What is Positive Expectancy?

Positive expectancy sounds like something a motivational speaker would talk about or a psychiatrist. In fact, there are some people that use the term for those reasons. This article is about using the term in the context of Forex trading strategies, STATISTICS, and MATH. One of the major advantages from using an automatic Forex trading system is built in discipline that maintains a high POSITIVE EXPECTANCY that can lead to large profits. Positive expectancy defined in its most simple form, is that on the average, there is a probability that you will make more money than you will lose.

If the Forex trader gets nothing else from this article the MOST IMPORTANT POINT that must be understood is that WITHOUT POSITIVE EXPECTANCY in any Forex trading system automatic or otherwise, there are no money management procedures or trading techniques that will prevent you from losing all your money.

Most traders confuse positive expectancy with the probability of winning. Forex traders and especially Forex system developers love to brag that their system “picks winners 97. 3% of the time”, and fall for the easy but incorrect logic and “feeling” that a high percentage of wins means a high profit. Sadly, this is NOT TRUE! Winning 97. 3% of the time will not generate Forex profits if the 2. 7% of losing trades wipe out your account. Confusing win probability with positive expectancy is what ultimately leads to Trader’s Ruin.

Trader’s Ruin is the mathematical certainty that over time the trader will lose all his money to the market if he trades without positive expectancy. Many very successful traders and auto Forex trading systems have a win probability of about 40%, with a high positive expectancy that returns huge profits.

If an automatic currency trading program wins 9 out of 10 times (90% wins! )#), and the average win is $10 but the average loss is $100 – that system has a negative expectancy and will lose money!

If an automatic Forex currency trading system wins once every 20 trades (5% wins! )#), losing an average $5 each losing trade but makes an average $100 on each win, that system has positive expectancy and over the long run will make money.

Did that tie your brain in a knot? Let’s explain a little further.

To be able to say an automatic Forex trader, or any system, has positive expectancy means that on average the system will make more money than it loses. On any given trade, it may win or it may lose, but the average over time and many trades is profitable. This should include costs and slippage and be measured over an absolute minimum of 30 to 100 trades, preferably many more.

 

This analysis assumes the Forex trader and the Forex trading tool are properly capitalized and the trades are properly sized to reasonably ensure the system will survive the inevitable periods of losses.

“Properly capitalized” means you have enough money in your account that you can make properly sized trades and survive long enough for the average returns to grow your account. If the account is too small, it is much more likely a run of losses will wipe you out before you have time to generate profits.

“Properly sized” trades means that the average size of expected profit on any trade is large enough to cover expected average losses plus trading costs and still have positive expectancy.

“Exit loss” will be defined for this article as the amount the trade will be allowed to move against us before it is “stopped out” by our stop loss setting and we exit the trade. This applies to both winning and losing trades.

“Costs” in Forex trading are usually in the form of “bid/ask” spreads, Forex brokerage fees or commissions are usually small or non-existent. There are still real costs that figure into the expectancy of the system.

“Slippage” is defined as the difference between the price a trader expected to pay when a trade is ordered and the actual price paid. The Forex market is always moving and if the market moves against our trade, the time between our contract order and when it is executed in the market may allow the price to change. A good Forex automated trading system has an average known slippage value figured into the system also.

To make this easier to understand, let’s put some numbers to it. These are simplified examples to illustrate the concept and the numbers may or may not match real FX trading strategies.

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