Books on Portfolio Optimization and Risk Budgeting
Summary
This discussion recommends literature for readers with a mathematical background who want to study optimization in finance. The suggestions range from treatments of efficient frontier calculations and Markowitz portfolio construction to a technical book covering linear, nonlinear, quadratic, conic, integer, dynamic, and stochastic programming. It also points to a work on risk parity and risk budgeting, with applications spanning bonds, alternative investments, and multi-asset portfolios.
The recommendations indicate several paths into the subject: optimization algorithms, portfolio theory, and risk-based allocation. The discussion gives no comparison of the books’ depth, prerequisites, or practical results, and it contains no worked examples or assessment of competing methods. Readers should treat the list as a starting point for further selection rather than a systematic review of the literature.
Key ideas
- Efficient frontier methods connect portfolio theory with numerical optimization techniques.
- Risk parity and risk budgeting offer a portfolio construction perspective centered on risk allocation.
- The recommended optimization topics include linear, nonlinear, quadratic, conic, integer, dynamic, and stochastic programming.
- The suggested applications include bonds, alternative investments, and multi-asset portfolios.
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Full text
# What are the canonical books on optimization methods? # What are the canonical books on optimization methods? I am looking for some literature devoted to optimization methods in finance (portfolio optimization, asset pricing etc). Could you please recommend some books (perhaps, essentially non elementary: I have a master's degree in applied mathematics)? ## Answer by Chris Degnen (score 1) https://quant.stackexchange.com/a/22542 Some suggestions:- Modern Portfolio Theory and Investment Analysis, Ch. 6 Techniques for Calculating the Efficient Frontier Original 1970 paper An analytic derivation of the efficient portfolio frontier by Merton, Robert C Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques ## Answer by SRKX (score 1) https://quant.stackexchange.com/a/22556 I used Optimisation Methods in Finance, it covers: - Linear Programming - Nonlinear Programming - Quadratic Pogramming - Conic Programming - Integer Programming - Dynamic Programming - Stochastic Programming I haven't come across another book with such coverage or wider yet, although I've not been actively looking though. ## Answer by lehalle (score 0) https://quant.stackexchange.com/a/22561 I really like a lot Introduction to Risk Parity and Budgeting, by Thierry Roncalli. It covers a lot of aspect of portfolio construction, including portfolios of bonds, and provides a focus on risk management. The Table of Contents is - Part I. From Portfolio Optimization to Risk Parity Modern Portfolio Theory Risk Budgeting Approach - Part II. Applications of the Risk Parity Approach Risk-Based Indexation Application to Bond Portfolios Risk Parity Applied to Alternative Investments Portfolio Allocation with Multi-Asset Classes - Appendix A. Technical Appendix B. Tutorial Exercises
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