Why higher return R mean lower VAR. Looking at formula seems opposite. Var=r-z*std Therefore, higher r higher var?!?! Missed.
remember that 1) VAR is overall a NEGATIVE NUMBER.
Take 2 numbers and calculate…
R=1, Z=1.96, STD=10
VAR @ 5% -> 1 - 19.6 = -18.6
Now R increases to 2
VAR = -17.6
(17.6 is lower than 18.6)
i’m faily sure r should be left out of var calcs. for the simple reason that the number doesn’t scale when you adjust for time.
i.e. r goes as r^n, but std goes as n^1/t
(sure enough that i can’t be bothered to find the page number)
For daily VaR in in the real world, usually it is assumed that expected return is zero, as this gives a more conservative VaR figure…but r does scale with time, albeit it not in the same way as standard deviation scales with time.
Epected return just scales linearly with time, where as standard deviation scales with the square root of time.
All the examples I have seen in L3 include the time scaled expected return so it is:
E® - Zscore x standard deviation
Be careful to realise that a VaR number itself cannot just be scaled with time if expected return is included in the calculation due to the difference in scaling of E® and Std Dev.