Tail Risk Measures: Optimization Theory and Applications

Monday 26 October 2009

Course leader: Stan Uryasev, Professor, Director of the Risk Management and Financial Engineering (RMFE) Lab, UNIVERSITY OF FLORIDA; Editor-in-Chief, THE JOURNAL OF RISK

08:30 Registration and coffee

09:00 Fundamental relationships in risk management

- Risk measures estimating magnitude of loss
- Deviations estimating width of distributions
- Relations between risks and deviations: axiomatic approach
- Coherent risks and deviations
- Relations in risk management and statistics

10:30 Morning break

11:00 Pros and cons of tail risk measures

- Variance/(Standard Deviation) vs VaR, CVaR, and Maximum Loss
- VaR vs CVaR
- Dynamic versus static risk measures
- Drawdown (conditional drawdown-at risk) measure

12:30 Lunch

13:30 Portfolio optimization: recent developments

- Mean-Variance optimization
- CVaR functions and constraints
- VaR functions and constraints
- Max-loss constraints
- Drawdown functions and constraints
- Omega functions
- Probability functions

15:00 Afternoon break

15:30 Case studies

- Portfolio optimization of a Fund of Funds composed of Hedge Funds: comparison of Variance, Mean Absolute Deviation, CVaR and Drawdown risk management
- VaR vs CVaR optimization of a portfolio of active managers
- Portfolio optimization to assure compliance with BASEL II requirements including regulatory (VaR) constraints and economic capital (CVaR) constraints
- Portfolio optimization with drawdown constraints for dynamic strategies in futures
- Calibrating default probabilities with Maximum Entropy approach and structuring CDOs
- Credit risk hedging with Cardinality Constraints (constraints on number of hedging instruments)

17:00 End of seminar

Course leader

Professor Stan Uryasev at is director of the Risk Management and Financial Engineering Lab and director of the PhD Program with Concentration in Quantitative Finance at the University of Florida. His research is focused on efficient computer modeling and optimization techniques and their applications in finance and military projects. He published three books (monograph and two edited volumes) and about eighty research papers. He is a co-inventor of the Conditional Value-at-Risk and the Conditional Drawdown-at-Risk optimization methodologies. He is the founder of American Optimal Decisions (AORDA.com) developing optimization software in risk management area: VaR, CVaR, Default Probability, Drawdown, Credit Risk minimization.

Stan Uryasev is a frequent speaker at academic and professional conferences. He has delivered seminars on the topics of risk management and stochastic optimization. He is on the editorial board of a number of research journals and is editor-in-chief of the Journal of Risk.

More information

Risk management involves various risk measures: Variance, Value-at-Risk, Conditional Value-at-Risk, Drawdown, Omega, and others. This course is focused on comparative analysis of risk measures in portfolio optimization setting. We will discuss statistical stability of estimates of risk measures and inputs needed for portfolio optimization. We will present and explore portfolio optimization techniques with various tail risk measures.

WHAT YOU WILL LEARN

• Definitions of various tail risk measures , including VaR, CVaR, Drawdown, Omega
• Two groups of stochastic measures: Risks vs Deviations
• Key characteristics for comparing portfolios performance, such as Sharpe, Sortino and other ratios
• Portfolio optimization statements with various risk measures and constraints
• Settings of in-sample vs out-of-sample portfolio optimization runs

KEY OBJECTIVES AND LEARNING OUTCOMES

• Observe pros and cons of various risk measures
• Learn efficient optimization settings and approaches with tail risk measures
• Understand when portfolio optimization approaches can (and cannot) be used
• Learn about interface of optimization and statistics (e.g., statistics problems with constraints)
• Hand on experience in financial optimization case studies

WHO SHOULD ATTEND

• Investment Officers
• Insurance Company Managers; Fund and Investment Managers
• Market and Credit Risk Managers
• Analysts (Fixed Income and Equity) and Proprietary Traders
• Private Bankers and Wealth Management Professionals
• Venture Capitalists and Private Equity Team Members
• Securities Regulators, Central Bankers
• Software Providers, Systems Professionals and Information Providers
• Exchanges; Institutional and Corporate Investors
• Anyone invested in hedge funds or active trading strategies