hard · Quantitative Finance numerical
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?
- Asset j is given a large positive weight, since correlation is treated as boosting overall diversification.
- Asset j receives a weight of exactly zero in the optimization because it is treated as fully redundant next to asset i.
- Asset j's resulting portfolio weight stays completely unaffected by its correlation to i; it depends only on j's own variance term.
- 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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