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So we are interested in a PDF for equilibrium returns given the views. Why do we choose our view means as the mean parameter and observed market covariance as the covariance parameter? Seems a bit arbitrary.

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Since you add the bayes-theory tag here I'm gonna speak in bayesian interpretation; I'd say it's just because this is the simplest way to obtain the distribution of prior; A better way to do this is by finding a prior optimal (essentially finding best mean and variance that fits our assumption of return distribution based on the data you have; usually done in a normal-gamma setting) and then feed to your posterior.

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  • $\begingroup$ Not talking about the prior or the posterior. Talking about the parameters of the likelihood -- the way to get from prior to posterior. $\endgroup$ – A.L. Verminburger May 16 at 15:08
  • $\begingroup$ exactly; your likelihood funciton is about $\theta$ which is the parameter set and the choice of prior $\pi(\theta)$ is what we need before making to posterior; if we say $\pi(\theta) ~ N(\xi,v)$, the simplest way to get $\xi$ is to calculate views' mean $\endgroup$ – numerairX May 16 at 16:49

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