Why Financial Returns Have Heavy Tails
Summary
The document discusses why financial return distributions can have heavier tails than a normal distribution. One explanation is changing volatility: returns may be conditionally normal at each volatility level, yet combining low and high volatility periods produces an unconditional distribution with excess kurtosis. The example illustrates how a small share of high-volatility observations can make extreme returns more common.
Other proposed contributors include market shocks, jumps, leverage, autocorrelation, and human behavior that can turn near misses into large market moves. The discussion notes that different crashes may have different economic causes, so no single mechanism explains every episode. It also cautions that historical data and standard risk measures cannot fully capture rare tail events. These are conceptual explanations rather than a tested model comparison, and the claims about universal tail distributions are not supported with evidence in the document.
Key ideas
- Mixing returns across changing volatility states can create heavy unconditional tails even when returns are conditionally normal.
- Jumps, leverage, autocorrelation, and uneven sampling are also proposed as contributors to heavy tails.
- Human reactions may amplify near misses into market events.
- Historical samples and standard risk measures may not capture the full extent of tail risk.
- Different crashes can arise from distinct economic conditions.
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Full text
# economic facts that causes the financial time series to be heavy tailed # economic facts that causes the financial time series to be heavy tailed When reading a tutorail on extreme value theory, I once meet the following claim ``` Heavy tailed marginals are a preferable feature of models for financial time series. ``` Why finanical time series show a pattern of heavy tailed marginals? Are there any economic facts underlying this observation? ## Answer by Fortranner (score 3) https://quant.stackexchange.com/a/12802 Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility 3% standard deviation state will cause daily returns to exhibit fat tails. Mixtures of normals can be used to model distributions with tails that are heavier than normal. ## Answer by John (score 1) https://quant.stackexchange.com/a/12799 Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to the fundamental nature of human beings. Nevertheless, such underlying biological forces need some economic conditions to manifest themselves. These are often unique to each specific crash (i.e., the economic conditions behind the crash of 1987 are different than the internet crash are different than the subprime crisis). ## Answer by Simon (score 1) https://quant.stackexchange.com/a/12805 A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan. In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such metrics can truly estimate the tail risk. Major News, market shocks and dislocations, randomness, etc can all lead to extreme behaviors and heavily tailed marginals. I once wrote a thesis on Extreme Value Theory, and my work is basically concerned on modeling the occurrence of large-impact and low-probability extreme events on various domains. And our finding is that almost all extreme events will converge to a Generalized Pareto Distribution. ## Answer by Tom Au (score 0) https://quant.stackexchange.com/a/12806 It appears to be related to behavioral psychology. In "space," there will be a statistical chance to two asteroids colliding, and a much larger number of near misses. But no asteroid will observe the "near miss" of two other asteroids and adjust its behavior or trajectory accordingly. In human affairs, a "near miss" could produce just the result that was originally missed, as human beings panic and adjust their behavior to increase the possibility of a collision. Thus, "tail events" have to include not just the collisions that would have occurred naturally, but a number of (original) near misses that turned into "hits." ## Answer by experquisite (score 0) https://quant.stackexchange.com/a/12812 Inhomogeneous time/sampling. Autocorrelation. Stochastic volatility. Jumps. Leverage.
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