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

What is expectancy in a nutshell?

A trading system can be characterized as a distribution of the R-multiples it generates. Expectancy is simply the mean or average R-multiple generated.

What does that mean?

By now you should know that in the game of trading it is much more efficient to think of the profits and losses of your trades as a ratio of the initial risk taken (R).

But let’s just go over it again briefly:

One of the real secrets of trading success is to think in terms of risk-to-reward ratios every time you take a trade. Ask yourself, before you take a trade, “What’s the risk on this trade? Is the potential reward worth the potential risk?”

So how do you determine the potential risk on a trade? Well, at the time you enter any trade, you should pre-determine some point at which you’d get out of the trade to preserve your capital. That exit point is the risk you have in the trade or your expected loss. For example, if you buy a $40 stock and you decide to get out if that stock falls to $30, then your risk is $10.

The risk you have in a trade is called R. That should be easy to remember because R is short for risk. R can represent either your risk per unit, which in the example is $10 per share, or it can represent your total risk. If you bought 100 shares of stock with a risk of $10 per share, then you would have a total risk of $1,000.

Remember to think in terms of risk-to-reward ratios. If you know that your total initial risk on a position is $1,000, then you can express all of your profits and losses as a ratio of your initial risk. For example, if you make a profit of $2,000 (2 x $1000 or $20/share), then you have a 2R profit. If you have a profit of $10,000 (10 x $1000) then you have a profit of 10R. The same thing works on the loss side. If you have a loss of $500, then you have a 0.5R loss. If you have a loss of $2000, then you have a 2R loss.

But wait, you say, how could you have a 2R loss if your total risk was $1000? Well, perhaps you didn’t keep your word about taking a $1000 loss and you didn’t exit when you should have exited. Perhaps the market gapped down against you. Losses bigger than 1R happen all the time. Your goal as a trader (or as an investor) is to keep your losses at 1R or less. Warren Buffet, known to many as the world’s most successful investor, says the number one rule of investing is to not lose money. However, contrary to popular belief, Warren Buffet does have losses. Thus, a much better version of Buffet’s number one rule would be to keep your losses to 1R or less.

When you have a series of profits and losses expressed as risk-reward ratios, what you really have is what Van calls an R-multiple distribution. As a result, any trading system can be characterized as being an R-multiple distribution. In fact, you’ll find that thinking about trading system as R-multiple distributions really helps you understand your system and learn what you can expect from them in the future.

So what does all of this have to do with expectancy?

When you have an R-multiple distribution from your trading system, you need to get the mean of that distribution. (The mean is the average value of a set of numbers). And the mean R-multiple equals the system’s expectancy.

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.

So when you have a distribution of trades to analyze, you can look at the profit and loss of each one of the trades that was executed in terms of R (how much was profit and loss based on your initial risk) and determine whether the system is a profitable system.

Let’s look at an example:







So this “system” has an expectancy of 2R, which means you can “expect” to make two times what you risk over the long term using this system, based on the data that you have available.

Please note that you can only get a good idea of your system’s expectancy when you have a minimum of thirty trades to analyze, and the preference would be to have 100 to 200 trades to really get a clear picture of the system’s expectancy.

So in the real world of investing or trading, expectancy tells you the net profit or loss that you can expect over a large number of single unit trades. If the total amount of money in the losing trades is greater than the total amount of money in the winning trades, then you are a net loser and have a negative expectancy. If the total amount of money in the winning trades is greater than the total amount of money in the losing trades, then you are a net winner and have a positive expectancy.

Example, you could have 99 losing trades, each costing you a dollar. Thus, you would be down $99. However, if you had one winning trade of $500, then you would have a net payoff of $401 ($500 less $99)—despite the fact that only one of your trades was a winner and 99% of your trades were losers.

We’ll end our definition of expectancy here because it is a subject that can become much more complex.



Van Tharp has written extensively on this topic and it is one of the core concepts that he teaches. As you become more and more familiar with R-Multiples, position sizing and system development, expectancy will become much easier to understand.

To safely master the art of trading or investing, it is best to learn and understand all of this material. Although it may seem complex at times, we encourage you to persevere because like any worthwhile endeavor, as soon as you truly grasp it and then work towards mastering it, you will catapult your chances of real success in the markets.