Problem 3074. Compute the cokurtosis of a given portfolio.

Created by Ken Deeley

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As input data, you are given a nObs-by-nAssets matrix portRet of return series for assets in a portfolio along with an nAssets-by-1 vector portWeights of portfolio weights. Example:<pre> &gt;&gt; nObs = 504; % Number of observations</pre><pre> &gt;&gt; nAssets = 5; % Number of assets in the portfolio</pre><pre> &gt;&gt; portRet = randn(nObs, nAssets); % Sample portfolio return series</pre><pre> &gt;&gt; portWeights = rand(nAssets, 1); </pre><pre> &gt;&gt; portWeights = portWeights/sum(portWeights); % Portfolio weights are &gt;=0 and sum to 1.</pre>The task is to compute the portfolio cokurtosis , which is a scalar statistic associated with the portfolio. A full description of this statistic, along with sample MATLAB code for computing it, can be found here:<a href = "http://www.quantatrisk.com/2013/01/20/coskewness-and-cokurtosis/">http://www.quantatrisk.com/2013/01/20/coskewness-and-cokurtosis/</a>Write a function that accepts portRet and portWeights as input arguments and returns the scalar statistic portCokurt as its output. You can use the code at the website above as a starting point, but try to simplify and shorten it in the spirit of Cody.

As input data, you are given a nObs-by-nAssets matrix _portRet_ of return series for assets in a portfolio along with an nAssets-by-1 vector _portWeights_ of portfolio weights. Example:

>> nObs = 504; % Number of observations

>> nAssets = 5; % Number of assets in the portfolio

>> portRet = randn(nObs, nAssets); % Sample portfolio return series

>> portWeights = rand(nAssets, 1);

>> portWeights = portWeights/sum(portWeights); % Portfolio weights are >=0 and sum to 1.

The task is to compute the *portfolio cokurtosis* , which is a scalar statistic associated with the portfolio. A full description of this statistic, along with sample MATLAB code for computing it, can be found here:

http://www.quantatrisk.com/2013/01/20/coskewness-and-cokurtosis/

Write a function that accepts _portRet_ and _portWeights_ as input arguments and returns the scalar statistic _portCokurt_ as its output. You can use the code at the website above as a starting point, but try to simplify and shorten it in the spirit of Cody.

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21 Solutions
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Last Solution submitted on Apr 30, 2020

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2 Comments

bainhome on 30 Apr 2020

The author intenionally hide some info about the website's matlab code, since both of fomula and code calculate M4 with slightly different way, in Cody, you DO NOT NEED to minus the mean of P, unlike this website's code actually did that. I learned that in hard way, but deeply hope you guys enjoy to optimize this code.

Dyuman Joshi on 17 Nov 2021

A major part of the article including the code is not accessible to non-members of the website.

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