hard · Quantitative Finance

Consider the term Σ^-1μ. In a portfolio context, if asset j has a very high correlation with asset i, but a lower expected return, how does this correlation typically affect asset j's weight in the Σ^-1μ vector?

1. Asset j will have a large positive weight because the correlation increases diversification.
2. Asset j will have a weight of zero because it is redundant.
3. Asset j's weight is unaffected by correlation with i; it depends only on its own variance.
4. Asset j will likely have a negative weight (short position) as the optimizer uses it to hedge the risk of asset i.

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