Contents. Acknowledgements... Preface... Chapter 1. Advances in Portfolio Risk Control... 1 Winfried G. HALLERBACH

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1 Contents Acknowledgements... Preface... xv xvii Chapter 1. Advances in Portfolio Risk Control... 1 Winfried G. HALLERBACH 1.1. Introduction The empirical example and preliminaries Money allocation versus risk allocation Implied risk premia and the implied Sharpe ratios Maximum Sharpe ratio portfolio (MSRP) /N or equal-weighting Minimum variance portfolio (MVP) Maximum diversification portfolio (MDP) Equal risk contribution portfolio (ERCP): full risk parity Inverse volatility portfolio (IVP): naive risk parity Volatility weighting over time Evaluation Appendix Asset and portfolio (excess) returns Marginal and component contributions to portfolio (excess) return Portfolio risk premium Portfolio variance Decomposing portfolio volatility Portfolio optimality: maximize the Sharpe ratio Reverse optimization: implied risk premia Bibliography... 28

2 vi Risk-Based and Factor Investing Chapter 2. Smart Beta: Managing Diversification of Minimum Variance Portfolios Jean-Charles RICHARD and Thierry RONCALLI 2.1. Introduction Risk-based investing and variance minimization MV portfolio ERC portfolio Most diversified portfolio Comparing the trade-off relationships Managing the diversification Mixing the constraints A unified optimization framework Diversification profile of risk-based portfolios Understanding the behavior of smart beta portfolios Volatility reduction Normalizing the smart beta portfolios Performance of the smart beta portfolios Dynamic smart beta strategies Conclusion Appendix Managing the tracking error volatility Solving the general optimization problem using the CCD algorithm Bibliography Chapter 3. Trend-Following, Risk-Parity and the Influence of Correlations Nick BALTAS 3.1. Introduction Methodology Constructing a trend-following strategy Volatility-parity scheme Data description Performance evaluation of trend-following Volatility-parity ignores pairwise correlations Risk-parity principles Risk-parity Risk-budgeting Long-short risk-budgeting Trend-following meets risk-parity Performance evaluation of risk-parity trend-following Conclusion... 91

3 Contents vii 3.8. Appendix: solving for risk parity Bibliography Chapter 4. Diversifying Risk Parity: In Today, Out Tomorrow? Harald LOHRE, Heiko OPFER and Gábor ORSZÁG 4.1. Managing diversification Rationalizing principal portfolios Data and descriptive statistics Extracting and interpreting principal portfolios Risk-based asset allocation Risk-based asset allocation schemes Performance of risk-based asset allocation schemes How diversified are the risk-based asset allocation schemes? In today, out tomorrow? Risk-based strategies in a rising interest rate environment Conclusion Acknowledgments Bibliography Chapter 5. Robust Portfolio Allocation with Systematic Risk Contribution Restrictions Serge DAROLLES, Christian GOURIEROUX and Emmanuelle JAY 5.1. Introduction Portfolio allocation with risk contribution restrictions Minimum risk portfolios Portfolios with risk contribution restrictions Risk contribution restrictions and portfolio turnover Portfolio allocation with systematic risk contribution restrictions Systematic and idiosyncratic risks Systematic and idiosyncratic risk contributions Portfolios with systematic risk contribution restrictions Illustrations with different risk measures The volatility risk measure The α-var risk measure Distorsion risk measures Application The investment universe Portfolio management with total risk contribution restrictions

4 viii Risk-Based and Factor Investing Portfolio management with systematic risk contribution Restrictions Concluding remarks Bibliography Chapter 6. Risk-Based Investing but What Risk(s)? Emmanuel JURCZENKO and Jérôme TEILETCHE 6.1. Introduction Expected shortfall as risk measure Expected shortfall: definition and properties Contribution to expected shortfall and risk-based portfolios Broadening risk measures Volatility and correlation risks Valuation risk Asymmetry and tail risks Illiquidity risk Empirical results Data overview and preliminary analysis Equal risk contribution under different risk models Conclusion Mathematical Appendix Data Appendix Bibliography Chapter 7. Target Volatility Bernd SCHERER 7.1. Introduction Better leverage and the Samuelson puzzle Target volatility and Sharpe ratio improvement Informative or uninformative leverage Target volatility and tail hedging Asymmetric leverage Target volatility across asset classes Conclusions Bibliography Chapter 8. Smart Beta Equity Investing Through Calm and Storm Kris BOUDT, Joakim DARRAS, Giang HA NGUYEN and Benedict PEETERS 8.1. Introduction

5 Contents ix 8.2. A regime switching approach to market timing Faber s timing model based on rolling price averages Timing model based on the predicted return distribution from a mean-variance regime switching model with state variables driving the transition probabilities Performance evaluation Sample and variable description Choice of risky asset Variables in the multivariate regression model Results Impact of choice of smart beta equity strategies on portfolio performance Impact of market timing strategies on portfolio performance Conclusion Acknowledgments Appendix Hamilton s filter Calculation of expected shortfall of stock returns under the RS model Bibliography Chapter 9. Solving the Rebalancing Premium Puzzle Vladyslav DUBIKOVSKYY and Gabriele SUSINNO 9.1. Introduction Rebalancing as a risk premium Probing the limits: when simulations provide more insight Beating the best asset: a path to the low-risk anomaly explanation When rebalancing pays off Conclusions Appendix Rebalancing premium: the multi-asset case Bibliography Chapter 10. Smart Betas: Theory and Construction Attilio MEUCCI Introduction Signals Fundamental law of active management

