THE HAnDbook of TECHnICAl AnAlysIsLinear Exp R number of wins r number of losses T
R n=× −×
=×
( ) ( ) /
( ( uumber of wins T r number of losses T
R r/ )) ( ( / ))
( ( / )) (
−×
=×−10 20 ××
=×−×
=×−×
=
( / ))
( ) ( )
($. ) ($. )
10 20
1 0 5 1 0 5
R win ratio r loss ratio00 (Breakeven)Therefore we see that five wins followed by five losses returns the capital to
breakeven. The same result holds true regardless of the sequence of wins or losses.
We say there is no asymmetry associated with fixed sizing since it took the same
number of trades to neutralize an equal number of wins. See Figure 28.26.
Let us now turn our attention to dynamic sizing. Before that, it would be best to
review some of the basic mathematics associated with compounding profit and loss.
To increase an amount M by a certain percentage P, we simply multiply M
by the multiplication factor [1 + (P/100)]. For example, to make 10 percent on
$100, we simply multiply $100 by [1+ (10/100)] × $100 = 1.1 × $100 = $110.
To make 10 percent on the new amount, we simply multiply the new amount
by 1.1, or multiply the original $100 by 1.1 twice. To compound the original
amount three times by 10 percent, we simply multiply the $100 by 1.1 three
times. This can be shortened to multiplying the original amount by the multi-
plication factor raised to the power equal to the number of times an amount
is compounded, that is, to compound $100 five times, we simply multiply
$100 by [1 + (P/100)]^5. To compound a loss, we simply multiply an amount by
[1 − (P/100)], raised to the power equal to the number of times the amount is
compounded. In dynamic sizing, [1 + (P/100)] is called the reward ratio and
[1 − (P/100)] the risk ratio.
Assume now that we start off with a capital of $100 with a one‐to‐one R/r
ratio setup where each win or loss is 10 percent, that is, %R = %r = 10 percent.
Let us also assume that we experience five wining trades followed by five losing
trades. The final capital will be:
Capital after 10 trades=×$ 100 (Reward Ratio)wins×(Risk Ratioo)losses
$ [ ( / )] [ ( / )]
$=×+ ×−
=
100 1 10 100 1 10 100
95
5 5figure 28.26 No Asymmetry via a Fixed‐Sizing Approach.