132 THE HANDBOOK OF PORTFOLIO MATHEMATICS
more and more important to use the optimalf. The point is you must give
the program time when trading at the optimalfand not expect miracles in
the short run. The more time (i.e., bets/trades) that elapses, the greater the
difference between using the optimalfand any other money-management
strategy.
Why You Must Know Your Optimalf
Figures 4.3 through 4.6 demonstrate the importance of using optimalfin
fixed fractional trading. The graphs are constructed by plotting thefvalues
from 0 to 1.0 along the X axis and the respective TWRs along the Y axis.
Values are plotted at intervals of .05.
Each graph has a corresponding spreadsheet. Each column heading in
the spreadsheet has a differentf value. Under eachfvalue is the corre-
sponding start value, figured as the biggest loss divided by the negativef
value. For every unit of start value you have in your stake, you bet one
unit. Along the far left is the sequence of 40 bets. This sequence is the only
difference between the various spreadsheets and graphs.
As you go down through the sequence of trades you will notice that each
cell equals the previous cell divided by that cell’s starting value. This result is
then multiplied by the outcome of the current bet, and the product added to
the original value of the previous cell, to obtain the value of the current cell.
When you reach the end of the column you can figure your TWR as the last
value of the column divided by the start value of the column (i.e., the biggest
loss divided by negativef). This is the alternative and somewhat easier way
to figure your TWRs. Both methods shown thus far make the calculations
non-quantum. In other words, you do not need an integer amount to multiply
the current bet result by; you can use a decimal amount of the starting value
as well. An example may help clarify.
In the+1.2,−1 sequence (Figure 4.3), for anfvalue of .05, we have a
starting value of 20:
−1/−.05= 20
In other words, we will bet one unit for every 20 units in our stake. With
the first bet, a gain of 1.2, we now have 21.2 units in our stake. (Since we
had 20 units in our stake prior to this bet and we bet one unit for every
20 in our stake, we bet only one unit on this bet.) Now the next bet is a
loss of one unit. The question now is, “How many units were we betting on
this one?”
