You
will see proof that using only one strategy with positive expectancy can make
your rich but can also make you poor. Trading results depend upon the
statistical distribution of trades which nobody can control.



What
you CAN control are many other factors, amongst them is your investment portfolio
structure, or better, the various strategy-market combinations. Doing this
right increases the chance of your trading being a profitable activity. See how
it is done.



Note of caution. This article is for
a serious trader who is prepared to put to use parts of his brain that process
mathematics and related sciences. Traders need to use mathematics and statistics for
proper analysis in order to develop proper trading approaches.

Please note also that numbers are shown using the European format ie. a comma is used as a decimal separator and a full stop as a thousands separator.



What is the standard advice you hear/read about money management (MM)?



The standard
advice one gets when s/he starts trading is to trade (very) small. “Risk 1% or
less per trade. Maybe 2%. Maximum 3% not too often!”



Such advice
is normally not supported by any serious background information. Why not risk
0,1% or 10% for example?



By the way,
there is nothing wrong with 10%, 1% or 0,1% or x% as long as one understands
why s/he uses that and what to expect as a probable result. Most traders don’t
understand this from a mathematical point of view because they hate mathematics
or find it boring, not to mention statistics or probability calculations. And
most importantly, nobody ever explained this to them.



Most MM
seems to be based on the logic that:



  • Most
    traders lose therefore a lower risk per trade will at least prolong their trading.
  • Most
    traders cannot control their emotions and by risking more they wipe out their account
    unnecessarily fast so they should risk less per trade.


Furthermore,
very few traders seem to understand more than the simplest MM aspects. Of those
who understand MM, not many are prepared to go through an emotional rollercoaster of a large drawdown which is INEVITABLE with aggressive MM
techniques.



However,
such a drawdown can be optimised with a proper portfolio structure which is
described below.



We will compare the
performance/profitability of 3 strategies



Backtesting
of these strategies showed the following parameters:



Strategy
A



  •  Win% =
    40%, RRR (Reward to Risk Ratio) = 3
  • Expectancy
    = 60%
     


A
simple explanation of expectancy is that it defines how much of your risk you
get back per trade if the statistical distribution of trades is ideal (which
never is!)



One
possible formula for calculating expectancy = 
(Win% * RRR – Loss% * 1)/100%



Strategy
B



  • Win% =
    75%, RRR = 1
  • Expectancy
    = 50%.


Strategy
C



  • Win% =
    50%, RRR = 1.5
  • Expectancy
    = 25%.


We have one BIG problem with these strategies:



  • Strategies
    A and B are proprietary and we don’t know how they function. We only know
    their results.
  • Strategy
    C is our newly developed strategy. According to the numbers from
    backtesting it is inferior to the
    proprietary strategies. But those two strategies are out of our reach so
    what can we do to compete with them (if this is what we need to do)?


What happens when we apply standard MM?



Let’s assume
we have an account with $100.000. I used a Monte Carlo
simulation of 1.000 iterations of 200 trades with trades distributed in a
random fashion but in line with the theoretical W/L ratio of each strategy.



Note: This Monte Carlo simulation worked
in a mathematically ideal trading world with no spread, commission, slippage, broker stop hunting, central bank interventions and without the changing mind of the market.



Why 200
trades? If you have 1 trade per day this is about a year’s worth of trading.



Here are the
results, based on Excel calculations using RAND()
function.





Not surprisingly, strategies line up in
profitability according to their expectancy.



If
we run 10.000 simulations, we should expect wider extremes but also an average
which is not too far from the one calculated in 1.000 iterations.



The
results are below but only for 2% risk per trade and only for the first 2
strategies. We already know that Strategy C cannot compete with the other two
strategies due to its low expectancy.






If
we want to compete with Strategies A and B as far as profitability is concerned
we need to employ aggressive money management. Let’s say we decide to risk 5%
per trade.



The
results of Monte Carlo simulations are below.






The average
and highest final equity of Strategy C is now the best. Not surprising with a
risk of 5%!



However, we
have a PROBLEM. The lowest final
equity is way below the initial equity of $100.000. So we can see that by
applying aggressive money management it is possible to make as much money and
more with Strategy C as with the other two strategies but also to lose a lot of
money.



How can we solve a problem of the potential negative extremes in the
portfolio equity?



So far we
have used one strategy in one account. If we got hit by a statistically “good”
set of 200 trades, our performance was good. If we got hit by a “bad” set of
trades, we lost money.



We cannot
control the win/loss distribution. The
market does what the market wants to do.
So if we trade this way with
aggressive MM, we will rely on LUCK a lot! We may end up extremely rich or
extremely poor. Not a persuasive enough argument if one cannot afford to lose
much money.



In the next
section you can see how we can minimise
our reliance on luck
and increase our chance of success.



What happens if we use a different
portfolio structure?


One good way
to approach this is to show what happens when we divide our account into 10
sub-accounts of $10.000, each running one strategy-market combination which is
not correlated with other strategy-market combinations. (I told you it was a simulation in an ideal trading world. We need to start with a simple example to be able to understand it!)



All
strategies in those sub-accounts have the same parameters as Strategy C to keep
things simple. Of course, the trade outcome distribution is randomly
distributed in line with W/L ratio. We still risk 5% of the sub-account per
trade.



The results
after 10.000 iterations are shown below. Previous results are also included for
comparison. 






The average
final amount in the portfolio is similar to the average final amount when
trading Strategy C on one large account. The BIG difference is in the highest
and the lowest final equity!!!



While we
lose a lot on the upside, we also gain a lot on the downside. In fact, we
sacrifice the upside to minimise the downside potential. But as capital
preservation should be a prime concern (no profit can be generated with no money!)
this is a good outcome.



The worst
case scenario in this particular portfolio situation is not any more a loss of
the initial equity but a decent profit which is higher that the
lowest final equity with strategies A and B.



The explanation of why this is so is beyond the scope of this article.
The reader who is interested in exploring the topic of money management in more
detail will surely find appropriate books for his/her perusal.



What is a possible conclusion of this simulation/study?



A conclusion
is simple: a diversified portfolio of non-correlated strategy-market
combinations minimises the profit and loss potential but allows us to use an
aggressive MM approach.



Please do
not forget that in trading we are always talking probabilities. Nothing is 100%
certain. An optimised portfolio structure cannot eliminate the possibility of a
failure. We can still lose it all despite our knowledge, experience and an
optimised portfolio structure if we get hit by a long enough losing streak.
However, the described approach can at least increase our chances of success.



What does this mean for YOUR
TRADING?



If
you have never looked at money management, strategy correlation and market correlation in
more detail I suggest you do it if you want to be successful in the long run.
While you can be successful without this knowledge and understanding, the
chances are vastly improved if you become more proficient in the mentioned
topics.



An
added benefit is that you will be able to participate actively in any
discussion about 0,1% or 10% or whatever % risk per trade. Trading "gurus" will
not be able to pull wool over you eyes.



Last
but not least: The more you know in trading the less luck and reliance on
others is required.





Wishing
you profitable trading with whatever money management you use.

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