Statistical Trading consists of using statistical tools on historical price data in order to improve trading returns. The idea behind statistical trading is that if a trader can find even a slight statistical edge, then the expected return over a large number of trades will be positive.
I'm talking about the same kind of edge that a casino owner or an insurance company has. This is a statistical edge based on the law of large numbers. The casino doesn't know if a particular spin of the roulette wheel will be a win or a loss, but they know that after 1000 spins they will very likely be richer. Their edge is simple to describe using the game of roulette as an example.
The player has a 1/38 chance of winning on any given spin, but will only receive 36 times their money if they win. So for 3,800 spins, the player will win 100 of them on average, yielding $3,600. But the player will lose the other 3,700 spins at a dollar each for a loss of $3,700. So what's the average take for the house? It's $100 for every 3800 spins, or a little under 3 cents per spin. It adds up...and all other casino games of pure chance (these don't include poker or blackjack which can involve some skill) are variations on this theme. That's why casinos get rich and gamblers go broke.
Insurance companies get rich in pretty much the same way. The company has no idea if a particular person will die this year, but they do have a pretty accurate idea how many people out of 1,000,000 policyholders with a given profile will die this year. Let's say that statistically the death rate of a given class of people (males over 55, smokers, and in moderate health for instance) is 4% so that we expect 40,000 to die this year.
If each policy pays $10,000 for a death, then the company expects to shell out $400 million dollars in benefits...wow! So how much should the company charge in premiums for those one million policies each year then? Well how about $500 each? That gives the company $500 million in revenues for an expected $400 million benefit payout, leaving $100 million for salaries, expenses, profits and whatever. That's their statistical edge.
Now let's look at some ways that we can use this idea of a "statistical edge" in trading.
A very common way that traders try to apply the ideas of statistics is by planning trades in such a way that the potential gain exceeds the potential loss. This is the classic "cut losses short and let profits run" argument. For instance if you set up a trade so that you lose only $100 if you're wrong but gain $300 if you're right, then you only have to be right 1/4 of the time to break even.
That's because for every four trades (on average) you would lose $100 three times and gain $300 one time, which is a wash (not counting commissions). And any numbskull can be right more than a quarter of the time right?
Right. Sure. So why aren't we all rich? After trading currencies for a while in 2004, I figured out what the problem was. A tight stop and a wide target will tend to make you wrong a lot simply because it's easier for the stop to get hit. On the other extreme, suppose you decide that you like to have a lot of winning trades, so you place very wide stops and very close price targets.
Fine, now you'll win a lot of the time but the amounts will be small. And one loss, although uncommon, will tend to wipe out many little wins. So no matter where you are on the "trading setup" spectrum, wide stops and tight targets, tight stops and wide targets, or any combination in between, statistically it ends up being a wash. There is no intrinsic "edge" in any given trading setup scheme, including "cutting losses short and letting profits run." Heresy, I know.
Getting a real statistical edge requires that you can identify situations in which the price tends to move in such a way that you can set up trades which have a positive expected return. Expected return is just the percentage of wins multiplied by the win amount, minus the percentage of losses multiplied by the loss amount. An example will make this clearer.
Suppose you know that every time the USD/JPY rate crosses above its 20 day moving average, the price tends to move up more often than it moves down. Investigating this in more detail using historical data, you determine that there is a 40% probability that the price rises by 25 pips before it ever drops by 10 pips. Now even though this only happens less than half the time, it still allows you to set up trades with a positive expected return.
This is because if you set your target at 25 pips and your stop at 10 pips, you will win 25 pips 40% of the time and lose only 10 pips during the other 60% of the time. The expected return is:
(40% x 25 pips) - (60% x 10 pips) = 10 pips - 6 pips = 4 pips
So on the average, you can expect to get 4 pips per trade using this strategy, even though you lose most of the time! But remember that this whole example is predicated on the knowledge that a positive crossover of the 20 day moving average tends to skew the expected return in your favor. That's your edge in this example.
Scott Percival is the Director of Research for the FOREX Statistical Research Center at Market-geeks.com, a site which is devoted to using mathematics and the scientific method to study the behavior of prices in the FOREX market. Mr. Percival has a degree in Civil Engineering from Northeastern University, and has worked as a Registered Representative and trading instructor at Fidelity Investments. He is currently working toward the goal of becoming a full time FOREX trader.