> >
> >
> > That’s not exactly true; it can also be viewed
> > from a different way. if the market is highly
> > volatile for an example, the monthly return of
> the
> > stock can be like 10%, you lose on the first
> half
> > and recover on the second half, however, any
> given
> > day the return can be more than 20%.
>
>
> Just do the calculation. Same portfolio.
>
> $100million
> 20% return
> 10% SD
> 5% level.
>
> Then do one day against one month.
>
> Which one is bigger? Not that hard; you are
> overthinking it.
I don’t think that’s overthinking it at all. Maybe you can answer this question first. would Variance, standard deviation increases or decrease moving from daily to monthly
SanFranMatt
New member
- Jun 18, 2026
- 0
- 0
whystudy Wrote:
——————————————————-
> SanFranMatt Wrote:
> ————————————————–
> —–
> > VAR is estimating the minimum expected loss (or
> > maximum expected loss, depending on how you
> look
> > at it). You can lose more in a month than you
> can
> > lose in a day, so VAR would increase when you
> go
> > from daily to monthly.
>
>
> That’s not exactly true; it can also be viewed
> from a different way. if the market is highly
> volatile for an example, the monthly return of the
> stock can be like 10%, you lose on the first half
> and recover on the second half, however, any given
> day the return can be more than 20%.
With VAR you’re not looking at expected return. You’re looking at the negative tail end of returns, almost like a ‘worst case scenario’. You have more potential to lose money in a month compared to a day.
——————————————————-
> SanFranMatt Wrote:
> ————————————————–
> —–
> > VAR is estimating the minimum expected loss (or
> > maximum expected loss, depending on how you
> look
> > at it). You can lose more in a month than you
> can
> > lose in a day, so VAR would increase when you
> go
> > from daily to monthly.
>
>
> That’s not exactly true; it can also be viewed
> from a different way. if the market is highly
> volatile for an example, the monthly return of the
> stock can be like 10%, you lose on the first half
> and recover on the second half, however, any given
> day the return can be more than 20%.
With VAR you’re not looking at expected return. You’re looking at the negative tail end of returns, almost like a ‘worst case scenario’. You have more potential to lose money in a month compared to a day.
markdirtbags
New member
- Jun 18, 2026
- 0
- 0
whystudy Wrote:
——————————————————-
> mark@dirtbags Wrote:
> ————————————————–
> —–
> > whystudy Wrote:
> >
> ————————————————–
>
> > —–
> > > SanFranMatt Wrote:
> > >
> >
> ————————————————–
>
> >
> > > —–
> > > > VAR is estimating the minimum expected loss
> > (or
> > > > maximum expected loss, depending on how you
> > > look
> > > > at it). You can lose more in a month than
> > you
> > > can
> > > > lose in a day, so VAR would increase when
> you
> > > go
> > > > from daily to monthly.
> > >
> > >
> > > That’s not exactly true; it can also be
> viewed
> > > from a different way. if the market is
> highly
> > > volatile for an example, the monthly return
> of
> > the
> > > stock can be like 10%, you lose on the first
> > half
> > > and recover on the second half, however, any
> > given
> > > day the return can be more than 20%.
> >
> >
> > Just do the calculation. Same portfolio.
> >
> > $100million
> > 20% return
> > 10% SD
> > 5% level.
> >
> > Then do one day against one month.
> >
> > Which one is bigger? Not that hard; you are
> > overthinking it.
>
>
> I don’t think that’s overthinking it at all.
> Maybe you can answer this question first. would
> Variance, standard deviation increases or decrease
> moving from daily to monthly
The answer is “stay the same”
——————————————————-
> mark@dirtbags Wrote:
> ————————————————–
> —–
> > whystudy Wrote:
> >
> ————————————————–
>
> > —–
> > > SanFranMatt Wrote:
> > >
> >
> ————————————————–
>
> >
> > > —–
> > > > VAR is estimating the minimum expected loss
> > (or
> > > > maximum expected loss, depending on how you
> > > look
> > > > at it). You can lose more in a month than
> > you
> > > can
> > > > lose in a day, so VAR would increase when
> you
> > > go
> > > > from daily to monthly.
> > >
> > >
> > > That’s not exactly true; it can also be
> viewed
> > > from a different way. if the market is
> highly
> > > volatile for an example, the monthly return
> of
> > the
> > > stock can be like 10%, you lose on the first
> > half
> > > and recover on the second half, however, any
> > given
> > > day the return can be more than 20%.
