Money Management
We observe that we do not return to the original capital after the same number
of wins and losses. To calculate the profit and loss, we first need to multiply the
initial capital by the return ratio, which is simply:Return Ratio= Reward Ratiowins× Risk Ratiolosses
=+( ) ( )
[ (10 1100/1 1 10 100
0 95099
)]^5 [ ( / )]^5
.
×−
=
It should be noted that the effects of asymmetry increase with the number of
times an amount is compounded. For example, a return ratio of 1.2^5 × 0.8^5 gives
0.815, while 1.2^10 × 0.8^10 gives 0.664. In this example, we see greater negative
expectancies with more compounding, for an equal number of wins and losses.
The geometric profit and loss (P/L) is therefore:Geometric P L/ =(Initial Capital Return Ratio× )−Initial Capitaal
=Initial Capital Return Ratio−
=×−
=−( )
$ (. )
$ (
1
100 0 95099 1
5 rrounded to the closest integer)The geometric expectancy may be calculated by finding the Tth root of the
return ratio:Geometric Exp Return Ratio = T
=+×−( / )
[[ ( / )] [ ( /
1
1 10 100^5 1 10 100))] ]
.
( / )5 1 10=0 99498We may also use the geometric expectancy to calculate the geometric P/L
accordingly:Geometric P L Initial Capital Geometric Exp/ T
$ (.= ×
=×100 0 99498))
$
10= 95Assume now that we have seven winning trades where we risked 50 percent
per trade. Assume that the R/r ratio is one to one. How many trades do we need
to lose to fall back to breakeven? We therefore set the return ratio to 1.(. ) (. )
(. ) /(. ).
ln (. ) / ln (. )1 5 0 5 1
0 5 1 1 5 0 0585
0 0585 0 5
7
7×=
==
=
=
N
N
N
44 tradesWe say there is asymmetry associated with dynamic sizing since it took a lesser
number of trades to neutralize a larger number of wins. See Figure 28.27.