Covariance matrix

A covariance matrix, in finance, is a square matrix that contains covariances between portfolio assets. Because, for example, the element in row 2/column 2 is an assets covariance with itself, the diagonal of the covariance matrix contains asset variances. Recall that COV[A,A] = correlation[A,A]*Volatility[A]*Volatility[A], and since Correlation[A,A] = 1, it follows that COV[A,A] = 1*Variance[A]. The brief video reviews a spreadsheet in Carol Alexanders Market Risk Analysis: Quantitative Methods in Finance (v. 1). It is a simple but key idea: the covariance matrix embed a correlation matrix. So, if matrix D is the diagonal matrix of return volatilities, and matrix C is the correlation matrix, then the covariance matrix is a matrix product: DCD.

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[RDXRD]

Hello David,

Correlation is unit less. any reason to represent as %?

thanks

[bionicturtledotcom]

@RDXRD my mistake, i agree: correlation is unitless and should not really have %. thanks for spotting that!

[sergo1989]

hi david, i disagree on the your order. because you can not have correlation matrix before covariance matrix. correlation matrix is found from covariance matrix. if i'm wrong, please explain to me how did you find correlations before variance-covariance?

[bionicturtledotcom]

I agree with you, correlations are function of covariance, not vice versa. But here, it is simply a practical idea: bivariate correlations inform an n-asset covariance matrix. Where did this asset correlations come? As you say, from bivariate covariances. So, the correlations-as-inputs do come from covariances...the exercise is only meant to show the MATRIX equivalent of the bivariate COV= COR*vol*vol ...

[geiko187]

thanks david, very cool, love your videos - huge help

[Riverdale270]

And again a very nice video... I'm giving you a big thanks in the foreword of my masterthesis on portfolio optimization!

[kaattiiex]

Hi, when i try and apply the array formula to the matrix it doesn't work... it doesn't fill it like yours! even though i copy you step by step...

I press ctrl shift enter and brackets surround the formula but it doesn't fill the cells... any advice?

[godseeker11]

excellent , thank you

[whirmark]

@sergo1989 In fact the variances (D) could be derived by direct measurement upon securities and the correlation matrix (C) could be derived/implied from a factor-model, so that covariance is calculated as above frequently in practice for portfolio optimization.

[csmd2011]

Hello. I have a question but it's too long to post. May I send you a msg?

[sdytfx]

very very help!!!

[bvoorhees]

If you have a matrix of variances instead of standard errors (call it matrix D), can you multiply D by C (as opposed to DCD) to get the VCM? Thanks

[elenafv]

What's the name of the book, that you mentioned in the video?