*The speculator’s chief enemies are always boring from within. It is inseparable from human nature to hope and to fear… Instead of hoping he must fear; instead of fearing he must hope. He must fear that his loss may develop into a much bigger loss, and hope that his profit may become a big profit."*

*— Edwin Lefèvre (1923)*

When it comes to placing and executing stops, there are various factors to consider including psychological aspects, statistical probabilities, money management, market volatility and order placement. Experienced traders study all of these areas and use that knowledge to form an approach that integrates these domains into an actionable structured discipline. This is what separates skilled from unskilled traders.

**Psychological aspects**

The human mind is susceptible to perceptual distortion, inaccurate judgment and illogical interpretation. Such mental trickery impacts decision-making, and colloquialisms like "markets can remain irrational longer than you can remain solvent" are intended to address these concerns. Ironically, such "rules of thumb" are exactly the kind of readily accessible and loosely applicable problem solving strategies, known as *heuristics*, that lead to the issue of *cognitive bias* in the first place.

The phenomenon of human behavior to make judgment calls not identical to the rules of formal logic or statistical probabilities likely evolved as an adaptation for making decisions under uncertainty. In many circumstances, heuristics can enable a faster thought process as well as lead to effective actions in a given context. On the other hand, cognitive bias reflects the inability to reason properly in comparison to a set of independently verifiable facts. How a situation is framed is key to influencing our choices.

Let’s suppose you were given a choice between an 80% opportunity of winning $50,000 and a 20% risk of not winning anything, vs. a 100% assurance of receiving $35,000. Which option would you choose? Alternatively, given the choice between an 80% risk of losing $50,000 and a 20% opportunity of not losing anything, vs. a 100% assurance of losing $35,000, which option would you choose now?

In an experiment by Kahneman and Tversky (1979) who introduced the notion of cognitive bias, 80% of the participants chose $35,000 in the first scenario, even though the riskier choice had a higher expected value ($50,000 x 0.8 = $40,000); and 92% of the participants in the second scenario chose to gamble on a 20% opportunity of not losing anything. This framing occurs because people’s fear of loss induces them to take greater risks in a losing situation (e.g., holding onto losses), whereas in a winning situation people have a tendency to become risk averse and prematurely take profits (i.e., not let profits run).

**Statistical probabilities**

This leads directly into a discussion on money management techniques evolved from betting systems. Most gambling, such as a coin toss, is based on pure random outcomes — if you toss a coin 10 times and each time it comes up heads, the odds that it will come up heads again on the eleventh try are still 50/50. Mathematical systems designed around trade sizing are an attempt to best utilize a limited bankroll to exploit favorable situations.

One example is the *Martingale strategy* where a trader doubles his/her trade after a loss. The strategy derives from the idea that by always doubling your trade after a loss, you eventually would win enough to cover all past losses plus one unit. In real life, however, minimum and maximum lot sizes imposed by either a casino or futures broker effectively place a stop on the simple mathematical system of doubling up.What should be apparent then is that such systems increase a player’s bankroll volatility, thereby increasing the risk of ruin. Not surprisingly, there are numerous variations on modified doubling-up systems, or strategies that act in reverse and increase trade sizes after a win. The *D’Alembert strategy* is one such system whereby a trader increases his next trade by one unit upon winning, and reduces his next trade size by one unit after a loss. In the final analysis, however, it is impossible to convert a game with *negative expectations* (less then 50/50 chance) into *positive expectations* (greater than 50/50 chance) through an optimized betting system alone.