Optimalf 123
above, or by taking the TWR, as formulated above, as an input to the
equation:
Geo. Mean=exp((l/N)*log(TWR))where: N=Total number of trades.
log(TWR)=The log base 10 of the TWR.
exp=The exponential function.By looping through all values forfbetween .01 and 1, we can find
that value forfwhich results in the highest TWR.This is the value for
fthat would provide us with the maximum return on our money using
fixed fraction. We can also state that the optimalfis thefthat yields the
highest geometric mean. It matters not whether we look for highest TWR
or geometric mean, as both are maximized at the same value forf.
Doing this with a computer is easy. Simply loop fromf=.01 tof= 1. 0
by .01. As soon as you get a TWR that is less than the previous TWR, you
know that thefcorresponding to the previous TWR is the optimalf.You
can also calculate this by hand, but that is a lot more tedious, especially as
the number of trades increases. A quicker way to do it is to use iteration
to solve for the optimal f(you can use the iterative approach whether
you are doing it by hand or by computer). Here, you are initially bounded
on fat f=0 and f= 1 .00. Pick a start value, say f=.10, and find the
corresponding TWR. Now step the fvalue up an arbitrary amount. The
example that follows steps it up by .10, but you can use any amount you
want to (so long as you do not have anfvalue greater than 1.00, the upper
bound). As long as your TWRs keep increasing, you must step up the f
value you are testing. Do this untilf=.30, where your TWR is less than at
f=.20. Now, yourfbounds are .20 and .30. Keep on repeating the process
until you zero in on the optimalf. The following illustration demonstrates
the iterative process as well as the calculations:
Atf=.10
TRADE HPR
9 1.052941
18 1.105882 The HPRs are equal to 1+(f*(−trade/biggest loss))
7 1.041176
1 1.005882
10 1.058823
− 5 0.970588
− 3 0.982352
− 17 0.9
− 7 0.958823
TWR=1.062409 The TWR is all of the HPRs multiplied together