ASSET ALLOCATION AND PORTFOLIO CONSTRUCTION DECISIONS IN THE OPTIMAL DESIGN OF THE PERFORMANCE-SEEKING PORTFOLIO

Modern portfolio theory provides again some useful guidance with respect to the optimal design of a PSP that would best suit investors’ needs. More precisely, the prescription is that the PSP should be obtained as the result of a portfolio optimization procedure aiming at generating the highest risk-reward ratio.
Portfolio optimization is a straightforward procedure, at least in principle. In a mean-variance setting for example, the prescription consists of generating a maximum Sharpe ratio (MSR) portfolio based on expected return, volatility and pairwise correlation parameters for all assets to be included in the portfolio, a procedure which can even be handled analytically in the absence of portfolio constraints.
More precisely, consider a simple mean-variance problem:
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Here, the control variable is a vector w of optimal weight allocated to various risky assets, μp denotes the portfolio expected return, and σp denotes the portfolio volatility. We further assume that the investor is facing the following investment opportunity set: a riskless bond paying the risk-free rate r, and a set of N risky assets with expected return vector µ (of size N) and covariance matrix Σ, (of size N × N), all assumed constant so far.
With these notations, the portfolio expected return ...

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