TomDoan wrote:With p=.01, the Poisson approximation to the binomial is MUCH better than the Normal. You can also do an exact calculation using the %BETAINC (incomplete beta) function:

compute p=.01,n=250
do i=0,10
?i %poisson(n*p,i) %betainc(1-p,n-i,i+1)
end do i

though there is no practical difference between the Poisson approximation and the exact calculation.

Your 10 and 4 are specific to a particular combination of N and alpha. Why would you restricted yourself that way?

The "ES Traffic Light" is (a) not really about the ES and (b) looks like gibberish (mainly because of (a)). What they are analyzing is not the "expected shortfall" (which would be a $ amount) but the observed percentile. If the distribution is thin-tailed, a loss of 10% over the VaR might give you a .50 value, while in a thick-tailed distribution, a loss of 50% over the VaR might give you a .25 value.

TomDoan wrote:With p=.01, the Poisson approximation to the binomial is MUCH better than the Normal. You can also do an exact calculation using the %BETAINC (incomplete beta) function:

compute p=.01,n=250
do i=0,10
?i %poisson(n*p,i) %betainc(1-p,n-i,i+1)
end do i

though there is no practical difference between the Poisson approximation and the exact calculation.

Your 10 and 4 are specific to a particular combination of N and alpha. Why would you restricted yourself that way?

The "ES Traffic Light" is (a) not really about the ES and (b) looks like gibberish (mainly because of (a)). What they are analyzing is not the "expected shortfall" (which would be a $ amount) but the observed percentile. If the distribution is thin-tailed, a loss of 10% over the VaR might give you a .50 value, while in a thick-tailed distribution, a loss of 50% over the VaR might give you a .25 value.

Yes, I am using a different size window than N=250.