本研究主要的目的為基於條件風險值(CVaR)以差分進化算法建構多種投資組合並說明傳統風險測度標準差與CVaR在管理風險上之效度，過去學術及實務界主要以標準差量測投資組合風險，若以其建構投資組合，雖能於市場衰退時有效縮減投資組合跌幅，但亦會於市場狀態反彈時限制其漲幅，為了改善此狀況，本文依照Boudt (2013)和Dowling (2015) 提出之目標式建構多種投資組合，並以多元資產ETF作為樣本以提高樣本之多樣性，根據實證結果，基於最小化CVaR所建構之投資組合因其能同時於熊市縮減跌幅並於正常市場時增加漲幅，使其整體表現優於其他投資組合；而若分別單獨以CVaR和標準差作為風險測度並基於最小化風險建構投資組合，CVaR於熊市時減緩損失之能力會略遜於標準差，但其於市場正常時所增加之漲幅將能彌補其於熊市之不足，CVaR作為一風險測度能有效因應市場狀態轉換並管理投資組合所面對之風險。

The purpose of this study is to construct portfolios based on Conditional Value-at-Risk (CVaR) by differential evolution and explain the effectiveness of CVaR and standard deviation on risk management. In the past, the academic and practical circles mainly measured the risk of a portfolio using standard deviation. Though it can indeed decrease loss of the portfolio efficiently, it will also prevent portfolios from earning higher returns when the conditions of the market change from bear to normal. In this study, we construct a variety of portfolios according to the goals proposed by Boudt (2013) and Dowling (2015) and use a multivariate asset ETF as a sample to increase the diversity of samples. The portfolio whose objective function is minimizing CVaR can simultaneously control risk in bear markets and raise return in normal markets and the overall performance is better than other portfolios. We also construct portfolios based on CVaR and standard deviation to compare which one is better at measuring risk. In the bear markets, the ability of CVaR to mitigate loss is slightly inferior to standard deviation but its increase in the normal markets will be able to make up for its lack in bear markets. CVaR as a risk measure can efficiently respond to the transition of the market state to manage risk compared to standard deviation.

論文審定書 i
誌謝 ii
摘要 iii
ABSTRACT iv
I. INTRODUCTION 1
1.1 Background Information 1
1.2 Research Purpose 4
1.3 Research Structure 5
II. LITERATURE REVIEW 6
2.1 Value-at-Risk (VaR) 6
2.2 Conditional Value-at-Risk (CVaR) 7
2.3 Portfolio Conditional Value-at-Risk Budgets 9
III. METHODOLOGY 12
3.1 Data Description 12
3.2 Differential Evolution 15
3.3 Measuring Tail Risk 19
3.4 Portfolio Construction 20
3.5 Marginal Contribution to Conditional Value-at-Risk 21
3.6 Exchange-Traded Funds 22
IV. EMPIRICAL RESULTS 27
4.1 Optimization Results of Index Portfolios 27
4.2 Optimization Results of ETF Portfolios 34
4.3 Marginal Contribution to Conditional Value-at-Risk 39
V. CONCLUSION 41
REFERENCES 44

Alexander, G. J., and Baptista, A. M. (2004). A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model. Management science, 50(9), 1261-1273.
Ardia, D., Boudt, K., Carl, P., Mullen, K., and Peterson, B. (2011). Differential evolution (DEoptim) for non-convex portfolio optimization. R Journal, 3(1), 27–34.
Artzner, P., Delbaen, F., Eber, J. M. and Heath, D. (1997). A characterization of measures of risk. Technical report, Cornell University Operations Research and Industrial Engineering.
Artzner, P., Delbaen, F., Eber, J. M. and Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-228.
Boudt, K., Ardia, D., Mullen, K. M. and Peterson, B. G. (2014). Large-scale portfolio optimization with DEoptim. Soft-Computing in Capital Market: Research and Methods of Computational Finance for Measuring Risk of Financial Instruments, BrownWalker Press.
Bodnar, G., and Smithson, C. (2001). Risk allocation. RISK, 58-59.
Boudt, K., Carl, P. and Peterson, B. G. (2013). Asset allocation with conditional value-at-risk budgets. The Journal of Risk, 15(3), 39-68.
Boudt, K., Peterson, B. and Croux, C. (2008). Estimation and decomposition of downside risk for portfolios with non-normal returns. The Journal of Risk, 11(2), 79-103.
Hendricks, D. (1997). Evaluation of value-at-risk models using historical data. Economic Policy Review, 2(1).
Huisman, R., Koedijk, K. C. and Pownall, R. A. (1999). Asset allocation in a value-at-risk framework. Working paper, Erasmus University.
Chew, D. H. (2008). Corporate risk management. Columbia University Press, 163-164.
Chiappini, C., Cortelezzi, F. and Serraino, G. (2012). A CVaR Model for ETF Portfolio Selection. Working paper, University of Florida.
Denault, M. (2001). Coherent allocation of risk capital. The Journal of Risk, 4, 1-34.
Downing, C., Madhavan, A., Ulitsky, A. and Singh, A. (2015). Portfolio Construction and Tail Risk. The Journal of Portfolio Management, 42(1), 85-102.
Ellis, J. H. (2005). Ahead of the curve: A commonsense guide to forecasting business and market cycles. Harvard Business Press.
Junior, A. M. D., and Alcantara, S. D. R. (1999). Mean-Value-at-Risk Optimal Portfolios with Derivatives. Derivatives Quarterly, 6(2), 56-63.
Krokhmal, P., Palmquist, J. and Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. The Journal of Risk, 4, 43-68.
Lee, W. (2011). Risk-Based Asset Allocation: A New Answer to an Old Question? The Journal of Portfolio Management, 37(4), 11-28.
Maillard, S., Roncalli, T. and Teiletche, J. (2010). The properties of equally weighted risk contribution portfolios. The Journal of Portfolio Management, 36(4), 60-70.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
Morgan, J. P. (1994). Introduction to riskmetrics. New York: JP Morgan.
Pflug, G. C. (2000). Some remarks on the value-at-risk and the conditional value-at-risk. Probabilistic constrained optimization, Springer US,272-281.
Price, K., Storn, R. M. and Lampinen, J. A. (2006). Differential evolution: a practical approach to global optimization. Springer Science & Business Media.
Qian, E. (2005). Risk parity portfolios: Efficient portfolios through true diversification. Panagora Asset Management, September.
Rockafellar, R. T. and Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2, 21-42.
Scaillet, O. (2004). Nonparametric estimation and sensitivity analysis of expected shortfall. Mathematical Finance, 14(1), 115-129.
Stoyanov, S. V., Rachev, S. T. and Fabozzi, F. J. (2013). Sensitivity of portfolio VaR and CVaR to portfolio return characteristics. Annals of Operations Research, 205(1), 169-187.
Topaloglou, N., Vladimirou, H., and Zenios, S. A. (2002). CVaR models with selective hedging for international asset allocation. Journal of Banking and Finance, 26(7), 1535-1561.