Ralph Vince - Portfolio Mathematics

Optimalf 127

profits and losses are not the product of the amount of money put up as
margin (they would be the same whatever the size of the margin). Rather,
the profits and losses are the product of the exposure of one unit (one
futures contract). The amount put up as margin is further made meaningless
in a money-management sense, since the size of the loss is not limited to the
margin.

HOW TO FIGURE THE GEOMETRIC MEAN
USING SPREADSHEET LOGIC

Here is an example of how to use a spreadsheet like to calculate the geo-
metric mean and TWR when you know the optimalfor want to test a value
forf.

(Assumef=.5, biggest loss=−50)

col col col col col

AB C D E

row 1 1

row 2 15 0.3 0.15 1.15 1.15

row 3 − 5 −0.1 −0.05 0.95 1.0925

cell(s) explanation

A1 through D1 are blank.

E1 Set equal to 1 to begin with.

A2 down These are the individual trade P&Ls.

B2 down=A2/abs value of (biggest loss)

C2 down=B2/f

D2 down=C2+ 1

E2 down=E1*D2

When you get to the end of the trades (the last row), your last value in
column E is your TWR. Now take the Nth root of this TWR (N is the total
number of trades); that is your geometric mean. In the above example, your
TWR (cell E3) raised to the power 1/2 (there are a total of two trades here)=
1.045227. That is your geometric mean.

Geometric Average Trade

At this point you may be interested in figuring your geometric average trade.
That is, what is the average garnered per contract per trade, assuming