Question on VAR

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cpk123

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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
 
Thanks CPK. Yes you are correct. Could you care to explain what statement B means.
 
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(R) - x * Std Dev(R)
E(R) higher -> VAR would be a different number for comparison. You cannot compare different period VARs either. If you assumed E(R) would be 0 - it makes the job of comparison easier.
From my copy of Finquiz notes
Quote:
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(R) = 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.
Click to expand...
hope this helps.
 
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)
 
all those assume the E(R) 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(R) for a day, and std dev for a day and needed to calculate var for a day vs. a year
Daily VAR = E(R) - x * std dev
Year VAR = E(R)*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(R) is different from how you adjust the Std Dev. It would be the same way only if the E(R) is ZERO. For a non-zero number of E(R) the 1st statement is NOT true.
 
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