Ralph Vince - Portfolio Mathematics

Optimalf 129

the optimal f, one that some readers may find simpler and more to their
liking. It will give the same answer for optimalfas the technique previously
described.
Under this method we still need to loop through different test values
for fto see which value for fresults in the highest TWR. However, we
calculate our TWR without having to calculate the HPRs. Let’s assume the
following stream of profits and losses from a given system:

+$100

−$500

+$1500

−$600

Again, we must isolate the largest losing trade. This is−$600.
Now we want to obtain the TWR for a given test value forf. Our first
step is to calculate what we’ll call thestarting value.To begin with, take the
largest loss and divide it by the test value forf. Let’s start out by testing a
value of .01 forf. So we will divide the largest loss, –$600, by .01. This yields
an answer of –$60,000. Now we make it a positive value. Therefore, our
starting value for this example sequence of a .01 test value forfis $60,000.
For each trade we must now calculate aworking value.To do this, for
each trade we must take the previous working value and divide it by the
starting value. (For the first trade, the answer will be 1, since the previous
working value is the same as the starting value.) Next, we multiply the
answer by the current trade amount. Finally, we add this answer and the
previous working value to obtain the current working value.

P&L WORKING VALUE

60000 ←−−−−−−−−−This is the starting value

+ 100 60100

− 500 59599.166667

+ 1500 61089.14583

− 600 60478.25437

Our TWR is obtained simply by taking the last entry in the working value
column and dividing it by our starting value. In this instance:

TWR= 60478. 25437 / 60000

= 1. 007970906

Now we repeat the process, only we must increment our test value for

f. This time through, rather than dividing the absolute value of the largest