---------------------- Forwarded by Vince J Kaminski/HOU/ECT on 03/21/2001 
12:52 PM ---------------------------


Tanya Tamarchenko
03/21/2001 09:58 AM
To: Naveen Andrews/Corp/Enron
cc: Vince J Kaminski/HOU/ECT@ECT, David Port/Market Risk/Corp/Enron 
Subject: Re: estimating tail of distribution and additional risk measures  

Naveen,
the "analytical VAR" approach is working for Equity portfolio. 
It gives us the tool to examine the tails' behavior for this portfolio and 
calculate "Expected Tail Loss".
The same should be done for commodities portfolio as well.

Meanwhile, as we discussed, we can give some rough estimates of the losses 
corresponding to percentiles other than 5th.

Look at the figure below. You can see VAR numbers for 5%, 1%, 0.5% and 0.1% 
calculated with 
1) simulations (100 thousand simulations);
2) analytical VAR (gamma-delta positions representation)

 1) and 2) are very close because there are not many options in Equity 
portfolio.

3) simulations (1000 simulations) to calculate 5% VAR. Then in order to 
approximately estimate VAR for 1%, 0.5% and 0.1%
I scaled 5% VAR with factors corresponding to normal distribution (for 
example: Norminv(0.001,0,1)/Norminv(0.05,0,1) for 0.1%).
The result of such extrapolation in this case is quite good (just 5% 
different from the correct number). 
We probably can use such rough estimates of tail for commodities portfolio 
until we have proper methods implemented. 





Tanya Tamarchenko
02/28/2001 01:17 PM
To: Wenyao Jia/HOU/ECT, Debbie R Brackett/HOU/ECT@ECT
cc: Vince J Kaminski/HOU/ECT@ECT 
Subject: Re: "analytical" var implementation in RisktRAC  

Debbie,
I am forwarding to you a 2 page document describing implementation of 
"analytical" VAR in RisktRAC.

Here is why this effort is very important:
1. We need to calculate VAR for other percentile but 5 (1% or even 0.2% as 
mentioned by Rick Buy)
and our simulation model can not handle required number of simulations;
2. We need to present additional risk measures (such as Mean Tail Loss) to 
the Board.

The analytical approach is implemented in a spreadsheet and fully tested 
already so there will be no problems
with the algorithm itself.

We need to get together and discuss IT implementation.

What do you think?

Tanya