to put into one trade; the wider the stop loss, the less capital you need to put into
one trade.
A good trader also tries to balance the steepness of the equity curve with its
smoothness, so that the steeper the better and the smoother the better. The more you
risk, the more erratic the equity curve and the riskier the trading in general terms.
The major flaw with the Kelly formula is that it assumes two outcomes
only—a winner of a certain magnitude and a loser of a certain magnitude.
Therefore, it is better to use the formula for optimal f, as popularized by Ralph
Vince.
In Ralph Vince’s original version of the formula, fdepends on the worst his-
torical loser, because we’re implicitly assuming that one reason to trade this sys-
tem is that its largest historical loser is within the limits for what we can tolerate,
given the profit potential of the system.
To make a long story short, calculating the ending equity, which Ralph Vince
dubbed terminal wealth relative (TWR), is done using the following formula:TWR GMN HPR1 * HPR2 * HPR3 * ... * HPRiWhere:
GM (APM^2 SD^2 )(N/2)
HPRn 1 f * (Profitn/ WCS)
TWR Terminal wealth relative, expressed as the percentage compounded
return over a trading sequence
GM The geometric mean
N Number of trades
APM The average profit multiplier, calculated as the average percentage
profit per trade divided by 100, plus one
SD Standard deviation of all trades, measured in percentage terms
HPRnThe holding period return for trade n, expressed as a percentage of
your total equity going into the trade
f The fixed fraction of your capital to risk in all trades
ProfitnThe profit or loss from trade n in dollars on a constant-shares
invested basis
WCS The historical worst-case scenario in dollars on a constant-shares
invested basis (expressed as a positive number)
Thus, given the largest historical loser, by altering fwe can alter the size of
the profit or loss of any individual trade (HPRn) and consequently alter the TWR.
However, from the formula it also follows that TWR depends on how large the
average trade is in relation to the outcome of all trades (the larger the better) and
the number of trades (the more trades the better).380 PART 4 Money Management