VaR and expected return

CFA Level III Derivatives
#1

From the curriculum, at 5%, VaR = μ_p_ – 1.65σ_p_. The increase in expected return would result in a lower calculated VaR (smaller losses).

From the formula, if the expected return increase, the VaR should also increase. Isn’t it so?

#2

From the formula if zeta and sigma increase VAR increases. Thus if confidence interval is higher, 99 % instead 95 % and if standard deviation of return is higher, VAR is higher.

#3

why don’t you look at it with some numbers instead of a formula.

mu=10% sigma = 12%

initially => 10 - 1.65 * 12 = -9.8% loss

say for some reason mu increases to 12% and there is no change in sigma … VaR = 12 - 1.65 * 12 = -7.8% loss (Lower Loss).

So VAR reduces…

The thing to remember is that the absolute value of mu - 1.65*sigma reduces as mu increases.

#4

Thank you. Fully understand the VaR formula now.