Expected Shortfall

[afterworkguinness]

Hello,
I don't understand how to calculate the expected shortfall of bond portfolios given their probabilities of default, I'm not following the examples in these cases. I have no problem with the 'historical sim" type of examples like given these worst 15 returns over the past 1,000 days what is the 99% ES.

I would be very appreciative if someone who understands this could walk me through an example.

 

[ShaktiRathore]

Hi, i can give you some rough idea
Consider a 2 bond portfolio where the bonds 1 and 2 are their
Bond 1 and 2 PDs are 2% and their expected losses are x1 and x2 in case of default. if both default then PD of both is .02*.02=.04% if any one defualt probability is .98*.02*2=3.92% and if neither defaults probability=.98*.98=96.04% now if we have 95% CL and find ES that is the expected loss once the Var at 95% limit is crossed the loss can happen when both bonds defualts, or wither of bond defaults which gives us cumulative probability of defualt=.04%+3.92%=3.96% and the rest probability 1.04%(5-3.96%) is filled with no default so that our net ES is average loss in area over 95% limit=total area/base so that only loss possible is under area 3.96% out of a total of 5% probability area.
now we find net weighted average expected loss by multiplying defaults probabilities with their respective losses,
Expected loss(95%CL)=(x1+x2)*P(1&2 defaults)+x1*P(1 default not 2)+x2*P(2 default not 1)+0*P(neither 1 or 2 default)/5%
Expected loss=(x1+x2)*3.92%+(x1+x2)*.04%+0*1.04%[p1 and p2 are independent events]/5%
Expected loss=(x1+x2)*3.92%+(x1+x2)*.04%/5%
for more visit
http://forum.bionicturtle.com/threads/expected-shortfall.6935/
thanks