Rationale for describing kurtosis as “peakedness”? Planned maintenance scheduled April 23,...
Why are vacuum tubes still used in amateur radios?
What is the chair depicted in Cesare Maccari's 1889 painting "Cicerone denuncia Catilina"?
Simple Http Server
If Windows 7 doesn't support WSL, then what is "Subsystem for UNIX-based Applications"?
Flight departed from the gate 5 min before scheduled departure time. Refund options
One-one communication
Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted?
Does the Mueller report show a conspiracy between Russia and the Trump Campaign?
Where is the Next Backup Size entry on iOS 12?
How to change the tick of the color bar legend to black
White walkers, cemeteries and wights
Nose gear failure in single prop aircraft: belly landing or nose-gear up landing?
After Sam didn't return home in the end, were he and Al still friends?
Are the endpoints of the domain of a function counted as critical points?
Why complex landing gears are used instead of simple,reliability and light weight muscle wire or shape memory alloys?
How can I save and copy a screenhot at the same time?
Rationale for describing kurtosis as "peakedness"?
What does 丫 mean? 丫是什么意思?
How to ask rejected full-time candidates to apply to teach individual courses?
Is there public access to the Meteor Crater in Arizona?
Is multiple magic items in one inherently imbalanced?
How do living politicians protect their readily obtainable signatures from misuse?
What is the origin of 落第?
RSA find public exponent
Rationale for describing kurtosis as “peakedness”?
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?Calculating Portfolio Skewness & KurtosisDistribution for High Kurtosisderivation of formula for portfolio skewness and kurtosisSkewness and Kurtosis under aggregationHow to annualize skewness and kurtosis based on daily returnsHigh values of skewness and kurtosis of realized protfolio returnsHow do I get Value-at-Risk for a GED distribution in R?How to estimate option implied skewness and kurtosis in RKurtosis in GARCH
$begingroup$
Despite plenty of evidence to the contrary, many quantitative finance sources of information, including teaching resources such as CFA prep, persist in defining kurtosis as a measure of "peakedness." Can anyone give a logical rationale for this characterization in terms of distributions of asset returns?
kurtosis
New contributor
$endgroup$
add a comment |
$begingroup$
Despite plenty of evidence to the contrary, many quantitative finance sources of information, including teaching resources such as CFA prep, persist in defining kurtosis as a measure of "peakedness." Can anyone give a logical rationale for this characterization in terms of distributions of asset returns?
kurtosis
New contributor
$endgroup$
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago
add a comment |
$begingroup$
Despite plenty of evidence to the contrary, many quantitative finance sources of information, including teaching resources such as CFA prep, persist in defining kurtosis as a measure of "peakedness." Can anyone give a logical rationale for this characterization in terms of distributions of asset returns?
kurtosis
New contributor
$endgroup$
Despite plenty of evidence to the contrary, many quantitative finance sources of information, including teaching resources such as CFA prep, persist in defining kurtosis as a measure of "peakedness." Can anyone give a logical rationale for this characterization in terms of distributions of asset returns?
kurtosis
kurtosis
New contributor
New contributor
New contributor
asked 9 hours ago
Peter WestfallPeter Westfall
1062
1062
New contributor
New contributor
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago
add a comment |
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Quailtatively a (zero skewness) Leptokurtic distribution, after being standardized to have zero mean and unit variance shows three features when you plot the density and compare it to a standard normal N(0,1) distribution: higher peak, higher (fatter) tails, and lower mid-range(*). All three properties go together, even though people sometimes mention only one of them ("a fat tailed distribution"). After all there has to be an area of 1 under the curve, and a variance of 1, so a deficit in the mid-range has to be made up by an excess elsewhere, i.e. in the tails and near the centre. Otherwise it would not be a probability distribution or would not have unit variance. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance.
So "peakedness in the centre" and "fat in the tails" describe exactly the same thing. You can't have one without the other.
(*) By mid-range is meant the two areas, one on each side, located approximately one standard deviation from the centre.
$endgroup$
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
add a comment |
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "204"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Peter Westfall is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f45215%2frationale-for-describing-kurtosis-as-peakedness%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Quailtatively a (zero skewness) Leptokurtic distribution, after being standardized to have zero mean and unit variance shows three features when you plot the density and compare it to a standard normal N(0,1) distribution: higher peak, higher (fatter) tails, and lower mid-range(*). All three properties go together, even though people sometimes mention only one of them ("a fat tailed distribution"). After all there has to be an area of 1 under the curve, and a variance of 1, so a deficit in the mid-range has to be made up by an excess elsewhere, i.e. in the tails and near the centre. Otherwise it would not be a probability distribution or would not have unit variance. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance.
