Ralph Vince - Portfolio Mathematics

100 THE HANDBOOK OF PORTFOLIO MATHEMATICS

System B

No Reinvestment With Reinvestment

Trade No. P&L Accum. P&L Accum.

100 100

1 15 115 15 115

2 − 5 110 −5.75 109.25

An important characteristic of trading with reinvestment that must be
realized is thatreinvesting trading profits can turn a winning system
into a losing system but not vice versa!A winning system is turned into
a losing system in trading with reinvestment if the returns are not con-
sistent enough. Further,changing the order or sequence of trades does
not affect the final outcome. This is not only true on a nonreinvestment
basis, but also true on a reinvestment basis (contrary to most people’s
misconception).

System A

No Reinvestment With Reinvestment

Trade No. P&L Accum. P&L Accum.

100 100

1 − 40 60 − 40 60

2 50 110 30 90

System B

No Reinvestment With Reinvestment

Trade No. P&L Accum. P&L Accum.

100 100

1 − 595 − 595

2 15 110 14.25 109.25

This is not just an aberration caused by a two-trade example. Let’s take
system A and add two more trades and then examine the results under all
four possible sequences of trades.