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Trading Rules - What Is Mathematically Optimal Is Psychologically Impossible

by Boris Schlossberg and Kathy Lien

Novice traders who first approach the markets will often design very elegant, very profitable strategies that appear to generate millions of dollars on a computer backtest. The majority of such strategies have extremely impressive win-loss and profit ratios, often demonstrating $3 of wins for just $1 of losses. Armed with such stellar research, these newbies fund their FX trading accounts and promptly proceed to lose all of their money. Why? Because trading is not logical but psychological in nature, and emotion will always overwhelm the intellect in the end, typically forcing the worst possible move out of the trader at the wrong time.

Trading Is More Art Than Science

As E. Derman, head of quantitative strategies at Goldman Sachs, a leading investment banking firm, once noted, "In physics you are playing against God, who does not change his mind very often. In finance, you are playing against God's creatures, whose feelings are ephemeral, at best unstable, and the news on which they are based keeps streaming in."

This is the fundamental flaw of most beginning traders. They believe that they can "engineer" a solution to trading and set in motion a machine that will harvest profits out of the market. But trading is less of a science than it is an art; and the sooner traders realize that they must compensate for their own humanity, the sooner they will begin to master the intricacies of trading.

Textbook Vs. Real World
Here is one example of why in trading what is mathematically optimal is often psychologically impossible.

The conventional wisdom in the markets is that traders should always trade with a 2:1 reward-to-risk ratio. On the surface this appears to be a good idea. After all, if the trader is only correct 50% of the time, over the long run she or he will be enormously successful with such odds. In fact, with a 2:1 reward-to-risk ratio, the trader can be wrong 6.5 times out of 10 and still make money. In practice this is quite difficult to achieve. (for related readings, see Using Pivot Points In FX.)



Imagine the following scenario: You place a trade in GBP/USD. Let's say you decide to short the pair at 1.7500 with a 1.7600 stop and a target of 1.7300. At first, the trade is doing well. The price moves in your direction, as GBP/USD first drops to 1.7400, then to 1.7360 and begins to approach 1.7300. At 1.7320, the GBP/USD decline slows and starts to turn back up. Price is now 1.7340, then 1.7360, then 1.7370. But you remain calm. You are seeking a 2:1 reward to risk. Unfortunately, the turn in the GBP/USD has picked up steam; before you know it, the pair not only climbs back to your entry level but then swiftly rises higher and stops you at 1.7600.

You just let a 180-point profit turn into a 100-point loss. In effect, you created a -280-point swing in your account. This is trading in the real world, not the idealized version presented in textbooks. This is why many professional traders will often scale out of their positions, taking partial profits far sooner than two times risk, a practice that often reduces their reward-to-risk ratio to 1.5 or even lower. Clearly that's a mathematically inferior strategy, but in trading, what's mathematically optimal is not necessarily psychologically possible.

Risk Can Be Predetermined; Reward Is Unpredictable


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