> >
> >
> > Just do the calculation. Same portfolio.
> >
> > $100million
> > 20% return
> > 10% SD
> > 5% level.
> >
> > Then do one day against one month.
> >
> > Which one is bigger? Not that hard; you are
> > overthinking it.
>
>
> I don’t think that’s overthinking it at all.
> Maybe you can answer this question first. would
> Variance, standard deviation increases or decrease
> moving from daily to monthly
The answer is “stay the same”
From the formula alone, we can agree that CFAI is correct, in general, let me repeat in genral like (95% of the time), the monthly return is higher than the daily return ( otherwise , we should stay in the market to sell and buy every single day), therefore , it make sense that the monthly VAR will be higher than the daily.
You can make a case for when return is zero, but as you move in time, you expect return to be higher. You may have recall, higher retrun always, I mean always come with higher risk. Is that make sense?
Otherwise, dude know it cold. And we will have time for all the semantic on the 7th of June
You can make a case for when return is zero, but as you move in time, you expect return to be higher. You may have recall, higher retrun always, I mean always come with higher risk. Is that make sense?
Otherwise, dude know it cold. And we will have time for all the semantic on the 7th of June
PhillyBanker
New member
- Jun 18, 2026
- 0
- 0
I don’t know, it intuitively makes sense to me that your value at risk is higher the further out you go.
old_akakaraka
New member
- Jun 18, 2026
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- 0
There are some rules for converting standard deviations across varying time periods:
sigma.daily = sigma.annual / sqrt(250)
sigma.monthly = sigma.annual / sqrt(12)
sigma.daily = sigma.monthly / sqrt(22)
So, sigma.monthly = sigma.daily * sqrt(22); thus, VaR decreases (it has a negative sign!), as std.dev. increases:
VaR = (R - z * sigma) * PFvalue
However, the return will ALSO increase, reducing the VaR, but supposedly to a lesser degree (neglegible effect).
Hope this is right, can someone verify?
sigma.daily = sigma.annual / sqrt(250)
sigma.monthly = sigma.annual / sqrt(12)
sigma.daily = sigma.monthly / sqrt(22)
So, sigma.monthly = sigma.daily * sqrt(22); thus, VaR decreases (it has a negative sign!), as std.dev. increases:
VaR = (R - z * sigma) * PFvalue
However, the return will ALSO increase, reducing the VaR, but supposedly to a lesser degree (neglegible effect).
Hope this is right, can someone verify?
- Thread starter
- #17
old_akakaraka Wrote:
——————————————————-
> There are some rules for converting standard
> deviations across varying time periods:
>
> sigma.daily = sigma.annual / sqrt(250)
> sigma.monthly = sigma.annual / sqrt(12)
> sigma.daily = sigma.monthly / sqrt(22)
>
> So, sigma.monthly = sigma.daily * sqrt(22); thus,
> VaR decreases (it has a negative sign!), as
> std.dev. increases:
>
> VaR = (R - z * sigma) * PFvalue
>
> However, the return will ALSO increase, reducing
> the VaR, but supposedly to a lesser degree
> (neglegible effect).
>
> Hope this is right, can someone verify?
This is the exact reason why i think the VaR will decrease as you move from daily to monthly to quarterly.
It’s true that they can say the return can or cannot be greater in magnitude. however, your risk has increase if you doing daily as opposed to monthly
——————————————————-
> There are some rules for converting standard
> deviations across varying time periods:
>
> sigma.daily = sigma.annual / sqrt(250)
> sigma.monthly = sigma.annual / sqrt(12)
> sigma.daily = sigma.monthly / sqrt(22)
>
> So, sigma.monthly = sigma.daily * sqrt(22); thus,
> VaR decreases (it has a negative sign!), as
> std.dev. increases:
>
> VaR = (R - z * sigma) * PFvalue
>
> However, the return will ALSO increase, reducing
> the VaR, but supposedly to a lesser degree
> (neglegible effect).
>
> Hope this is right, can someone verify?
This is the exact reason why i think the VaR will decrease as you move from daily to monthly to quarterly.
It’s true that they can say the return can or cannot be greater in magnitude. however, your risk has increase if you doing daily as opposed to monthly