The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

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:

Here, the control variable is a vector w of optimal weight allocated to various risky assets, μ_p denotes the portfolio expected return, and σ_p 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 ...