Joint presentation with Rui Ding. The paper presents a new dynamic portfolio performance risk measure called Expected Regret of Drawdown (ERoD) which is an average of the drawdowns exceeding a specified threshold (e.g. 20%). ERoD is similar to Conditional Drawdown-at-Risk (CDaR) which is the average of some percentage of the largest drawdowns. CDaR and ERoD portfolio optimization problems are equivalent and result in the same set of optimal portfolios. Necessary optimality conditions for ERoD portfolio optimization lead to Capital Asset Pricing Model (CAPM) equations. ERoD Beta, similar to the Standard Beta, relates returns of the securities and those of a market. ERoD Beta is equal to [average losses of a security over time intervals when market is in drawdown exceeding the threshold] divided by [average losses of the market in drawdowns exceeding the threshold]. Therefore, a negative ERoD Beta identifies a security which has positive returns when the market has drawdowns exceeding the threshold. ERoD Beta accounts only for time intervals when the market is in drawdown and conceptually differs from Standard Beta which does not distinguish up and down movements of the market. Moreover, ERoD Beta provides quite different results compared to the Downside Beta based on Lower Semi-deviation. ERoD Beta is conceptually close to CDaR Beta which is based on a percentage of worst case market drawdowns. However, ERoD Beta has some advantage compared to CDaR Beta because the magnitude of the drawdowns is known (e.g. exceeding a 20% threshold), while CDaR Beta is based on a percentage of the largest drawdowns with unknown magnitude. We have built a website reporting CDaR and ERoD Betas for stocks and the SP 500 index as an optimal market portfolio. The case study showed that CDaR and ERoD Betas exhibit persistence over time and can be used in risk management and portfolio construction.
Stan Uryasev is Professor and Frey Family Endowed Chair of Quantitative Finance at the Stony Brook University.
He received his M.S. in Applied Mathematics from the Moscow Institute of Physics and Technology (MIPT), Russia, in 1979 and Ph.D. in Applied Mathematics from the Glushkov Institute of Cybernetics, Kiev, Ukraine in 1983. From 1979 to 1987 he held a research position at the Glushkov Institute. From 1988 to 1992 he was a Research Scholar at the International Institute for Applied System Analysis, Luxenburg, Austria. From 1992 to 1998 he held the Scientist position at the Risk and Reliability Group, Brookhaven National Laboratory, Upton, NY. From 1998 to 2019 he was the George and Rolande Willis Endowed Professor at the University of Florida, and the director of the Risk Management and Financial Engineering Lab.
His research is focused on efficient computer modeling and optimization techniques and their applications in finance and DOD projects. He published four books (two monographs and two edited volumes) and more than 130 research papers. He is a co-inventor of the Conditional Value-at-Risk and the Conditional Drawdown-at-Risk optimization methodologies. He developed optimization software in risk management area, including Drawdown and Credit Risk minimization.
His joint paper with Prof. Rockafellar on Optimization of Conditional Value-At-Risk in The Journal of Risk, Vol. 2, No. 3, 2000 is among the 100 most cited papers in Finance. Many risk management/optimization packages implemented the approach suggested in this paper (MATLAB implemented a toolbox).
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 Emeritus and Chairman of the Editorial Board of the Journal of Risk.