Mathematics in Trading – Proven Results or Mythical Belief?

Disclaimer : This article may upset traders and quants and many of those stuck in between. This article reflects my opinion and is in no way meant to be defamatory or critical of any school of thought. If you have a rock solid system that you believe is the secret to trading the markets and need no further guidance, read no further.

What is it?

Over the years, i have always been intrigued by the study of the markets from a mathematical perspective. Indicators, systems, money management and with guidance from the stars and planets even, almost everything these days with the abundance of information and millions of intelligent minds engaged in a myriad of computers called cyberspace, the possibilities are endless.

More often than not, the rationale of numbers can only exist with 2 possible benchmarks;

1) Mathematical validation/justification of the current/proposed study assembled using pre-existing formulas

2) Past Statistics

Ever so often, results in financial trading, with specific focus to retail trading, has always revolved around systems. The composition of a system is often easy. Entry/Exit criteria is defined by a set of rules/filters and perhaps with specific focus towards a currency pair/instrument/timeframe. A more detailed system(note that it need not necessarily be a better system) might include money and order management routines.

Now, what is more difficult is the evaluation of the system. Here is where it gets tricky and perhaps self defeating too at times. Let me explain.

Evaluation of the system will quite naturally require us to test the system against real market data. With strategy backtesting available in MT4 and with many trading platforms giving you easily programmable modular development tools, putting your system to the sword and generating “possible” results of what could have been is achieved within minutes, at most.

The Difficult Part

As most developers will tell you, the first release and its results can be mediocre and may need “some work”. Often more than not, this may involve setting up more filters or tweaking parameters to give the most optimal results over time.

This process is quite simply called Optimization. A less fanciful word is market-fitting, where in simple english, we bend the model to fit what the market has done(often biased towards a specific period which is most congruent with the systems abilities).

I Hate Math

Marketing BS or Proven results?

As a system that does best with past market data, it looks great during sales pitches. However, though hindsight “intelligence” is very edifying, can we assume that these models will work as well in the future? Will it even generate the same results within the next 5 years, the next year or even as soon as it starts trading live in the real market?

The Inconvenient Truth

Even with a basic component of a strategy/system as an indicator, the obvious shortcoming is that they all lag. When they have known to perform the way they have all these while, can we know that they will perform the same, more importantly provide the same results, as those achieved in the past?

A simple trip down memory lane during the financial crisis of 2008 will tell us that nothing can be taken for granted. It was just less than 2 years ago we experienced a market condition where indicators were mostly wrong. Currency correlations were all non-existent. Market fundamentals just didn’t make sense. Statistics were pure crap. Martingale accounts simply lost sight of the end of the road. Traders trying to pick tops and bottoms lost their money, pants,(not to mention lots of hair) and of course went into a whole emotional frenzy. Many traders who i know haven’t recovered from the setback yet emotionally, let alone financially. Anyone who has a single mechanical system that did well pre, actual and post 2008 can write to me personally. I have yet to meet one.

“As far as reviews go, it is a wonderful piece of work. It is wise after the event, unfortunately, but hopefully it will enable us to be wise before the next event. ” – Brian O’Kelly, principal of Irish private equity firm QED equity and adjunct professor of finance at Dublin City University.

Brilliant Math - Still has logic, right?

So, Bottomline is,

My standpoint is, there is an over reliance of mathematical models and statistics to holster our beliefs and trading rules about the market. I have been asked countless times on the trading results and systems that we use about “Can the results be guaranteed?” As always, we are conveniently blessed with disclaimers that make the job easy for us such as “Past results do not guarantee future results”.

More to that than just an evasion of commitment, there is a serious mentality that what works before, should always work in the future. This is called over reliance. I strongly recommend “Fooled by Randomness” by Nassim Nicholas Taleb as a good read to understand what the market can provide. Honestly, as belittling as it might sound, the market is always the omnipresent, ever evolving intelligent being. Whatever, and i mean whatever conditions your system cannot handle or will “suffer” when faced with, will be the exact situation that the market will provide you with. It is only a matter of time. Given such a market condition, can your system tolerate such a period of drawdown?

That is the question you need to answer.

As one of my favourite site always quotes, “On a long enough timeline, the survival rate for everyone(systems/strategies/traders implied) drops to zero”

The bottom line is,

I am not saying that relying on mathematics and statistics is a recipe to disaster. In fact, to the contrary, i strongly recommend it. Given a world of pure random activity and that strongly personified in the financial markets, everyone is capable of coming up with a system. God bless us that without mathematics and technology, we will be down and out in the market even before we know it without proper empirical validation.

However, with increased focus on quantitative analysis, quants and risk managers being paid craploads of money, the emphasis on such validation is ill founded. As a financial institution, driven by capitalist means, how do you drive to provide better yields in an increasingly competitive financial world, yet pay your own experts to justify and validate your own goals who are meant to be your inhibitors of risk?

On the other hand, you being a paid staff(rather well i might add), whose benefits will obviously commensurate with how well the firm’s bottom line has been, will you tell the folks who are paying you to slow down or ramp up knowing that eventually, that will drive their bottomline and yours as well?

All forces have to co-exist with a certain sense of compromise. More often than not, in a capitalist system, it is always at the expense of risk.

“Those who understand well the financial questions that need answering … are often not quantitatively proficient … As for the quants, they love nothing more than having to tackle technically difficult problems … Not only will the pleasure in solving the puzzle be greater, but … the quants’ indispensability to the firm will be further confirmed,”

“So it is not surprising after all that the quant suggesting that a simpler, less quantitative approach should be used to solve a problem is only slightly less rare than a turkey voting for Christmas.” - Peter Bernstein, Against The Gods: The Remarkable Story of Risk.

In my own words, here is my 2 cents of what you can do

1) Rely on these numbers, but do not over rely on them. Always question, what if?

2) Backtest your systems

3) Backtest your systems, with as much data as you can get. We use as much as 10 years data, now 11th year counting to backtest our systems.

4) Find the worst drawdown periods – both absolute and relative. Multiply that by 2 at least to give a worst case scenario.

5) Given point 4, should it happen, imagine that it happens on your first trading day, on your next trade itself.

6) Given all goes wrong, as in 2008, be willing to keep everything you know by the sidelines and approach the market from a fresh new perspective, like you learn trading on your first day looking at the charts. Often, the simple stuff never goes wrong. Once things fall back into “normal conditions”, then re-visit your normal trading rules. An argument of subjective evaluation of these condition beckons, but i think you get the idea

As always, be happy when you trade

Happy Trading,
Seeni

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