Question on VAR

[broadex]

[cpk123]

Statement 1 I believe is NOT true. Reason - way you adjust for returns say for Annual to monthly period is divide by 12 - but for Std Dev it is divide by sqrt(12). So it is not the same way.

Statement 2 is correct - therefore by elimination… So B

[FrankCFA]

I think both are not correct?

[broadex]

Thanks CPK. Yes you are correct. Could you care to explain what statement B means.

[cpk123]

When you are comparing multiple companies VAR’s - the difference is Return between 2 companies would cause an issue. because a higher return could mean a different number for comparison.

VAR = E® - x * Std Dev®

E® higher -> VAR would be a different number for comparison. You cannot compare different period VARs either. If you assumed E® would be 0 - it makes the job of comparison easier.

From my copy of Finquiz notes

Implications of Using of Zero expected value in VAR estimation:

• · It leads to greater VAR because expected returns are typically positive for longer time horizons.
• · It represents a more conservative approach as it leads to higher VAR.
• · It avoids the problem to estimate expected return since E® = 0.
• · It makes easier to adjust VAR for a different time period i.e. short term VAR cannot be converted to long term VAR (or vice versa) * when average return is not zero.

hope this helps.

[Unemployed]

Isn’t conversion of VaR between different period is also multiply with square root of number days?

Var (year) = VaR (1-days) x sqrt(250)

Var (month) = VaR (1-days) x sqrt(20)

Var (week) = VaR (1-days) x sqrt(5)

[Galli]

^ yes

[cpk123]

all those assume the E® to be zero. then you can do the math the way you have done it.

If however it is a non-zero return and you have E® for a day, and std dev for a day and needed to calculate var for a day vs. a year

Daily VAR = E® - x * std dev

Year VAR = E®*250 - x * std dev * sqrt(250)

assuming a 250 day year

and Year VAR <> sqrt(250) * Daily VAR.

I think this is what the 1st statement is talking about. What you do to adjust the E® is different from how you adjust the Std Dev. It would be the same way only if the E® is ZERO. For a non-zero number of E® the 1st statement is NOT true.