the maximum % loss that the portfolio can suffer in terms of percentage is r*=cutoff return=mean - volatilty * deviate
This essentially implies that the minimum value that the portfolio can have is P2* =P1 * (1 - EXP(r*)) where r*=cutoff return is the return at which portfolio suffers max loss.
The Var is the maximum loss that the portfolio can suffer at a given confidence level=P1 - P2*,where P2* is the minimum value that the portfolio can attain therefore P1 - P2* is the maximum loss that the portfolio can suffer which is nothing but Var.The P1 - P2* is the Value at Risk(Var).
Hi @ShaktiRathore@David Harper CFA FRM, If we had to scale the lognormal VAR using the square root rule i.e. if we are given annual return and volatility, should we scale down the mean and volatility before calculating lognormal var or scale down the calculated log normal var. In the below question from GARP
The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)?
what if it was 1-day 95% VAR. Just calculate lognormal var ?
Sorry I still have trouble in understanding the lognormal VaR calculation method. Could you confirm with me that the VaR calculation method shown on the "2016 Financial Risk Manager Examination (FRM) Part II Practice Exam" is not correct?
The annual mean and volatility of a portfolio are 12% and 30%, respectively. The current value of the portfolio is GBP 2,500,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption?
[Solution Key] The lognormal VaR is calculated as follows:
Lognormal VaR(%)=0.12-exp[0.12-(1.645*0.3)]=0.56832 = 56.83%.
Do you know where this VaR formula above is coming from?
Hi @frmqiu It is a mistake in the practice paper. Per Dowd, lognormal VaR(%) = 1 - exp(µ - σ*z), which in this case is 1-exp(12% - 30%*1.645) = 31.16% or 31.16%*2,500,000 = GBP 779,122 such that the answer looks like it should be (37.35% - 31.16%)*2,500,000 = GBP 154,518 is how much higher is the normal VaR than the lognormal VaR. I hope that is helpful!