It is mentioned that hedge fund returns are usually skewed with significant leptokurtosis (fat tails), so standard deviation does not accurately measure the profitability of returns in the tail. Questions - What is fat tails? Is that positively or negatively skewed? So does equity return also exhibit fat tails? Appreciate it if anyone can advise - thanks.
Fat tails means a bell curve that has excessive risk of a ‘tail’ event. The skewness is irrelevant since we are only talking about the ‘peakedness’ of the bell curve. Leptokurtosis means the bell curve is > 3 kurtosis which is the normal kurtosis.
Tails and skewness are different. Tails is got to do with kurtosis. Fat tails means, returns more prevelant (more extreme results)in the tails of the normal distribution, than what a regular normal distribution would indicate.
Kurtosis, either positive or negative, still has a symmetrical distribution. It has to do with how many of the oberservations (probably a bad stats term here) are near the mean vs near the tails. Skewness is about asymmetry.
Just to add to already excellent explanations. Kurtosis is a measure of fatness of tails: extreme events happen often. For example, if distribution is normal chances of 3 standard deviation move is practically zero. However, in real world such events are very common. That’s an indication of fat tails (high kurtosis) Skewness is a measure of asymmetry. One way to look at that: given that there is a big move, is there a higher chance it’s positive or negative? Stocks exhibit negative skewness. There are rarely large positive days (positive days tend to be relatively small), but there are often large negative days.
maratikus Wrote: ------------------------------------------------------- > Just to add to already excellent explanations. > > Kurtosis is a measure of fatness of tails: extreme > events happen often. For example, if distribution > is normal chances of 3 standard deviation move is > practically zero. However, in real world such > events are very common. That’s an indication of > fat tails (high kurtosis) yeah, and as you mention in your original post, hedge funds do often face leptokurtic distributions, such as Long Term Capital Management (LTCM) back in '98 their models were off and if they considered that they had fat tails, they could have possibly avoided implosion
Thanks to all the CFA forumers’ replies. To wrap up, as a result of leptokurtosis: Using standard deviation to measure the risk of a hedge fund can produce misleading results i.e. peakedness (lower standard deviation) or fatter tails (higher standard deviation). If both offset each other, it is still possible the probability distribution function of a hedge fund has the same standard deviation as a normal random variable.
I used to date a girl who was leptokurtic.