2 Define the cVaR to be the value v such that there is only

2). Define the c%-VaR to be the value |v| such that there is only a c% chance that the loss from an investment will be greater than c.

a). Derive a formula for 5%-VaR on an investment with gain G that is normally distributed with mean and standard deviation

b). If G has mean 15 and standard dev 1.8, compute the 5%-VaR on this investment

Solution

1.

We have to find the value x such that P(X<x)=0.05

=>x=mean-Z*standard deviation

Here, Z=norminv(0.95)=1.65

Hence, x or 5% VaR=mean-1.65*standard deviation

2.

5% VaR=15-1.65*1.8=12.03