Expectancy: How Profitable is your Trading Strategy?

11 févr. 2015

As we all know, when we open a trade, there is no guarantee it will be a winner. Given the win rate of a certain trading strategy, there is a random distribution between wins and losses. We trade to make money over a larger number of trades, not to win every individual trade, which would simply be unrealistic. That is why it’s important to be confident when we place a trade. So we don’t “panic close” the trade when the market goes against us, or exit too soon when we are in profit.

If you know the expectancy of your trading strategy, you will be able to deal with these situations better. There is a psychological aspect here: knowing the predictable profitability of a larger number of trades you undertake will build your confidence, which in turn reduces your tendency to shortcut winners and to let losers run too long. Having this confidence will thereby improve your overall results. In December I developed a spreadsheet for myself, linked to my trading records, where I calculate several performance indicators, among which expectancy.

How to determine the expectancy of your trading system? Assuming you keep records of your trades, you should go back and look at all your trades that were profitable versus all your losing trades. Do this over a period of at least 3 months and at least 100 trades. The more data you can use, the more accurate the result. We only need 4 pieces of information: number of winning trades, number of losing trades, amount of money won and amount of money lost. From this data we can calculate the following:

Net profit = amount of money won - amount of money lost

Win rate = number of winning trades / total number of trades

Lose rate = 1 - win rate

Average winner = amount of money won / total number of winners

Average loser = amount of money lost / total number of losers

Average reward / risk = average winner / average loser

Expectancy per trade = win rate x average winner – lose rate x average loser

Or, alternatively, expectancy per trade = net profit / total # trades

Expectancy per month (profit forecast) = expectancy per trade x average # trades per month

Expectancy per amount of money risked = win rate x (average reward / risk + 1) – 1

Or, alternatively, expectancy per amount of money risked = net profit / average loser / total # trades

I will illustrate this with an example for a euro account. Lets assume we have been trading for 6 months and made a total of 540 trades. 297 of them were profitable and 243 were not, with €35.640,00 profit coming from the winning trades and €19.440,00 loss stemming from the losing trades. Lets make the calculations:

Net profit = €35.640,00 - €19.440,00 = €16.200,00

Win rate = 297 / 540 = 55%

Lose rate = 1 - 55% = 45%

Average winner = €35.640,00 / 297 = €120,00

Average loser = €19.440,00 / 243 = €80,00

Average reward / risk = €120,00 / €80,00 = 1,5

Expectancy per trade = 55% x €120,00 – 45% x €80,00 = €30,00

Or, alternatively, expectancy per trade = €16.200,00 / 540 = €30,00

In our example the expectancy per trade is €30,00. This means, on average (over many trades), each trade will contribute €30,00 to the overall P&L.

Expectancy per month = €30,00 x 540 / 6 = €2.700,00

In our example we can forecast a monthly profit of €2.700,00 based on prior performance.

Expectancy per € risked = 55% x (1,5 + 1) – 1 = 38%

Or, alternatively, expectancy per € risked = €16.200,00 / €80,00 / 540 = 0,38

In our example the expectancy of the trading strategy is 38%. That means the trading strategy will eventually (over many trades) return 38 eurocents for each euro risked.

Once you know your expectancy, as a function of your own trading statistics, you can forecast how much you could make per week, per month and per year.