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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?

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Could this effect (if statistically real at all time periods) be due to the traders who set stop losses (causing the price to fall further and more stop losses to trigger), and trailing stops, but don't set limit orders? I.e. cut your losses early and ride your winners. – Darren Cook Nov 30 '11 at 1:29
See also this question and answers there: quant.stackexchange.com/questions/2652/… – vonjd Jan 18 '12 at 12:58
up vote 10 down vote accepted

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.

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Thanks. Can you expand just a bit on "positive kurtosis (> 3)" -- i.e. give more feeling/understanding for that statistical quantity. – Ray Nov 26 '11 at 22:00
Kurtosis greater than 3 means that extreme values are more common than for the normal distribution. Part of the reason for the fat tails is that there is volatility clustering (the garch effect) -- there are high volatility periods and low volatility periods. Even accounting for that there are fat tails though. If no one knew what others were doing, we could expect a normal distribution. But people do copy what others do and so we get extreme movements. – Patrick Burns Nov 27 '11 at 8:42
Thanks Bootvis and Patrick for enhanced explanations. – Ray Nov 28 '11 at 6:54
For this interested in @PatrickBurns comment about people following the crowd, you may be interested in the herding literature which finds that this does in fact happen to some non-trivial extent in most countries. – Jase Dec 12 '12 at 0:59

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.

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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.

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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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