6 x Risk-Based and Factor Investing Factors construction Direct construction Characteristic portfolios Conclusions Bibliography Chapter 11. Low-Risk Anomaly Everywhere: Evidence from Equity Sectors Raul Leote DE CARVALHO, Majdouline ZAKARIA, Xiao LU and Pierre MOULIN Introduction Low volatility or low beta? Sector-neutral low-risk investing Motivation Universality of the low-risk anomaly in equity sectors Diversification in sector-neutral low-volatility investing Tail risk in sector-neutral low-volatility investing Sector-neutral versus non-sector neutral low-risk investing Performance and sector exposures Persistence of volatility Liquidity of low-volatility strategies Conclusions Acknowledgments Bibliography Chapter 12. The Low Volatility Anomaly and the Preference for Gambling Jason C. HSU and Vivek VISWANATHAN Introduction A brief review of the literature Lottery and volatility double sort International evidence Conclusion Appendix Bibliography Chapter 13. The Low Beta Anomaly and Interest Rates Cherry MUIJSSON, Ed FISHWICK and Steve SATCHELL Literature review The anomaly and interest rates Model specification Empirical analysis and results

7 Contents xi The anomaly and interest maturity mismatch Model specification Results Concluding remarks Bibliography Chapter 14. Factoring Profitability Lisa R. GOLDBERG, Ran LESHEM and Michael BRANCH Quality is an active investment strategy with a long and distinguished history Replicating gross profitability with style factors The four-factor Fama French Carhart model does not explain gross profitability The Barra USE4 model explains a substantial portion of gross profitability over the past two decades Conclusion Disclosure Bibliography Chapter 15. Deploying Multi-Factor Index Allocations in Institutional Portfolios Jennifer BENDER, Remy BRIAND, Dimitris MELAS, Raman Aylur SUBRAMANIAN and Madhu SUBRAMANIAN Introduction Implementing factors through multi-factor index allocations Multi-factor indexes: a new approach for institutional mandates Deploying factor allocations Selecting the right blend of factors Correlations matter when selecting factors: the diversification effects of multi-factor index allocations Considerations for combining factor indexes Implementation considerations Understanding the exposure versus investability trade off Reducing trading costs by leveraging the benefits of natural crossing Multi-factor index allocations: examples Example #1: Strategic long-term risk-adjusted return Example #2: De-risking with yield enhancement

8 xii Risk-Based and Factor Investing Conclusion Bibliography Chapter 16. Defining the Equity Premium, a Framework Yves CHOUEIFATY and Christophe ROEHRI Introduction Defining the equity premium Risk-rewards homogeneity and the equity premium A taxonomy of smart beta and risk factors driven strategies Being practical: a core-satellite portfolio allocation Conclusion Bibliography Chapter 17. Designing Multi-Factor Equity Portfolios Noël AMENC, Romain DEGUEST, Felix GOLTZ, Ashish LODH, Lionel MARTELLINI and Eric SHIRBINI Introduction Designing efficient and investable proxies for risk premia Risk allocation with smart factor indices Absolute return perspective Absolute risk management without factor risk exposure constraints Introducing risk-budgeting constraints Long-term evidence in the USA universe Relative risk perspective Methodology Risk contributions and performance Relative risk allocation using long-term USA factor indices Conclusion: index design and allocation decisions for multi-factor equity portfolios Bibliography Chapter 18. Factor Investing and Portfolio Construction Techniques Yin LUO and Spyros MESOMERIS Introduction Risk factor investing: the new paradigm Theory meets practice Taxonomy of risk premia strategies

9 Contents xiii Is risk premia allocation inherently superior to asset-class allocation? Efficient frontier analysis Portfolio construction techniques An alternative approach for defining diversification Introducing the copula model Minimum tail dependence portfolio optimization algorithm Alternative beta portfolios An alternative definition of risk Minimum CVaR portfolio CVaR optimization theory Mean-CVaR efficient frontier and minimum CVaR portfolio Robust minimum CVaR optimization Choice of alpha parameter Comparison of different risk-based portfolio construction techniques The philosophy of portfolio construction A horse race of risk-based portfolio construction techniques Conclusion Bibliography Chapter 19. Multi-Factor Portfolio Construction for Passively Managed Factor Portfolios Jennifer BENDER and Taie WANG A short history of passively managed factor portfolios Single-factor portfolio construction Why combine multiple factors? Multi-factor portfolio construction Conclusion Appendix A: description of tilted factor portfolios Bibliography Chapter 20. Statistical Overfitting and Backtest Performance David H. BAILEY, Stephanie GER, Marcos LOPEZ DE PRADO and Alexander SIM Introduction Backtest overfitting in finance and investments Quantifying backtest overfitting effects An online demonstration of backtest overfitting

10 xiv Risk-Based and Factor Investing Simple example of backtest overfitting (SEBO) How SEBO is used Understanding the results Conclusion Acknowledgments Bibliography List of Authors Index