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On Optimal_f
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The point where you get the maximum possible return from this
investment is at the top of the investment curve (see second chart).
This point gives the maximum "terminal wealth relative" as Ralph
Vince calls it and is the point he calls Optimal_f. Anyone operating
at this point would have to have a utility curve that is a flat
horizontal line.
A flat utility curve would imply that you value return above all
else, no matter what risk is involved. No rational person would have
such a utility curve so this is one reason why operating at Optimal_f
is not popular. At that point on the chart the leverage factor is
about 7 for this "system" and at one point in the five years period
you would have lost 70% of your account value in one week. How many
people would have stayed in at that point to see the recovery?
At a leverage factor of about 15, you would have "gone broke" in that
correction week, losing all of your account. The "gone broke" point
is fairly far from the Optimal_f point because this is a pretty lousy
trading system with a Sharpe Ratio of less than one. With a better
system, the "gone broke" point is only slightly higher than the
Optimal_f point.
Futures Traders use of Leverage
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A futures trader inherently is using leverage. One S&P 500 contract
is worth 250 * $1400 = $350,000 now. With an account size of $35,000
today he would be using a leverage factor of 10 on this "system",
which would be well to the right of the peak, which would be stupid.
Operating to the right of the peak increases variability and
decreases returns. Operating at the peak with this "system" with a
leverage factor of about 7 would require an account size of about
$50,000 today.
Summary
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So different people have different utility curves depending upon
their personal circumstances. The optimum operating point is where
their utility curve just touches the curve describing the
market/system combination they are using. No rational person would
operate at the peak of the curve, the Optimal_f point, since that
would imply a utility curve that values only return with no
consideration for risk.
Bob Fulks
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