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Constrained Quadratic Optimisation: 6. Portfolio optimisation

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6.            Portfolio optimisation

 

In a (mean-variance) portfolio optimisation context, the objective that we typically want to maximise is the following (or some monotonic equivalent):

 

 

Here  are the portfolio weights (so typically we impose at least the following constraint ),  is the benchmark (or ‘minimum risk’ portfolio),  is a vector of assumed returns on each asset and  is the covariance matrix (, where  is the vector of risks on each asset class, here assumed to be characterised by their volatilities, as this approach is merely a mean-variance one, and  their correlation matrix).

 


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