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As it is often presented, Extreme Value Theory (EVT) is applied to financial losses (and gains as well, but always focusing in the tails). By EVT, I especially refer to:

1) Mean excess plot to find an appropriate threshold 2) Generalized Pareto Distribution (GPD) to fit to the data in the tail, beyond the estimated threshold in 1).

My question is: does it make sense to apply steps 1) and 2) to daily (arithmetic) returns, and not to PnL?

I have also seen some cases where steps 1) and 2) are applied to the residuals of a fitted model, e.g. ARMA or GARCH.

Which approach is the best?

Thanks

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  • $\begingroup$ Any reason for downvote?!?! $\endgroup$ May 22 '17 at 16:58
  • $\begingroup$ It is unclear to me, what you mean by "apply steps 1) and 2) to daily (arithmetic) returns, and not to losses?". Losses are one side of the return distribution. Do you mean applying EVT to the other side of the distribution, the wins? $\endgroup$
    – Ami44
    May 25 '17 at 11:35
  • $\begingroup$ @Ami44 No, I mean PnL... Well spotted, I will correct it for clarity. $\endgroup$ May 25 '17 at 11:51
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    $\begingroup$ The "return" is just the profit or loss on an initial investment of 1.00. So it seems to me you are making a distinction without a difference. $\endgroup$
    – noob2
    May 25 '17 at 17:08
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I don't see a reason why it should not be possible to apply peak-over-threshold to the returns.

Also see page 15 of https://www.soa.org/library/newsletters/risk-management-newsletter/2009/september/jrm-2009-iss17-levine.pdf

They use EVT on returns.

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