Although portfolio management didn't change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in the deepening of the relationship between risk and asset management. Risk parity then became a popular financial model of investment after the global fina

It provides the key concepts and methods to implement quantitatively-driven portfolio construction. Areas include satellite investing, estimation error heuristics, scenario optimisation, mean variance investing, Bayesian methods, budgeting active risk, non-normality and multiple manager allocation. The emphasis is on practical applications and problem-solving written in a highly accessible style. The title contains quantitative analysis that is supported by extensive examples, tables and charts to help practitioners adopt the subject matter in their day-to-day work.

Risk budgeting models set risk diversification as objective in portfolio allocation and are mainly promoted from the asset management industry. Albina Unger examines the portfolios based on different risk measures in several aspects from the academic perspective (Utility, Performance, Risk, Different Market Phases, Robustness, and Factor Exposures) to investigate the use of these models for asset allocation. Beside the risk budgeting models, alternatives of risk-based investment styles are also presented and examined. The results show that equalizing the risk across the assets does not prevent losses, especially in crisis periods and the performance can mainly be explained by exposures to known asset pricing factors. Thus, the advantages of these approaches compared to known minimum risk portfolios are doubtful.

The mean-variance optimization framework has been the traditional approach to decide portfolio allocations based on return-risk trade-offs. However, it faces practical drawbacks, including sensitivity to estimated input parameters and concentration of portfolio risk. Risk budgeting portfolio optimization is a popular risk-based asset allocation technique where risk budgets are assigned to each assets' risk contribution, and equalizing all risk budgets in the portfolio is known as risk parity strategy. Unlike mean-variance, the risk parity strategy provides a balanced risk concentration in the portfolio and does not require expected asset return estimates as input. However, its performance can depend on the selected asset universe. Furthermore, its mathematical formulation imposes some computational challenges due to the non-convex structure.In this thesis, the risk budgeting problem is studied with modern optimization and machine learning approaches to enhance the portfolio model and address the aforementioned challenges. The second chapter introduces regime-switching risk parity portfolios with two primary components: regime modeling and prediction with supervised learning methods and identifying a regime-based strategy to improve the performance of a nominal risk parity portfolio. In the third chapter, we formulate a multi-period risk parity portfolio optimization problem in a transaction cost environment with a model predictive control approach. We provide a successive convex program algorithm that provides faster and more robust solutions. Lastly, we present an end-to-end portfolio allocation method by embedding the risk budget optimization problem as an implicit layer in a neural network. This approach combines prediction and optimization tasks in a single decision-making pipeline and constructs dynamic risk budgeting portfolios. Furthermore, we introduce a novel asset selection property with stochastic gates that protects the risk budgeting portfolio against the unprofitable assets.

Portfolio optimization and construction methodologies have become an critical ingredient of asset and fund management, while at same time portfolio risk assesment has become an essential ingredient in risk management.