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2

Yes, indeed. It's a simple Linear Algebra and Expectation result: Given: $Var(w'r) = \mathbb{E}[(w'r)^2] = \mathbb{E}[(w'rr'w)]$ With $w$ and $r$ the vectors of weights and returns. As $w$ is constant, it holds: $\mathbb{E}[w'rr'w] = w'\mathbb{E}[rr']w$ The sample variance, $\hat{\Sigma}$, is a estimator of for $\mathbb{E}[rr']$. Therefore, it holds what you ...

2

A quant technique that could be used to (partially) address this problem is the Mean Variance Spanning Test of Huberman and Kandel (1987). Abstract This is a statistical test of whether adding K new assets to an existing set of N assets improves the Efficient Frontier or not. Roughly speaking the test involves checking whether the new assets "add ...

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The first article on this was Fisher and Lorie "Some studies of variability of returns on investments in common stocks" JB April 1970. https://www.jstor.org/stable/2352105 The Statman article you quote "How many stocks make a diversified portfolio" is from 1987, it is still referenced and broadly agrees with the other. A more recent ...

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Defining asset classes from a quantitative perspective is an interesting question that is not really addressed "officially" as far as I know. Let's try to write some requirements you want strategic decisions to make sense: each asset class should have at least one or two different "economic drivers" than the others you want tactical ...

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