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" Optimal-f " and " Rumery and Lehman Fixed Ratio " are
two approaches to determining betsize when trading
futures.
Optimal-f bets a single, constant, fixed fraction of
equity on every trade. It wagers a FIXED fraction of
equity, *regardless* of recent equity history.
Fixed Ratio, on the other hand, VARIES the fraction
of equity that is placed at risk, based upon the
recent history of equity (the "equity curve"). If
you're currently in a drawdown, Fixed Ratio
has you DECREASE the fraction of equity that you're
betting on every trade. And if you're in a "drawup"
(i.e. not in a drawdown), Fixed Ratio has you bet
more and more contracts as your equity grows
bigger and bigger. A theory similar to this is
presented in Jack Schwager's "New Market Wizards",
in the interview of Randy McKay. It's on page 98
of the paperback edition, in the answer to Schwager's
question "/bold What other advice would you have
for traders? /nbold"
This is why the advertising promos are careful
to say "outperforms in scenarios WITH A DRAWDOWN" --
because Fixed Ratio cuts exposure during a drawdown,
thus equity doesn't suffer as big a %loss as
does fixed fraction, thus when winning trades
appear, fixed ratio is trading them from a
bigger equity pool, so it pulls away.
Since the Fixed Ratio algorithm needs to know
*EQUITY* *HISTORY* (rather than merely knowing
the account equity on the day of the entry signal),
it's very hard to program into standard trading
packages. They just don't give you access to
equity history. For example, you can't do it in
Omega TradeStation without resorting to writing
your own DLL's. You *can* program the "ROI"
half of the algorithm into TradingRecipes, but
I haven't figured out a way to program the "ROD"
half of the FixedRatio algorithm into T.R.
Luckily, you *can* program jolly well anything
you can imagine, if you use the tool "Microsoft C++",
so that's the research vehicle I have selected
to investigate Fixed Ratio. But it's a lot of
work.
Mark Johnson
postscript: mathematically inclined readers of the
optimal-f books have surely noted another difference:
optimal-f gets the same final equity (so called TWR)
for a sequence of trades REGARDLESS OF THE ORDER IN
WHICH THE TRADES OCCUR. But since Fixed Ratio
explicitly looks at equity history, it gives different
final equity results for different orderings of the
same sequence of trades. I will leave it for you
to ponder whether this is a bug or a feature :-) .
Mark Johnson Silicon Valley, California mark@xxxxxxxxxxxx
"... The world will little note, nor long remember, what we
say here..." -Abraham Lincoln, "The Gettysburg Address"
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