Mathematical Expectation in Futures Trading

A successful trading system needs to have a positive Mathematical Expectation or a statistical edge in order for it to have a chance to be profitable in the real world. It can be expressed as a percentage or in dollar terms. In dollar terms, it is equivalent to the average trade.

To calculate the Mathematical Expectation will require a few variables. The variables are the percentage of winning trades and the average winning and losing trades of the system we are testing.

In order to obtain the best results possible for our system metrics, we want to remove any optimization of cherry picking markets in our test. We accomplish this by backtesting the system over a very long time (35 or more years, and on many liquid markets, 70 or more).

Do not confuse this with a backtest of a trading program. This is a test to generate the Mathematical Expectation of our system; this is not a structure we would trade.

In our 35 year, 70 market test, a system that trades 5-6 times per year will generate 12,250 – 14,700 trades. The more trades and longer the time period in our test, the more reliable our results will be.

We can now calculate the Mathematical Expectation of our system. For this example, we will use the system metrics for a commercially available futures trading system:

Percent Winning trades = 40.84%

Percent Losing trades = (100 - 43.84) = 59.16%

Average winning trade = $2,443.94

Average Losing trade = -$1,079.15

From the given metrics, above, we can calculate the following:

Payoff Ratio = absolute (Avg winning Trade / Avg losing trade)

= absolute (2443.94 / -1079.15)

= 2.26

Expectation % = Percent wins * (Payoff ratio) – (% losers)

= .4084 * 2.26 - .5916

= .3314

= 33.14%

Expectation $ = (% wins * Avg Win) – (% Losses * avg Loss)

= (.4084 * 2443.94) – (.5916 * 1079.15)

= $359.68

Our Mathematical Expectation in percent is 33.14. This means that for every dollar we risk we can expect to make 33.14 cents. Note, this does not mean we will make a 33.14% rate of return on our account.

Our Expectation in dollars is $359.68. Combined with our Expectation in percentage, we can state we will be risking $1085.34 per trade to obtain the average trade ($359.68 / .3314).

When we structure a portfolio of markets to trade with this system, if we trade an average of 5-6 times per year per market in 25 markets, we will be making about 110 trades per year.

Since we are risking on average $1085.34 per trade, we will be risking about $119,387 throughout the year (110 trades * $1085.34 risk per trade).

According to our Expectation in percentage we should then earn on average $39,564 per year (.3314 x $119,387). If we trade this structure with $140k, we would be attempting to earn 28.6% per year on our money.

These calculations, though helpful, fail to consider drawdown. And, as we know, managing drawdown is crucial to long-term successful trading. Positive Mathematical Expectation is only one characteristic of a winning trading system.

At Commodity Trading Solutions, our strategies combine high positive Mathematical Expectations with advanced money management controls.

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Futures and options trading involve substantial risk. The valuation of futures and options may fluctuate, and as a result, clients may lose more than their original investment. In no event should the content of this website be construed as an express or an implied promise, guarantee or implication by or from Commodity Trading Solutions, LLC that you will profit or that losses can or will be limited in any manner whatsoever. Past performance is not necessarily indicative of future results. Information provided on this website is intended solely for informative purposes and is obtained from sources believed to be reliable. Information is in no way guaranteed. No guarantee of any kind is implied or possible where projections of future conditions are attempted.