大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Part 1: Understanding Behaviors of Robust Portfolios
Part 2: A Uniformly Distributed Random Portfolio

Woo Chang Kim (Korea Advanced Institute of Science and Technology)

1. ホーム
2. セミナー・集中講義
3. セミナー
4. Part 1: Understanding Behaviors of Robust Portfolios
   Part 2: A Uniformly Distributed Random Portfolio

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第61回

Part 1: Understanding Behaviors of Robust Portfolios
Part 2: A Uniformly Distributed Random Portfolio

Woo Chang Kim (Korea Advanced Institute of Science and Technology)

Part 1: Understanding Behaviors of Robust Portfolios
Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean-variance model. The main idea is to introduce an uncertainty set for the model parameters, and to obtain the portfolio with worst-case optimization approach. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. In this presentation, we discuss the recent finding on the qualitative characteristics of the robust portfolios. More specifically, there are three main questions to be addressed:
1) Is robust portfolio really robust?
2) Robust portfolio is different from traditional mean-variance portfolio. Is there any consistent pattern in regard to this qualitative difference in two portfolios?
3) If robust portfolio is consistently different from traditional mean-variance portfolio, is it possible to reduce the difference without losing the robustness?

References
[1] Kim, Woo Chang, and Min Jeong Kim (2015) “Qualitative Properties of Robust Support Vector Machines”, Working Paper
[2] Kim, Woo Chang, John M. Mulvey, Frank J. Fabozzi, and Jang Ho Kim (2015) “Towards Robust Equity Investing”, International Journal of Financial Analysis, 39, 19-31
[3] Kim, Woo Chang, Jang Ho Kim, and Frank J. Fabozzi (2014) “Deciphering Robust Portfolios”, Journal of Banking and Finance, 45, 1–8
[4] Kim, Woo Chang, Frank J. Fabozzi, Patrick Cheridito, and Charles Fox (2014) “Controlling Portfolio Skewness and Kurtosis without Directly Optimizing Third and Fourth Moments”, Economics Letters, 122, 154-158
[5] Kim, Woo Chang, Min Jeong Kim, Jang Ho Kim, and Frank J. Fabozzi (2014) “Robust Portfolios That Do Not Tilt Factor Exposure”, European Journal of Operational Research, 234, 411-421
[6] Kim, Jang Ho, Woo Chang Kim, and Frank J. Fabozzi (2014) “Recent Developments in Robust Portfolios with a Worst-Case Approach”, Journal of Optimization Theory and Applications, 161, 103-121
[7] Kim, Woo Chang, and Je-Hyuk Lee (2013) “Characteristics of Robust Portfolios in a Varied Asset Universe”, Quantitative Finance Letters, 1, 18-28
[8] Kim, Jang Ho, Woo Chang Kim, and Frank J. Fabozzi (2013) “Composition of Robust Equity Portfolios”, Finance Research Letters, 10, 72-81
[9] Kim, Woo Chang, Jang Ho Kim, So Hyung Ahn, and Frank J. Fabozzi (2013) “What Do Robust Models Really Do?”, Annals of Operations Research, 205, 141-168

Part 2: A Uniformly Distributed Random Portfolio
We consider a portfolio manager who picks her model parameters randomly, and analytically derive the probability distribution of the Sharpe ratio of this uniformly distributed random portfolio. This allows us to answer several questions in portfolio thoery:
1) Is 1/n portfolio superior to mean-vairance optimal portfolio?
2) Have mutual funds and hedge funds provided superior performance?
3) Is asset allocation approach better than security selection?

References
[10] Kim, Woo Chang, and Yong Jae Lee (2015) “A Uniformly Distributed Random Portfolio”, submitted
[11] Kim, Woo Chang, and Yong Jae Lee (2015) “An Analytical Justification for Asset Allocation”, Working Paper
[12] Kim, Woo Chang, Yong Jae Lee, and William T. Ziemba (2015), “Is 1/n Really Better than Optimal Mean-Variance Portfolio?”, submitted