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Tanya, Naveen,
Just a thought. Changes in the portfolio values may combine both the changes of prices and positions. This happens if one tracks changes in the value of our historical gas portfolio. A big jump in the volumetric position from day to day, combined with a moderate price movement may produce an observation that looks artificially big. If the volumetric position was frozen, it's just a scaling factor and there should be no discrepancy between your numbers. Of course, the correct approach is to separate the price process from the position changes. Vince Tanya Tamarchenko 11/13/2000 08:38 AM To: Naveen Andrews/Corp/Enron@ENRON cc: Vince J Kaminski/HOU/ECT@ECT, Vladimir Gorny/HOU/ECT@ECT Subject: Re: looking for "Fat Tails" in time-series for NGI-SOCAL Naveen, I am trying to answer the question: what is the appropriate stochastic process to model the behavior of commodities' prices in our VAR model. So what I do care about is the behavior of log-returns. Any help is appreciated. Tanya. Naveen Andrews@ENRON 11/10/2000 04:35 PM To: Tanya Tamarchenko/HOU/ECT@ECT cc: Vince J Kaminski/HOU/ECT@ECT, Vladimir Gorny/HOU/ECT@ECT Subject: Re: looking for "Fat Tails" in time-series for NGI-SOCAL Tanya, We care about PORTFOLIO VALUE CHANGES, not log-returns of a single contract, which has extremes in the behavior and can be fit to a fat-tailed distribution. A 1.20 basis move, with 500 BCF position, is an extreme event, anyway you slice it.In the literature, as elsewhere, I agree for a single contract log-returns, they don't divide by vols. Regards Naveen Tanya Tamarchenko@ECT 11/10/2000 04:17 PM To: Naveen Andrews/Corp/Enron@ENRON cc: Vince J Kaminski/HOU/ECT@ECT, Vladimir Gorny/HOU/ECT@ECT Subject: Re: looking for "Fat Tails" in time-series for NGI-SOCAL Naveen, I got NGI-SOCAL prices for prompt, prompt+1,...,prompt+59 contracts. For each contract I calculated moving average based on 21 log-returns as well as moving volatility. Then I calculated normalized log-returns: [ return(t)-ave(t) ] / vol(t) and compared the results to normal distribution. I COULD NOT FIND Fat Tails! Volatility changes a lot from day to day, so when people look at log-returns (not normalized) it seems that there fat tails (big spikes, large returns more frequent than normal), which comes from the fact that volatility is not constant (at all). See the spreadsheet is under O:\_Dropbox\Tanya Tanya
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