An analysis of a Risk Management Strategy

[This post is for the curious and the seeker. The mathematics overall is simple, but I might use some technical terms and thus caveat emptor!]

Often risk management forms a very important part of the trading system, if not the most. If you consider your entire trading setup formed of multiple blocks, one of trend/setup detection, entry,exit and money management, then the last one will definitely be the king in the pack. It is the alpha and omega and has the final call on a trade.

Basically what is money management?
The basic modus operandi of managing your money,defending the capital and deciding on volatile exposure, is money management.
Yes, I know you do it.
Its like sex, everybody does it. And nobody talks about it.
I was going through some of the TA books, I have and I was surprised that very minisule part is there on money management. Even web throws up very few results.

Till now, I found the simplest type of money management strategy to risk a constant percentage of your liquid portfolio. Beware, this might look deceptively simple, but in reality it is far more powerful than you being given a free rein(rain?) on(of) tips!
So lets dive into the nitty gritty details. Over the Friday night I ran some quick simulations over Scilab, on the portfolio management.
Let us assume, Pi is initial portfolio, Ri, risk = 0.5% of Pi and X is a random binary variable which throws up either 0 or 1 with a bias, p, .X in fact is the variable which will decide whether we lose or win, in the trade. The bias ‘p’ will help us in simulating real world percentage wins, and look out for the worst case ones.
If, the system loses, it will lose 0.05*P and if the system wins, a variable G will be simulated which is actually a Gaussian variable with mean profit of 3times the risk level and standard deviation of 2times the variance level, which is often realistic, in numerous systems like trend following, positional even fundamental picks etc.

Simulation of a realistic trading scenario over 500 traders after 100 trades[click to enlarge

If a trader uses this risk management strategy of constant exposure for 100 trades, then he will observe certain profit and deviation and thus final appreciation and drawdown in his portfolio. This appreciation and drawdown will differ based on the random variable gain.
Hence when the trader repeats his results, and the maximum appreciation and drawdown is traced, it technically should be a stationary ergodic process.

That is, one which is invariant over time and its statistical properties dont change.

But mathematics aside, certain important observations can be noticed from this.

• 95% of the instances, after 100 trades, the appreciation is range bound between 1.2x-1.4x.Even if we assume that we trade one position daily, then after 100 days effectively you should see an appreciation of 30%[give or take 10%].  So roughly 10% appreciation per month. If this is the case and the present inflation rate is 11.95%, then either stricter stop loss or stay out of the volatile markets, if the strategy can’t be bettered.
• More importantly, 90-95% of the drawdowns are localised between 2%-5%, which is healthy because it will prevent too high emotional swings, driving the trader more and more towards the edge.
• One important thing in a trade is if a trader is able to catch hold of returns around 5-6 times the risk level, then a trader immediately increases her[I honestly would love to have a couple of females in D-street]  mean of maximum appreciation by at ~ 38-40%.
  

  Equity Curve over 200 runs

Signing off!

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