Ralph Vince - Portfolio Mathematics

186 THE HANDBOOK OF PORTFOLIO MATHEMATICS

System C

Trade P&L Bank

Optimalfis 1 unit for

every 4.00 in equity:

100.00

− 1 −25.00 75.00

2 37.50 112.50

− 1 −28.13 84.38

2 42.19 126.56

2 63.28 189.84

2 94.92 284.77

− 1 −71.19 213.57

− 1 −53.39 160.18

The end result here is better not because the optimalfs differ slightly
(both are at their respective optimal levels), but because there is a small
efficiency loss involved with simultaneous wagering.This inefficiency is
the result of not being able to recapitalize your account after every single
wager as you could betting only one market system.In the simultaneous
two-bet case, you can recapitalize only three times, whereas in the single
eight-bet case you recapitalize seven times. Hence, the efficiency loss in
simultaneous wagering (or in trading a portfolio of market systems).
We just witnessed the case where the simultaneous bets were not cor-
related. Let’s look at what happens when we deal with positive (+ 1 .00)
correlation:

System A System B

Trade P&L Trade P&L Bank

Optimalfis 1 unit for every
8.00 in equity:
100.00
− 1 −12.50 − 1 −12.50 75.00
2 18.75 2 18.75 112.50
− 1 −14.06 − 1 −14.06 84.38
2 21.09 2 21.09 126.56

Notice that after four simultaneous plays where the correlation between
the market systems employed is+1.00, the result is a gain of 126.56 on a
starting stake of 100 units. This equates to a TWR of 1.2656, or a geometric