Monday, June 4, 2012

Possibly the most important metric for any trading system - "expectunity"

Many newbie traders like to define their success by the amount of pips they win per trade. For others, it's the win rate (%). Both are important, but by themselves, tell an incomplete story.

Measuring your success by the amount of pips you win seems simple. In fact, I would use this metric as a way of measuring your ability to predict market movement. Obviously the higher the better. However, it ignores your position size (the amount, or number of lots, you decided to buy or short). Example: I decide to buy a single lot of AUDUSD and win 100 pips. Feeling super-confident about a trend reversal, I decide to short the AUDUSD with three lots, with a stop loss of 50 pips. The trend continues and hits my stop loss.

According to my metric, I'm still up 50 pips (100 pips won - 50 pips lost) and should be in profit, right? Nope. If you take position size into account, you are in negative territory.

100 pips * 1 lot won - 50 pips * 3 lots lost = - 50 pips lot

Disregarding pips altogether:

1 lot won - 3 lots lost = - 2 lots

Suppose your win rate is 90%. This looks marvellous on the surface, but tells nothing about the size of your wins or losses. Hitting a 90% win rate is extremely easy. Just set a tiny profit target per trade, or worse yet, use no stop loss. In fact, with no stop loss or leverage, it's conceptually possible to win 100% of the time (disregarding something catastrophic like deregisteration of a currency). Just keep your trades open when they turn against you and wait, wait, wait until the market turns back in your favour.

Of course, the process may take years if you bought at the absolute top or shorted at the absolute bottom. But as long as you don't close your losers, your win rate remains at a solid 100%. Yep, impressive, but not realistic nor optimal. If you take opportunity cost into account, you end up as a strong loser.


A better metric to use is expectancy. Expectancy is average win rate (%) * average amount won. Amount won can either be absolute pips, dollars or a risk:reward ratio (my preference).

The trouble with using pips is that not only is the average daily movement for each currency pair different, but they shift over time. An expectancy of 50 pips isn't so useful if it was based on data with an average daily movement of 120 pips, and today's average daily movement has dropped to 80 pips. Some currency pairs are also much more volatile, such as the GBPJPY, making an expectancy from a less-volatile pair like the USDCAD incomparable. Apples and oranges. You can try standardising your expectancy across different currencies, but it's a tedious exercise and not needed, as I'll explain a few paragraphs below.

Using dollars is acceptable if you're risking the same amount of dollars per trade. But if you're profitable, this shouldn't be happening as you'll be increasing your dollars per trade. Not really useful.

My preference is using R:R. It's unitless, thus allowing comparison with other trading systems and markets. It also describes your system in terms of risk, and risk management is what trading is all about.


And that brings me to my next point. A high expectancy is good, but what's the point if your system only allows you trade once a year? Thus we arrive at the most important metric for any system: "expectunity".

Expectunity = expectancy * opportunities to trade

Decreasing our expectancy is acceptable if we compensate by increasing our opportunities to trade(e.g. trading on lower timeframes, loosening our requirements). High-frequency traders understand the concept of expectunity by trading with extremely low expectancy, thousands of times per day.

The role of a trader is to optimise their system in terms of expectunity. At this point, it becomes psychological. Everybody wants to be right 100% of the time. There's comfort to be found in predictability, but this will hurt your profitability. To maximise your expectunity, you must be willing to accept loss and being wrong. But in the end, it's all about seeing your bottom line growing.

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