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I have always estimated correlations and variances disjointly and later combine them to construct covariance matrices. Specifically, variances are estimated in a univariate setting (only using the data for each particular asset).

Is there any downside in this approach? Wondering if there is a benefit to estimate variances in a multivariate setting / or if there is any literature on this?

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    $\begingroup$ What is your formula for correlation, if it is not already subsuming the variance, i.e. calculating covariance and just dividing by the univariate variances? $\endgroup$
    – Attack68
    Mar 4 at 20:41
  • $\begingroup$ The potential downside is that you are compounding the estimation errors of two separate procedures when you aggregate them into ones $\endgroup$
    – Vitomir
    Mar 5 at 8:55
  • $\begingroup$ Hi: if you google for "estimating covariance matrix in one fell swoop", the first MIT link points to a document that looks pretty good at a quick glance. I'd send the link itself but one is not provided. $\endgroup$
    – mark leeds
    Mar 5 at 20:35

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