Comments on: Hey! Who are you saying has a ‘fat tail’? http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/ Hedge funds, portable alpha, 130/30 and alpha-centric investing Thu, 18 Mar 2010 13:53:53 +0000 http://wordpress.org/?v=abc hourly 1 By: Matt http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-11380 Matt Thu, 14 Jun 2007 23:33:22 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-11380 I think normal distributions have some value as they can help describe most general asset returns, but the fat tail needs to be considered and the notion that large unexpected drops can occur needs to be remembered. I think normal distributions have some value as they can help describe most general asset returns, but the fat tail needs to be considered and the notion that large unexpected drops can occur needs to be remembered.

]]> By: JD http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-11294 JD Wed, 13 Jun 2007 23:56:11 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-11294 Did I miss something? The article suggests that a -50% return on stocks or multi strat funds is a 1 in 139 or 1 in 592 year event. -100% losses happen all the time. LTCM and Amaranth occured a bit closer than 592 years apart. Stop using normal distributions to consider the finer details of probabilities. Did I miss something? The article suggests that a -50% return on stocks or multi strat funds is a 1 in 139 or 1 in 592 year event. -100% losses happen all the time. LTCM and Amaranth occured a bit closer than 592 years apart.

Stop using normal distributions to consider the finer details of probabilities.

]]> By: Jon http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-6270 Jon Wed, 16 May 2007 13:57:56 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-6270 I've enjoyed the discussion - it's been quite educational for me. Technical matters aside, I agree with your sentiment that kurtosis is not just a hedge fund issue. It is unlikely that any financial asset has a return distribution that is truly normal, and so using kurtosis as a means of warning about hedge fund investing is sort of a weak argument. Regards, Jon I’ve enjoyed the discussion – it’s been quite educational for me.

Technical matters aside, I agree with your sentiment that kurtosis is not just a hedge fund issue. It is unlikely that any financial asset has a return distribution that is truly normal, and so using kurtosis as a means of warning about hedge fund investing is sort of a weak argument.

Regards,

Jon

]]> By: Tristram Lett http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-6168 Tristram Lett Tue, 15 May 2007 19:19:30 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-6168 Jon: As it turns out the point we are discussing has been of interest to some academics, but to date no one has come up with a proof that what I said is true, though clearly it is not a new thought. So I graciously concede the point to you... Tris Jon:
As it turns out the point we are discussing has been of interest to some academics, but to date no one has come up with a proof that what I said is true, though clearly it is not a new thought. So I graciously concede the point to you…
Tris

]]> By: Jon http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-6157 Jon Tue, 15 May 2007 13:40:41 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-6157 No problem - I'll check in later. Jon No problem – I’ll check in later.

Jon

]]> By: Tris Lett http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-6091 Tris Lett Mon, 14 May 2007 21:40:41 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-6091 Jon: I will get back to you on that point. Sorry it took so long to respond, but I could not see a response to the article, including my own. Tris Jon:
I will get back to you on that point. Sorry it took so long to respond, but I could not see a response to the article, including my own.
Tris

]]> By: Jon http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-5989 Jon Mon, 14 May 2007 00:03:10 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-5989 Mr. Lett: Your comments are technically true, in that I can increase the excess kurtosis of a distribution without affecting the shape of the tails - I believe maybe that my statement in the comments section was too strong, and I should have been more careful with my wording. On that note, is there research that you could direct me to that suggests that any observed kurtosis in 'hedge fund' returns is due to returns clustering around the mean without any changes in the shape of tails of the distribution (when compared to, say, a normal dist.)? I think that empirically, with financial market returns, positive excess kurtosis does imply fat tails. Jon Mr. Lett:

Your comments are technically true, in that I can increase the excess kurtosis of a distribution without affecting the shape of the tails – I believe maybe that my statement in the comments section was too strong, and I should have been more careful with my wording. On that note, is there research that you could direct me to that suggests that any observed kurtosis in ‘hedge fund’ returns is due to returns clustering around the mean without any changes in the shape of tails of the distribution (when compared to, say, a normal dist.)? I think that empirically, with financial market returns, positive excess kurtosis does imply fat tails.

Jon

]]> By: Tristram Lett http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-5826 Tristram Lett Fri, 11 May 2007 15:10:02 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-5826 Two expansions of what you posted that are relevant: If you break a normal distribution synmmetrically up into thirds, kurtosis is when less observations are in the 1/3 to 2/3 portion than the normal and more in the first 1/3 and last 1/3. Therefore high kurtosis may say nothing about fat tails. Secondly kurtosis is notoriously unstable-one observation among 60 can alter the number significantly. To stabilize the measure you need to calculate the L-moment which bounds the set between 0 and 1 in quantile space as opposed to the unbounded set in probability space. Two expansions of what you posted that are relevant: If you break a normal distribution synmmetrically up into thirds, kurtosis is when less observations are in the 1/3 to 2/3 portion than the normal and more in the first 1/3 and last 1/3. Therefore high kurtosis may say nothing about fat tails.

Secondly kurtosis is notoriously unstable-one observation among 60 can alter the number significantly. To stabilize the measure you need to calculate the L-moment which bounds the set between 0 and 1 in quantile space as opposed to the unbounded set in probability space.

]]> By: Jon http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/comment-page-1/#comment-5825 Jon Fri, 11 May 2007 13:52:44 +0000 http://allaboutalpha.com/blog/2007/05/10/hey-who-are-you-saying-has-a-fat-tail/#comment-5825 I think this is a good post, and investors should consider as many moments of the return distribution and they can reasonably develop expectations for! However, your statement that "...kurtosis only refers to the shape of the return distribution, not the actual “probability of extreme returns” as Morningstar suggests." is simply false. I understand you 'get to the point' of ceteris paribus conditions later in the post, but that statement is simply misleading. Jon I think this is a good post, and investors should consider as many moments of the return distribution and they can reasonably develop expectations for! However, your statement that

“…kurtosis only refers to the shape of the return distribution, not the actual “probability of extreme returns” as Morningstar suggests.”

is simply false. I understand you ‘get to the point’ of ceteris paribus conditions later in the post, but that statement is simply misleading.

Jon

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