Negative Skew, Fat Tails, and Rapid Equity Market Declines
Summary
The discussion examines the claim that equity markets often decline sharply and recover gradually. One answer relates the pattern to negative skewness and excess kurtosis in return distributions: many returns may be small and positive, while a smaller number of large losses pull the distribution’s asymmetry downward. A severe market crash is offered as an example of an extreme negative return. Another response points to historical index-return analysis but cautions that observed log returns may show only modest negative skew, with symmetry still plausible.
Suggested explanations include loss aversion, leveraged positions that force selling after losses, and flights to liquidity. The answers also mention asymmetric GARCH model variants as a way to investigate volatility behavior. These are hypotheses and modeling directions, not a settled causal account. The discussion supplies no underlying dataset or formal test, so it does not establish how consistently the pattern occurs across markets or time periods.
Key ideas
- Negative skewness describes a return distribution with a heavier or longer downside tail.
- Excess kurtosis indicates more extreme outcomes than a normal distribution would imply.
- Leverage and liquidity pressure are proposed mechanisms that can intensify declines.
- Behavioral loss aversion is another suggested explanation, rather than a demonstrated cause.
- Historical index data and asymmetric GARCH models can be used to study the pattern.
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# Do markets typically fall fast, and rise slowly # Do markets typically fall fast, and rise slowly I'm wondering if there is some measurement or name to this notion, i.e.: Markets typically fall fast, but rise slowly. It seems like this is the case -- get some bad news out of Europe on the debt crisis there, and things drop fast. Then, in the absence of daily bad news, things tend to rise ... slowly. Is this the way markets operate most of the time? Do you know of data that backs this up, if it is true? ## Answer by Bob Jansen (score 12, accepted) https://quant.stackexchange.com/a/2440 Equity returns have persistent negative skewness and excess kurtosis[1] over longer periods. So yes you're right: a majority of the daily returns is positive and small and a minority of the returns is negative and larger. This can be quite extreme, for example Black Monday. I don't have the data right now but you can get returns on major indices freely. [1] There are two definitions of kurtosis, $K$ and $K'$ such that $K = K'-3$. The normal distribution has $K=3$. If a distribution or sample has $K>3$ we say it has excess kurtosis. This implies that the tails are fat compared to the normal distribution. ## Answer by Patrick Burns (score 4) https://quant.stackexchange.com/a/2791 The blog post "A slice of S&P 500 skewness history" http://www.portfolioprobe.com/2012/01/16/a-slice-of-sp-500-skewness-history/ has a bit of data on this question. It appears that log returns might have some negative skew, but symmetry is a possibility. ## Answer by MathAttack (score 4) https://quant.stackexchange.com/a/2848 Bootvis accurately describes the math - Skew plus Kurtosis. What's interesting is that many of the efficient market theorists (example: Eugene Fama) observed this phenomenon too. I consider two intuitive reasons for this: 1) Behavioral - According to prospect theory, the mental benefit of gaining a dollar is lower than the fear of losing a dollar. This means we're more likely to panic to avoid losing a dollar that irrationally join a gold rush. This is just a matter of degree though - the high Kurtosis means we're more likely to do either than a Gaussian distro suggests. 2) Leverage on Equity Bets - If you're levered up on equity 10 to 1, and your position drops 10%, you have to sell everything. The reverse doesn't exist. Many banks are leveraged even more than this. This means when bad things happen, there's system pressure which doesn't exist when good things happen. Or at least not as often - there are still short squeezes, but they seem small in comparison. ## Answer by arc (score 2) https://quant.stackexchange.com/a/2818 There is an ongoing trend in GARCH modeling that seeks explain the why of this phenomena. Some economic explanations iv'e read revolve around the effects of leveraged positions and flights to liquidity. The GARCH model derivatives used are usually classified as asymmetric power models I believe.
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