|
PureBytes Links
Trading Reference Links
|
Pavel Kotulsky wrote:
>I have some conceptual problem:
>
>how to reveal a positive expectancie (PE) of a strategy(system)?
Van K. Tharp wrote an excellent book that dealt extensively with
this subject. The book is called "Trade your way to financial
freedom." Despite the hyped-up sounding title, it really is a
good book which has affected the way I look at trading more than
any other book. (I'd like to thank Mark Brown and Mike Higgs for
recommending this to me.)
I personally disagree with some of his methodology, finding it
needlessly complex when one can achieve the same result more simply.
Now to the details: Given a system that has generated a
statistically significant number of trades, what Tharp does is this:
1. Separate the trades into two groups, winners and losers,
discarding those trades that broke even or won or lost insignificant
amounts.
2. Divide each win and loss by for each trade by the system's
minimum loss (typically this will be the smallest stoploss amount
the system would use). This gives you a risk multiple for each
trade. The winning trades represent your earnings, and the losing
trades represent your risk.
3. Construct a distribution for the winning trades (that is, divide
the win multiples up into several ranges and count the number
of trades that fall into each group), and do the same for the
losing trades. The peak of the distributions are your expected win
multiple and expected loss multiple.
4. The system's Expectation is the expected win divided by the
expected loss. This number tells you how much money you can expect
to earn for every dollar you risk.
5. The system performance is Expectation * Opportunity Factor,
where Opportunity Factor is the number of opportunities you have to
earn your expected return per a given time period. For example,
if your system generates 500 trades over 5 years, your Opportunity
Factor is 100 trades per year, or 8.33 trades per month. Whatever
time interval you use, it should be the same for comparing the
performance all your systems.
I disagree with Tharp in steps 2 and 3. In step 2, dividing by
the minimum loss gives you an overly optimistic assessment of your
earnings adjusted for risk. Nevertheless, this becomes irrelevant
in step 3 because if you write out the equations, the minimum loss
terms all cancel out anyway. So Tharp's step 2 is redundant.
I disagree with step 3 because it's needlessly complicated.
Constructing distributions is useful for locating outliers (that one
big booming winner or that one disastrous loser), and it allows you
to find the most likely occurrence on the winning and losing sides.
However, in practice I have found that these results agree closely
to the average win and average loss, anyway. If you have an outlier
you can eliminate it prior to calculating the averages. Or, you
can calculate the medians instead. Unlike means, medians are not
sensitive to large outliers.
What I do to evaluate system expectation is more conservative than
Tharp's method, and simpler.
I do step 1, I skip step 2, I substitute for step 3 the average of
all the winning trades EXCLUDING the maximum win, and the average
of all the losing trades (all the losers). I don't eliminate
near-break-even trades. I divide the average win by the average
loss to get expected return per dollar risked.
Then I multiply the result by the opportunity factor, as described
above.
This gives you a single score for system performance that you can
compare to the scores of other systems, or the same system with
different parameters. It gives you a single objective number which
you can maximize during an optimization. If you want, you can
multiply this score by Sharpe Ratio to get something more refined.
In any case, you now have a way to compare systems objectively.
--
,|___ Alex Matulich -- alex@xxxxxxxxxxxxxx
// +__> Director of Research and Development
// \
//___) Unicorn Research Corporation -- http://unicorn.us.com
|