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Have you considered using geometric average trade (GAT)? I do see it
applied every so often as a trade metric. Ralph Vince outlines its
derivation in Portfolio Management Formulas. The benefit is that GAT is
isomorphic to final equity, while expectation (either ME or R-Multiple ME)
is not ... a fancy way of saying you can project final equity from GAT and
visa versa. (You can read more about geometric average trade and system
performance on the Traderclub thread here
...http://www.traderclub.com/discus/messages/18/1431.html).
You're correct in saying that returns are not Gaussian ... so most any use
of StdDev is meaningless. So is "average" in many cases, since that makes
the same assumptions. This is one problem with ME (mathematical
expectation) as a metric. That doesn't imply it is not useful, just that ME
as a metric has limitations.
I would think you'd be able to get the equivalent of variance off any
probability distribution function (PDF), even if the curve is skewed. You
certainly can ask questions like "what percent of events fall within 65% of
the the PDF peak (roughly 'norm'), or any other point on PDF curve. Market
return PDFs are typical left skewed, with fat tails (Lepto-Kurtotik), so
for the metric you'd want to express a bounded range with an offset center.
This should tell you a lot about the return distribution.
In pondering this discussion, I'm finding that one reason there are many
metrics is their characteristic limitations. Another reason is that metrics
serve many purposes: comparison (which
systems/parameters/periods/time-frames are better), validation (can I
expect positive returns), and consistency (is this system performing like
it did in the past). In the first case, we can work to eliminate
limitations. In the second case, we probably don't want just one metric.
Cheers,
Kevin
At 01:52 PM 1/22/2004 -0800, you wrote:
I agree with Alex's assessment of Sharpe ratio. The entire point of active
trading is to create an asymmetrical (i.e., positively skewed) distribution
of returns, so using volatility around both sides of the mean as a risk
measure will perversely penalize strategies that generate positive skew.
Furthermore, when we look at the financial markets we realize that we are
not dealing with a Gaussian distribution---we are dealing with something
else, most probably a stable Paretian distribution. In a stable Paretian,
variance is undefinable.
High Sharpe ratios can be created---temporarily---merely by naively selling
fairly-priced options. During times of relative market dormancy, the
strategy will appear virtually "riskless;" then one day the music stops and
the options-seller (more specifically, his clients) are left without a
chair.
Just my $.02.
Sebastian Pritchard
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