All this talk about convergence and divergence can be confusing but for those interested in harvesting an edge in today’s modern efficient markets, the following diagram (of the typical market distribution of returns for a liquid instrument such as the S&P500) tells the story and is an invaluable guide towards your quantitative data mining efforts.

The market distribution of returns shows through the Law of Large Numbers where an edge resides in the market data itself and reveals why there are only two broad forms of approach that can harvest an edge made available by the market.

Convergent methodologies focus on the ‘finite’ peaks of the distribution, whereas Divergent methodologies focus on the ‘unbounded’ ‘tails of the distribution. All results that arise from harvesting returns that plot within the normal distribution can simply be attributed to ‘luck alone’. It is the non-normal zones of the market distribution where you need to invest your efforts if you want to be classed as a trader as opposed to a mere gambler.

Convergence relates to the edge that can be achieved when markets are fairly predictable in nature for a finite duration and oscillate around a central tendency (quasi-equilibrium)….whereas Divergence relates to the edge associated with market uncertainty arising from unpredictable market transitions (directional moves of endurance) between states of quasi-equilibrium.

Most traders are attracted to the lure of ‘convergence’ as they like to be ‘right’ about their predictions, but these conditions are finite in nature, require a concentrated strategy and if risk is not managed well, is the downfall of these trading solutions…..but seasoned traders that can manage risk at all times and diversify widely (across many different market distributions) know that the bounty arising from the ‘unbounded’ upside leads to long term wealth and sustainability….but you have to recognise that you will be wrong ‘most’ of the time.

It is not whether you are right most of the time and wrong less of the time. What matters is the degree of that rightness and wrongness. Your long term fate in this game ultimately is decided by the outlier events you experience in life. They can either be massive ‘wrongs’ that lead to the graveyard or massive ‘rights’ that lead to your fortunes.

How you fare in this game with the Law of Large numbers is ultimately decided by where you direct your efforts w.r.t the market distribution of returns.

Contrary to popular opinion, it is the market that determines your ultimate fate…..not your system. Your system is the method you use to constrain your options to those that (with the Law of Large numbers) harvest the ‘arbitrage’ that is made available by the market condition. A small sample of trades tells you nothing about your sustainable venture into the Law of Large numbers….but the next 1000 trades certainly tell you something that is more than ‘nothing’.

Trade well and prosper

The ATS mob

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