Expectancy

“At the heart of all trading is the simplest of all concepts—that the bottom-line results must show a positive mathematical expectation in order for the trading method to be profitable.” Chuck Branscomb

Dr. Van Tharp has written extensively on the subject of expectancy and using R multiples to categorize your trading results. We have taken excerpts from his book, Financial Freedom via Electronic Day Trading, Van K Tharp & Brian June, and from his newsletters to summarize how he uses R multiples and expectancy.

Van Tharp categorizes the risk you have in each trade as an R (risk) multiple. So your trading system can be characterized as a distribution of the R multiples it generates and expectancy is simply the mean of the R multiples generated.

Many people feel that trading the futures markets is extremely risky as they have “heard” of people losing all their money, and then some. This can certainly be done with the use of margin and no risk management rules. However if your trading plan is a function of R multiples you cannot suffer this fate in one blow. You could however still die a death of a thousand small cuts if your system does not have a positive expectancy.

The secret to survival is determining your maximum losing R multiple. So even though we are trading a contract worth $113,000.00 (1 contract of crude oil = 1000 barrels X current price $113.00) we only risk a maximum of 1R on each trade.

For our system the hard stop is equal to our 1R multiple, so the maximum we are prepared to lose is 1R.

We determine what dollar value 1R will be based on 2 factors. The first, as per our risk management rules, is we will only risk up to a maximum 0.60% of our total capital on each trade. That number in itself may not be realistic depending on how much capital you have and the product you wish to trade. If we need to risk more than that as per our stats then we either have to quit trading, trade a different product, or add more capital.

The other factor in determining our 1R multiple comes from our sim and live trading statistics with the product traded. These stats tell us where we should be setting our hard stop in order to give the trade room to oscillate while protecting our capital in the event the trade does not work for us. Therefore as long as the hard stop (1R) required is less than or equal to 0.60% of our total capital we know we can trade this contract.

To put this in dollar terms based on our stats the hard stop for the crude contract traded within our system is $120.00. So even though we are trading a $110,000.00 contract the most we are prepared to lose per trade is $120.00. So in our system 1R is equal to $120.00.
With the dollar value of 1R in hand we then categorize our winning trades as multiples of R. For example a $240.00 winning trade would be a R2 win, a $600.00 winning trade a R5 win and so on.

When you have a series of profits and losses expressed as R multiples you have what Van Tharp calls an R multiple distribution. Once you have a database of trades providing your R multiple distribution you can do 2 very important things. One, you can determine your systems expectancy and two, you can project your systems results over many more hypothetical trades.

Expectancy gives you the average R value that you can expect from the system over many trades. Put another way, expectancy tells you how much you can expect to make on the average, per dollar risked, over a number of trades.

Expectancy is calculated as follows:

Expectancy {[(Average Profit) * (Probability of Winning)] Less [(Average Loss) * (Probability of Losing)]}/ Average Risk Amount

After this calculation is done and you have proven your system’s positive expectancy number (if it’s negative you go back to the drawing board) you can then take your R multiple distribution and project future results.

We use a software program called Money Expert provided by MTPredictor for this projection. This spreadsheet beautifully demonstrates for us what Mark Douglas talks about in his book, Trading in the Zone, as we have previously discussed in our probabilities section.

“The successful trader understands that each individual trade is independent of every other trade; each trade is a unique event where the outcome is random. If you focus on each trade individually there will be a random unpredictable distribution between wining and losing trades. However on a collective basis the exact opposite is true. If a large enough number of trades are tracked patterns will emerge that produce a consistent, predictable and statistically reliable outcome.” Mark Douglas, Trading in the Zone

The Money Expert software allows us to see this “random distribution” of trades from our own R multiple distribution. We have found this to be extremely useful as we can take a 100 trade sample and run the random distribution to see the results over thousands of trades. This numerically shows the trader how drawdowns and losing months will occur even with a very successful trading system.

It gives you a major deposit of “emotional capital” to help you withstand these drawdowns to your financial capital.