*Expectancy*

*Expectancy*

July 26, 2013

Having a conversation with a few potential clients this past week about our strategy we realized that most people outside of the world of trading do not understand expectancy. This became evident to us when a question came up after they read our previous blog post that mentioned a trend following win/loss ratio averages 7 out of 10 trades being losers. They asked ”how does a trend follower make money if you lose more than half the time?”

This comes down to expectancy. This is old hat for most of the traders out there and probably a lot of our clients but we always like to freshen up on important fundamentals in trading.

Expectancy can be best shown through a coin flip example. This also illustrates the most important concept in being successful as a trader which is not the entries or setups but discipline in risk management and position size.

If a fair coin is used (50/50 outcome over a high number of flips) in a flipping game where on tails I pay you $1.00 (loss) and on heads you pay me $2.00 (win). How long should I play this game and what is the expectancy. Expectancy is found by taking the win size x the win percentage minus the loss size x loss percentage. Well since this is a fair coin the percentage is 50% for both win and loss. The payouts are $1.00 for a loss and $2.00 for a win. So the expectancy is (.50 x $2.00)- (.50 x $1.00). This equals an expectancy of $.50. This means I have a positive expectancy of $.50 per flip.

Does this mean I make $.50 cents every time I flip the coin? Well any person who has been to Vegas knows this isn’t how it works. Statistically over the long run I will average $.50 cents per coin flip which means I could have long streaks of winners and long streaks of losers. This is why a casino wants to keep players playing as long as possible, so they can statistically reach their positive expectancy and profit. This is also why traders have to be disciplined in risk management to manage equity draw-downs in order to get to their positive expectancy.

One must also understand that streaks happen, good and bad, which is why position sizing is so important in order to play as light as possible during a losing streak and as heavy as possible during a winning streak. Notice in the coin flip example that the losses were half that of the wins. This is why it is so important to cut losses quickly but take profits slowly.

We have mentioned in other articles that this is difficult because it flies against human nature but necessary if one wants to be consistently profitable. Trend followers see on average a 70% loss rate vs. a 30% win rate but also see much smaller losses and much bigger gains giving us a positive expectancy over a statistical number of trades.