So "peakedness in the centre" and "fat in the tails" describe exactly the same thing. You can't have one without the other.
(*) By mid-range is meant the two areas, one on each side, located approximately one standard deviation from the centre.
$endgroup$
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
add a comment |
$begingroup$
Quailtatively a (zero skewness) Leptokurtic distribution, after being standardized to have zero mean and unit variance shows three features when you plot the density and compare it to a standard normal N(0,1) distribution: higher peak, higher (fatter) tails, and lower mid-range(*). All three properties go together, even though people sometimes mention only one of them ("a fat tailed distribution"). After all there has to be an area of 1 under the curve, and a variance of 1, so a deficit in the mid-range has to be made up by an excess elsewhere, i.e. in the tails and near the centre. Otherwise it would not be a probability distribution or would not have unit variance. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance.
So "peakedness in the centre" and "fat in the tails" describe exactly the same thing. You can't have one without the other.
(*) By mid-range is meant the two areas, one on each side, located approximately one standard deviation from the centre.
$endgroup$
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
add a comment |
$begingroup$
Quailtatively a (zero skewness) Leptokurtic distribution, after being standardized to have zero mean and unit variance shows three features when you plot the density and compare it to a standard normal N(0,1) distribution: higher peak, higher (fatter) tails, and lower mid-range(*). All three properties go together, even though people sometimes mention only one of them ("a fat tailed distribution"). After all there has to be an area of 1 under the curve, and a variance of 1, so a deficit in the mid-range has to be made up by an excess elsewhere, i.e. in the tails and near the centre. Otherwise it would not be a probability distribution or would not have unit variance. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance.
So "peakedness in the centre" and "fat in the tails" describe exactly the same thing. You can't have one without the other.
(*) By mid-range is meant the two areas, one on each side, located approximately one standard deviation from the centre.
$endgroup$
Quailtatively a (zero skewness) Leptokurtic distribution, after being standardized to have zero mean and unit variance shows three features when you plot the density and compare it to a standard normal N(0,1) distribution: higher peak, higher (fatter) tails, and lower mid-range(*). All three properties go together, even though people sometimes mention only one of them ("a fat tailed distribution"). After all there has to be an area of 1 under the curve, and a variance of 1, so a deficit in the mid-range has to be made up by an excess elsewhere, i.e. in the tails and near the centre. Otherwise it would not be a probability distribution or would not have unit variance. The peakedness in the centre "balances" the thickness in the tails while staying with a unit variance.
So "peakedness in the centre" and "fat in the tails" describe exactly the same thing. You can't have one without the other.
(*) By mid-range is meant the two areas, one on each side, located approximately one standard deviation from the centre.
edited 8 hours ago
answered 9 hours ago
Alex CAlex C
6,72211123
6,72211123
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
add a comment |
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
I understand where you are coming from but I think this is fruitless. Distributions are functions, i.e. they have infinite degrees of freedom. Were your statement still true if the distribution is multimodal or had point masses?
$endgroup$
– g g
7 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
$begingroup$
Fat tails are a problem because so many of the models we use assume that the data are Gaussian IID. Fat tails means an increased probablility of events that we considered rare. For example the Black Scholes option pricing model assume your data are Gaussian. If they have a high kurtosis, this problematic.
$endgroup$
– Jacques Joubert
3 hours ago
add a comment |
Peter Westfall is a new contributor. Be nice, and check out our Code of Conduct.
Peter Westfall is a new contributor. Be nice, and check out our Code of Conduct.
Peter Westfall is a new contributor. Be nice, and check out our Code of Conduct.
Peter Westfall is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Quantitative Finance Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fquant.stackexchange.com%2fquestions%2f45215%2frationale-for-describing-kurtosis-as-peakedness%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
what is the "evidence to the contrary" ?
$endgroup$
– Alex C
9 hours ago
$begingroup$
Not trying to be a jerk here, but "Peakedness," "Tailedness" who cares? Is the characterization even important? For any metric, understanding use and interpretation are what matters.
$endgroup$
– amdopt
4 hours ago