Fooled by Negative Skewness
A short record of frequent gains can hide a payoff’s rare, severe losses. Taleb connects the appeal of negatively skewed strategies with overconfidence in small samples that have not captured their downside.
THE IDEA
CHAPTER 6
Fooled by negative skewness: The first hint of an explanation for the popularity of negatively skewed payoffs comes from the early literature on behavior under uncertainty, with the “small number problem.” Tversky and Kahneman (1971) write: “We submit that people view a sample randomly drawn from a population as highly representative, that is, similar to a population in all essential characteristics.” The consequence is the inductive fallacy: overconfidence in the ability to infer general properties from observed facts, “undue confidence in early trends,” the stability of observed patterns and deriving conclusions with more confidence attached to them than can be warranted by the data. Worst, the agent finds causal explanations or perhaps distributional attributes that confirm his undue generalization. It is easy to see that the “small numbers” get exacerbated with skewness since most of the time the observed mean will be different from the true mean and most of the time the observed variance will be lower than the true one. Now consider that it is a fact that in life, unlike a laboratory or a casino, we do not observe the probability distribution from which random variables are drawn: We only see the realizations of these random processes. It would be nice if we could, but it remains that we do not measure probabilities as we would measure the temperature or the height of a person. This means that when we compute probabilities from past data we are making assumptions about the skewness of the generator of the random series—all data is conditional upon a generator. In short, with skewed packages, the camouflage of the properties comes into play and we tend to believe what we see. Taleb (2004).
Philosopher sometimes playing scientist: Nozick (1993).
Hollywood economics: De Vany (2003).
People are sensitive to sign rather than magnitude: Hsee and Rottenstreich (2004).
Lucas critique: Lucas (1978).
When to use it
Evaluating investment strategies that involve rare, high-impact events (e.g., tail-risk hedging).
Making policy decisions based on limited economic data, such as recessions or financial crises.
Assessing insurance premiums for low-probability, high-severity events like earthquakes or pandemics.
Designing experiments or statistical models that account for skewness in small samples.
FROM THEORY TO EVERYDAY LIFE
In practice
Investment Portfolio Overconfidence
An investor reviews the past 10 years of stock market returns, which appear stable with low volatility. Based on this limited sample, they become overconfident and allocate heavily to risky assets, ignoring the possibility of a rare but severe market crash (negative skewness). The true distribution has a small probability of a large loss, but the observed sample misses it.
Insurance Underestimation
An insurer prices disaster coverage using a claims record that contains no major catastrophe. The sample understates the possible claims and variability. A later catastrophe can produce a severe loss for the insurer, whose net payoff has the negative-skew pattern at issue.
A MOMENT TO REFLECT
Put it to work.
How might the small number problem affect your confidence in early trends from data? Can you recall a time when you drew strong conclusions from a small sample?
In what ways does negative skewness make it harder to assess risk from historical data?
How do real-world environments differ from laboratory settings in terms of our ability to observe underlying probability distributions?
Often confused with
References
- Belief in the Law of Small Numbers — Tversky and Kahneman (1971)
- Fooled by Randomness — Taleb (2004)
- The Nature of Rationality — Nozick (1993)
- Hollywood Economics — De Vany (2003)
- The Numbers Effect — Hsee and Rottenstreich (2004)
- Econometric Policy Evaluation: A Critique — Lucas (1978)
CONTINUE THE CONVERSATION
Source texts
- Fooled by Randomness The Hidden Role of Chance in the Markets and in Life (Nassim Nicholas Taleb)