Expectancy and Trade Analysis

In my first article on money management I concluded by suggesting that good money management alone won’t save you if your trading strategy doesn’t give you an ‘edge’ in the market (though it’s a good start). In my article on the Kelly Formula I made the same point, and in the context of that article it becomes even more important because the formula specifically requires you to input the probability of a successful outcome.

You might like to think that your trading strategy does (or will) assure that 70% of your trades are winners, but in the absence of any proven statistics… you’re just guessing! Actually, I have no problem with that, because ultimately I think we’re all just guessing, but don’t go thinking that the use of a scientific formula will somehow correct your guesses. It’s a case of ‘garbage in, garbage out’ my friends.

Those of you who realise you are just guessing about your trading outcomes can throw away the Kelly Formula and simply bet a fixed low percentage (e.g. 1%)  of your available trading funds on each trade. Those of you who don’t like guesswork can perform some trade analysis in order to determine your trading system’s expectancy.

Trade Analysis and Expectancy

The idea of formal trade analysis is to gather some statistics on your real-life (ideally) or back-tested trades so that you have some plausible probabilities to feed into the Kelly Formula.

Do keep in mind, though, that probability is only half the story. The other half of the story is the relative size of your wins compared with your losses; i.e. what the Kelly Formula refers to as the “odds”. A success rate of 51% (giving you a slight edge) won’t save you if each loser loses you £200 and each winner wins you £100.

In his book ‘Trade Your Way to Financial Freedom’, Van Tharp proposes a function for calculating the ‘expectancy’ of your trading system by combining the probability of a win with the average gain from each win:

Expectancy = (PW * AW) – (PL * AL)

PW is the probability of a win, AW is the average size of win, PL is the probability of a loss, and AL is the average size of loss.

If your trading history or back-testing trade analysis doesn’t yield a positive expectancy, it’s time to shut up your trading shop. Or is it?

Moving Goalposts

The problem with calculating expectancy based on back-testing or your own real-life historic trades is that the game is always changing. Whereas roulette wheels don’t change, and the odds of winning at Blackjack don’t change, the financial markets do change.

The trading strategy that yielded a positive expectancy during the last bear market might become a losing strategy in the coming bull market. And vice versa.

Tony Loton is a private trader, and author of the book “Position Trading” (Second Edition) published by LOTONtech.