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Error SIGMA must be a symmetric positive semi-definite matrix

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Shakib Ishfaq
Shakib Ishfaq on 17 Jul 2019
Commented: Shakib Ishfaq on 20 Jul 2019
So I'm calculating CVAR of a portfolio of conventional bonds and Sukuk. I'm trying to simulate asset scenarios, using the Normal/Gaussian and Emprical (T) method.
My dataset, contains assets with varying starting dates, and therefore my dataset contains a number of zeros. When I run the code, I am running into this error.
This is my current code:
clear;
close all;
rng(0);
T = readtable('pak.xlsx');
symbol = {'PAK2014BOND','PAK2015BOND','PAKSUKUK2014'};
nAsset = numel(symbol);
ret = tick2ret(T{:,symbol});
plotAssetHist(symbol,ret)
nScenario = 2000;
simulationMethod = 'Normal';
switch simulationMethod
case 'Normal'
AssetScenarios = mvnrnd(mean(ret),cov(ret),nScenario);
case 'Empirical'
AssetScenarios = simEmpirical(ret,nScenario);
end
When I have zeros in my data, I'm getting this error.
Can someone please shed some light, on how I can overcome this?

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Shakib Ishfaq
Shakib Ishfaq on 17 Jul 2019
My first question, wasn't showing in my activity feed. I thought it did not post.
Thank you for pointing this out, very helpful.

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Answers (1)

the cyclist
the cyclist on 18 Jul 2019
This issue will arise when you get pairwise asset correlations that are inconsistent. (The zeros are not necessarily the problem.)
For example, suppose you have the following data (possibly from different sources):
  • Asset 1 and Asset 2 have a correlation coefficient of 0.9
  • Asset 1 and Asset 3 have a correlation coefficient of 0.9
  • Asset 2 and Asset 3 have a correlation coefficient of -0.3
Now, these can't all be true, because they are mutually contradictory. (Such a strong positive correlation between 1&2 and 1&3 means that 2&3 must be positively correlated.) Maybe the measurements were taken over different periods of time, or using different methodologies.
If you try to use that correlation matrix, you'll get the "must be symmetric positive semi-definite matrix" error. You need to figure out how to fix your correlation matrix.

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Shakib Ishfaq
Shakib Ishfaq on 18 Jul 2019
I thought this also, but then when I generate number in place of the zeros, my code works fine. Also, when I try different datasets.
the cyclist
the cyclist on 18 Jul 2019
OK. But often very small (close to -- or equal to -- 0) and very high (close to -- or equal to -- 1) are exactly the correlations that cause the problem I am talking about. They are matrix entries that cause inconsistencies with other entries.

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