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There are different methods to get parametric copulas that have tail negative dependence. You might be interested in the following paper: Tail negative dependence and its applications for aggregate loss modeling and the reference therein.


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The standard deviation of an asset is less relevant if you hold a portfolio and not a single asset. In the CAPM, every investor holds the same portfolio of risky assets - the market portfolio. The CAPM implies further that the market portfolio has the highest expected portfolio return per unit of portfolio standard deviation of all possible portfolios. ...



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