Optimalf 151
a much smoother equity curve than does fullf. Of course, the trade-off is
less return—again, a difference that grows as time passes.
Here, a word of caution is in order. Just as there is a price to be paid (in
reduced return and greater drawdowns) for being too far to the right of the
peak of thefcurve (i.e., too many contracts on), there is also a price to be
paid for being to the left of the peak of thefcurve (i.e., too few contracts
on). This price is not as steep as being too far to the right, so if you must
err, err to the left.
As you move to the left of the peak of the curve (i.e., allocate more
dollars per contract) you reduce your drawdowns arithmetically. How-
ever, you also reduce your returns geometrically.Reducing your returns
geometrically is the price you pay for being to the left of the optimal f
on thefcurve. However, using the fractionalfstill makes good sense in
many cases. When viewed from the perspective of time required to reach a
specific goal (as opposed to absolute gain), the fractionalfstrategy makes
a great deal of sense. Very often, a fractionalfstrategy will not take much
longer to reach a specific goal than will the fullf(the height of the goal and
what specific fraction of fyou choose will determine how much longer).
If minimizing the time required to reach a specific goal times the potential
drawdown as a percentage of equity retracement is your priority, then the
fractionalfstrategy is most likely for you.
Aside from, or in addition to, diluting the optimalfby using a percent-
age or fraction of the optimalf, you could diversify into other markets and
systems (as was just done by putting 50% of the account into cash, as if cash
were another market or system).
Equalizing Optimalf
Optimal f will yield the greatest geometric growth on a stream of out-
comes. This is a mathematical fact. Consider the hypothetical stream of
outcomes:
+2,−3,+10,− 5This is a stream from which we can determine our optimalfas .17, or
to bet one unit for every $29.41 in equity. Doing so on such a stream will
yield the greatest growth on our equity.
Consider for a moment that this stream represents the trade profits and
losses (P&Ls) on one share of stock. Optimally, we should buy one share
of stock for every $29.41 that we have in account equity, regardless of what
the current stock price is. But suppose the current stock price is $100 per
share. Further, suppose the stock was $20 per share when the first two
trades occurred and was $50 per share when the last two trades occurred.