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It depends on your investment process: more specifically, on how you generate views. Here are three practical cases which lead to different choices for $\Omega$: Let's assume you are an investor who acts on (more or less) arbitrary bits of opinion: e.g. you like Italian equities because you like Italy, and German equities because you find Angela Merkel's ...

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This problem is not interesting enough, because putting your money in the bank guarantees you zero volatility (and a zero return on investment). In practice, whatever set of assets you chose you would get a very extreme solution (e.g. 100% weight on one asset with very low volatility.) With a minor tweak, you can get a very interesting problem. You can ...

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If you give a covariance matrix an inverse Wishart prior, then it simplifies a lot of math in the calculations. This is called a conjugate prior. If you don't understand conjugate priors, you might want to work through the math on the univariate normal case with an inverse gamma or chi square prior for the variance. The Wishart distribution is just a ...

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