Many Risks, One (Optimal) Portfolio

217 Pages Posted: 30 Jul 2014

Date Written: July 28, 2014


This study investigates how to obtain a portfolio which would provide above average returns while remaining robust to most risk exposures. Emphasis is placed on risk management, given our perspective (shared by many other practitioners), that retaining above average portfolio performance in current market environment depends strongly on having an effective risk management process.

We rely on a comprehensive survey of the literature to describe stylized facts of market returns and main categories of asset allocation methodologies, including Modern Portfolio Theory, Black-Litterman model, factor-based and risk-based strategies. Furthermore, we present both criticisms and defenses of strategies, together with potential issues identified by practitioners and corresponding solutions (if they do exist).

We outline recent enhancements to various types of portfolio strategies, and analyze how to incorporate (in the asset allocation framework) constraints, regularization, personal views, stylized features of empirical market data, and forward information given by financial options market data.

More prominence is given to strategies (risk parity, risk factors, factor investing, smart beta, dynamic, etc.) that were shown to deliver better portfolio performance in terms of returns, diversification, risk, etc. We also discuss a wide ranging collection of performance measures proposed in the literature for quantifying portfolio return, risk and diversification, identify which such measures are most popular with practitioners, and which corresponding strategies have best results (as shown in the literature).

Since a major topic of this study is managing risks, we provide details on the types of risk that portfolios may be exposed to, on approaches and strategies to handle such exposures, with highlighting of tail risk management. Portfolio insurance is also discussed.

We also describe practical aspects needed for a successful portfolio management, including robust estimation of covariances, correlations and model parameters, numerical optimization methods, key questions and issues identified by practitioners, Monte Carlo simulation, comprehensive testing framework, stress testing, available software implementations (usually in R), etc.

To summarize, the study analyzes all ingredients that are required, in our opinion, to deliver portfolios with above average performances and resilient to most risks, and concentrates on the strategies which have emerged as frontrunners in the last few years, both in the literature and in the market.

Keywords: portfolio management, risk management, asset allocation, performance measures, risk parity, risk measures, factor investing, robust estimation, optimization, diversification, smart beta, leverage, Black Litterman model, Modern Portfolio Theory, Monte Carlo, testing, stress, tail risk

JEL Classification: C11, C12, C13, C14, C15, C51, C52, C63, G11, G12

Suggested Citation

Homescu, Cristian, Many Risks, One (Optimal) Portfolio (July 28, 2014). Available at SSRN: or

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