Expectancy = (Probability of Win * Median Win) - (Probability of Loss * Median Loss)

This is because most trades don’t end up with the same average winning. In fact, many get their biggest wins from a few trades each year. Thus, the average would be skewed and make the expectancy look better than what it should be. Perhaps if we want to get even more sophisticated with trading expectancy that we also incorporate variance.

Why? Because the higher the variance, the riskier and less reliable the results will be. For example, consider these two payoff trees:
     $900               $600
    /                      /
   /50%               /50%
 /                       /
[X]                   [Y]
 \                       \
   \50%               \50%
    \                       \
     $100                 $400

If they were payoffs will you prefer? For both on average, the expected value is $500, yet Y is the better choice in the real life situation. The variance (standard deviation) of X is greater than Y, thus more volitile and less reliable.

Just a thought, what do you think, Mike?

Good catch. I’ve corrected that example.

thanks for a very interesting post about Expectancy. I would like to bring the below (minor) mistake to your attention though:

If losing trades lose 4%, the first formula in your example should be

(0.3 * $1,000) - (0.7 * $400) = $20

not

(0.3 * $1,000) - (0.7 * $300) = $90

which is still > 0 by the way so your
example still makes sense

Greetings from Brussels, Belgium

Michael Covel’s ‘Trend Following: How Great Traders Make Millions in Up or Down Markets’ will certainly be regarded as a classic investment book. Everybody involved in the markets should read this book.

This discussion of frequency vs. magnitude is leads to thinking in terms of expected value, i.e. being right when it counts. Problem is that people tend to prefer asymetric payoffs.

Nassim Taleb puts it this way: “In some strategies and life situations, it is said, one gambles dollars to win a succession of pennies. In others one risks a succession of pennies to win dollars. While one would think that the second category would be more appealing to investors and economic agents, we have an overwhelming evidence of the popularity of the first.”

Commodity Trader highlighted an article entitled ‘Losing to Win over at Investopedia.com’. That article does a good job of expanding upon my expectancy article. After reading that article I discovered that Investopedia has a huge archive of articles on…