CHAPTER 25
Fixed Fractional Trading
Because winners and losers obviously aren’t always the same size, we need to find
a formula that can account for varied trade outcomes. One such formula is the for-
mula for optimal f, which was popularized by Ralph Vince in his book Portfolio
Management Formulas: Mathematical Trading Methods for the Futures, Options,
and Stock Markets(John Wiley & Sons, 1990). This formula is designed to maxi-
mize equity growth by making the outcome of each trade dependent on the amount
you are willing to risk in relation to the risk per share traded and the worst histor-
ical losing trade.
The formula works with compounded returns and the fixed fraction of your
capital to risk per trade that produces the highest compounded return, which Ralph
Vince named terminal wealth relative (TWR) or optimal f. Because the returns are
compounded, TWR is calculated by multiplying the percentage returns from each
individual trade, so that:
TWR = HPR1 * HPR2 * HPR3 * ... * HPRi
Where:
TWR = Terminal wealth relative, expressed as the percentage compounded
return over a trading sequence.
HPRn= The holding period return for trade n, expressed as a percentage of
your total equity going into the trade.
That is, the HPRnis the percentage profit for trade n, for a given fraction (f)
risked per trade, with the same fraction for all trades within the same test run or
sequence of trades. Altering the fraction to risk of the available equity will produce
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