In Peter Bernstein’s book, Against the Gods: The Remarkable Story of Risk, he briefly explores Prospect Theory. He outlines an experiment in which it is shown that “our choices between negative outcomes are mirror images of our choices between positive outcomes.”

Suppose in experiment (1) you are offered the choice between US$3000 for certain and an 80% chance of US$4000 or 20% chance of nothing. Even though the risky choice has a higher mathematical expectation, 80% of those surveyed chose the US$3000 for certain. The vast majority was risk averse.

In the second experiment (2) you have a choice “between taking the risk of an 80% chance of losing US$4000 and a 20% chance of breaking even versus a 100% chance of losing US$3000. Now 92% of those surveyed chose the gamble even though the mathematical expectation says you should take the certain US$3000 loss.”

This is the crux of trading like a trend follower. If you want to be a part of the majority that when faced with a choice of loss you continue to seek risk — forget it — you are doomed to failure.

What These Two Experiments Reveal

The mirror image is exact and damning. When facing gains, 80% of people take the certain smaller amount and reject the higher expected value gamble. When facing losses, 92% of people take the gamble and reject the certain smaller loss. In both cases the majority chose against mathematical expectation. In both cases the majority’s choice is driven by the same underlying force: the desire to avoid the feeling of loss.

In the gain scenario, taking the certain $3000 locks in the good feeling of winning. Risking it on the 80% chance of $4000 means accepting the possibility of feeling like you got nothing, even though the math says the gamble is worth more. In the loss scenario, accepting the certain $3000 loss locks in the bad feeling of losing. Gambling on the 80% chance of losing $4000 means there is a 20% chance of breaking even, which means a 20% chance of avoiding the bad feeling entirely. The math says take the certain loss. The emotion says gamble for the escape.

Translate these two scenarios directly into trading behavior. A trend follower holds a winning position through volatility because the math says the expected value of continuing to hold a trending position exceeds the expected value of locking in the current profit. Most traders cut the winner early, taking the certain smaller gain, rejecting the higher expected value, exactly as experiment (1) predicts. A trend follower cuts a losing position at the predefined stop because the math says taking the certain defined loss now has higher expected value than gambling on a recovery. Most traders hold the loser, seeking risk to avoid the certain loss, exactly as experiment (2) predicts.

The majority behavior in both experiments is the description of how most traders lose money. They cut winners early and hold losers long. Prospect Theory explains why. They are not making calculation errors. They are responding to the emotional structure of gains and losses exactly as the experiments predict. Trend following’s rules are designed to override both responses by substituting mathematical expectation for emotional response at every decision point.

Frequently Asked Questions

What is mathematical expectation in trading?

Mathematical expectation is the average outcome of a decision when calculated across all possible results, weighted by their probabilities. A trade with a 40% chance of winning $300 and a 60% chance of losing $100 has a positive mathematical expectation of $60 per trade. Decisions made on the basis of mathematical expectation rather than emotional preference will produce better outcomes over a large number of trades.

What is Prospect Theory and why does it matter for traders?

Prospect Theory, developed by Kahneman and Tversky, describes how people actually make decisions under risk as opposed to how rational economic models predict they should. The core finding is that losses feel roughly twice as painful as equivalent gains feel pleasurable, causing people to be risk-averse when facing gains and risk-seeking when facing losses. Both behaviors lead traders away from decisions that maximize mathematical expectation.

Why do most traders cut winners early and hold losers long?

Because of the emotional structure described in Prospect Theory. Cutting a winner early locks in the good feeling of a gain. Holding a loser avoids locking in the bad feeling of a loss by keeping open the possibility of recovery. Both choices are emotionally motivated and both violate mathematical expectation. Trend following rules override both by defining exits mechanically rather than emotionally.

How does trend following apply mathematical expectation in practice?

By defining entries, exits, and position sizes based on historical probabilities and payoff ratios rather than how a current position feels. The stop loss takes the certain defined loss rather than gambling on recovery. The trailing exit holds the winning position rather than taking the certain smaller gain. Both rules follow mathematical expectation over emotional preference.

More on expectations and trend following.

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