One of the major topics in the area of asset management is asset allocation. Harry Markowitz suggested a formal and elegant method to come to a solution that became then popularly referred to as Mean-Variance Optimization or Mean-Variance Analysis. It consists of a quantitative technique that identifies the best asset allocation solutions on the basis of the trade-off between risk and return. However, a large amount of financial literature has successively documented that, in spite of its theoretical appeal and rationality, it does not work quite so well in practice. In Chapter 2, we review the disappointing characteristics of the Markowitz portfolios that make them unreliable for asset managers. Most importantly, we outline that they are consequences of estimation errors in the optimization input parameters. In line with existing literature, we assign especially to estimation errors in the expected returns, the most deteriorating impact on the optimized portfolios. Since the 1980s, dissatisfaction regarding portfolios based on the Markowitz optimization has resulted in the search for alternative asset allocation solutions. More precisely, we are aware that various approaches have been developed to address the problem of estimation risk and reduce the impact of estimation errors on portfolio weights and performance. They are represented by Bayesian methods and heuristic methods. We emphasize that both Bayesian and heuristic methods certainly do not “revolutionize” the mean-variance framework which continues to serve as a “reference point”. Using these considerations as a starting point, we have decided to devote Chapter 3 and Chapter 4 to asset allocation approaches that provide an alternative, admittedly partial and, until few years ago, unusual response to the problem of estimation risk affecting the Mean-Variance Optimization: remove or drop the expected return estimates from the inputs for the portfolio construction process considering that related estimation errors are the most crucial. These solutions are called risk-based asset allocation approaches but they can also be referred to as -free strategies. We include in this group the following asset allocation methods: risk parity, equally-weighted, global minimum-variance and most diversified portfolio approach. Chapter 3 and Chapter 4 focus on a comprehensive analysis of the aforementioned risk-based approaches. The work provides the theory, the math, the algorithms necessary for understanding and implementing such solutions. Since it is obvious that omitting expected returns from the set of inputs leads to a focus on the risk dimension (which justifies the name given to these methods), we highlight fundamental notions about risk budgeting as a core tool for asset managers interested in these approaches and we include a review of them in Chapter 3. It is not viable to build or interpret a risk-based portfolio without being familiar with the concepts of risk allocation or risk decomposition, marginal risk and risk contribution. Although Chapters 2, 3 and 4 are deeply theoretical, they are continuously supplemented with examples in an attempt to allow readers to see how everything can be applied in practice. The final part of the book, Chapter 5, provides an extensive empirical investigation of the risk-based asset allocation approaches discussed in the previous chapters. The analysis is undertaken using three different real datasets that allow to present applications concerning two problems of allocation inside a specific, though large, asset class and a problem of allocation among multiple asset classes. In order to provide a deeper knowledge of the main features of these strategies that can be helpful for investment practice, we adopt three different evaluation criteria in the comparative analysis: financial efficiency, level of diversification and asset allocation stability.

### Risk-based approaches to asset allocation – Concepts and practical applications

#####
*BRAGA M*

##### 2016-01-01

#### Abstract

One of the major topics in the area of asset management is asset allocation. Harry Markowitz suggested a formal and elegant method to come to a solution that became then popularly referred to as Mean-Variance Optimization or Mean-Variance Analysis. It consists of a quantitative technique that identifies the best asset allocation solutions on the basis of the trade-off between risk and return. However, a large amount of financial literature has successively documented that, in spite of its theoretical appeal and rationality, it does not work quite so well in practice. In Chapter 2, we review the disappointing characteristics of the Markowitz portfolios that make them unreliable for asset managers. Most importantly, we outline that they are consequences of estimation errors in the optimization input parameters. In line with existing literature, we assign especially to estimation errors in the expected returns, the most deteriorating impact on the optimized portfolios. Since the 1980s, dissatisfaction regarding portfolios based on the Markowitz optimization has resulted in the search for alternative asset allocation solutions. More precisely, we are aware that various approaches have been developed to address the problem of estimation risk and reduce the impact of estimation errors on portfolio weights and performance. They are represented by Bayesian methods and heuristic methods. We emphasize that both Bayesian and heuristic methods certainly do not “revolutionize” the mean-variance framework which continues to serve as a “reference point”. Using these considerations as a starting point, we have decided to devote Chapter 3 and Chapter 4 to asset allocation approaches that provide an alternative, admittedly partial and, until few years ago, unusual response to the problem of estimation risk affecting the Mean-Variance Optimization: remove or drop the expected return estimates from the inputs for the portfolio construction process considering that related estimation errors are the most crucial. These solutions are called risk-based asset allocation approaches but they can also be referred to as -free strategies. We include in this group the following asset allocation methods: risk parity, equally-weighted, global minimum-variance and most diversified portfolio approach. Chapter 3 and Chapter 4 focus on a comprehensive analysis of the aforementioned risk-based approaches. The work provides the theory, the math, the algorithms necessary for understanding and implementing such solutions. Since it is obvious that omitting expected returns from the set of inputs leads to a focus on the risk dimension (which justifies the name given to these methods), we highlight fundamental notions about risk budgeting as a core tool for asset managers interested in these approaches and we include a review of them in Chapter 3. It is not viable to build or interpret a risk-based portfolio without being familiar with the concepts of risk allocation or risk decomposition, marginal risk and risk contribution. Although Chapters 2, 3 and 4 are deeply theoretical, they are continuously supplemented with examples in an attempt to allow readers to see how everything can be applied in practice. The final part of the book, Chapter 5, provides an extensive empirical investigation of the risk-based asset allocation approaches discussed in the previous chapters. The analysis is undertaken using three different real datasets that allow to present applications concerning two problems of allocation inside a specific, though large, asset class and a problem of allocation among multiple asset classes. In order to provide a deeper knowledge of the main features of these strategies that can be helpful for investment practice, we adopt three different evaluation criteria in the comparative analysis: financial efficiency, level of diversification and asset allocation stability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.