Examining the Distribution of Your Returns

Many traders track their profit/loss statements, but never examine their trading results in greater detail. This is like a baseball pitcher keeping tabs on wins and losses, but never examining statistics (pitches thrown per game, strikes vs. balls throwns, hits vs. outs for left-handed hitters vs. right-handed ones, etc) that capture how well he's really been pitching.

For traders, many of the metrics that reveal how well you're trading include the average heat you take on your positions (a nice measure of execution skill); the average sizes of your winning and losing trades; and the the number of winning and losing trades broken down by:

* Time of Day/Day of Week
* Specific Market or Stock/Stock Sector
* Specific Strategy or Setups
* Market Condition (trending up/down, non-trending)
* Size of Position
* Number of Trades

When coaching traders, I also like to look at what I call "contingent returns". How do you trade after a string of winning trades? After a string of losers? You can learn a great deal about emotional resilience, overconfidence, and coping with stress by pulling out those trades that occur after streaks.

One very simple metric that is easily within the grasp of traders is the distribution of returns. If you plot your daily returns (if you're a daytrader) or monthly returns (if you swing trade) over time, you can generate a histogram that is quite informative. You'll be able to see whether your average trades are skewed to the winning or losing side and whether the tails of the distribution are fatter at the profit or loss end. A trend follower often will have more losing trades than winners, but will show fat tails at the winning side over time if he has captured good trends. Very short-term traders I've worked with have relatively balanced distributions at the tails, but simply have more winning trades than losers: their distributions are shifted rightward compared to a normal distribution.

Over time, generating these distributions, you gain a sense for how you trade when you trade well and how you trade when you are off your game. A fattening of tails at the losing end of the histogram might suggest a loss of discipline; a small tail at the winning end might indicate cutting winners too quickly.

It also helps to take a look at the variability of your returns. The standard deviation of your returns represents the width of the histogram and is one way of capturing volatility. Over time, you can see how your current volatility of returns compares with past volatility: Are you putting on enough risk when you're seeing markets well? Are you swinging for the fences when opportunity isn't there? The volatility of your returns reveals your relative risk aversion vs. risk seeking.

Just about every professional trader at hedge funds that I work with knows these metrics for their trading. It's a way of keeping score, and it's a way of keeping on top of your craft. Examining the distribution of your returns and alerting yourself to shifts in the distributions, from my vantage point, is a best practice in trading and an excellent strategy for self-coaching.

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