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| Title: | 追蹤指數與控管CVaR之投資組合規劃模型
Portfolio Optimization under CVaR Control and Tracking Error Minimization |
| Authors: | 蔡依婷
Tsai, Yi Ting |
| Contributors: | 劉明郎
Liu, Ming Long
蔡依婷
Tsai, Yi Ting |
| Keywords: | 指數型基金
下方偏差
線性規劃
條件風險值
index fund,
downside absolute deviation
conditional value-at-risk
linear programming |
| Date: | 2010 |
| Issue Date: | 2010-12-08 02:00:22 (UTC+8) |
| Abstract: | 指數型基金透過追蹤指數來提供投資人被動管理的投資策略，因而成為保守投資人的熱門投資工具。本論文的目的在於建立一個追蹤指數的同時也能有效控管損失的指數型基金。在此目標下，該基金面臨到的不單是追蹤指數的績效，還有降低資產配置風險的問題。有鑑於此，本論文融合兩種下方風險的概念：指數追蹤的下方偏差(downside absolute deviation)以及條件風險值(conditional value-at-risk, CVaR)。針對兩者間的規避程度分別分配其權重，並以該基金之平均報酬大於指數的平均報酬作為限制條件，經由改寫下方偏差與離散化CVaR後得到一個新的線性規劃模型。本論文以台灣50指數與恆生指數的歷史資料做為實證探討的對象，驗證使用本線性規劃模型所建立之指數型基金的效能。
Index fund has become popular in these days among the conservative investors since it provides a passive investment strategy. The main purpose of this paper is to create an index fund which can replicate the performance of a broad-based index of stocks and has the ability to control the loss efficiently at the same time. For this purpose, the index fund we build confronts with not only the performance of index tracking, but also lowering the level of the risk of assets allocation. In order to accomplish the goal, we combine two concepts of downside risk: downside absolute deviation and conditional value-at-risk (CVaR). Under the constraint of average portfolio return being greater than average index return, and assign weights according to the degree of evasion to each of the risks, a linear programming model is formulated by rewriting downside absolute deviation and discretizing CVaR. The results obtained from the computational experience on Taiwan 50 index and Hang Seng index are provided for testing the efficiency of this model.
誌 謝 IV
摘 要 ....................................................................................................................V
ABSTRACT ...............................................................................................................VI
表 目 錄 ...............................................................................................................VIII
圖 目 錄 ..............................................................................................................IX
第一章 緒論 .............................................................................................................1
1.1 前言 ..............................................................................................................1
1.2 研究目的與架構 .........................................................................................3
第二章 文獻回顧 ......................................................................................................5
2.1 資產配置文獻之回顧............ .......................................................................6
2.2 指數追蹤文獻之回顧...................................................................................8
2.3 VaR與CVaR文獻之回顧….....................................................................12
第三章 相關模型探討 ...........................................................................................14
3.1 資產配置模型之探討.................................................................................14
3.2 指數追蹤模型之探討.................................................................................20
3.3 CVaR模型之探討......................................................................................32
第四章 考量CVAR及追蹤誤差之規劃模型 ......................................................40
4.1 考量追蹤誤差之數學模型 .......................................................................40
4.2 考量CVaR之數學模型 ….........................................................................44
4.3 同步考量追蹤誤差及CVaR之數學模型 .................................................48
第五章 實證研究 ....................................................................................................50
第六章 結論與建議 ................................................................................................78
參考文獻 ....................................................................................................................79 |
| Reference: | Andersen, J. V. and D. Sornette, Have your cake and eat it too: increasing return while lowering large risks! Journal of Risk Finance 2, 70-82 (2001).
Andersson, F., H. Mausser, D. Rosen and S. Uryasev, Credit risk optimization with conditional Value-at-Risk Criterion, Mathematical Programming 89, 273-291 (2001).
Andrews, C., D. Ford and K. Mallinson, The design of index funds and alternative methods of replication, The Investment Analyst 82 (October), 16-23 (1986).
Basak, S. and A. Shapiro, Value-at-Risk based risk management: Optimal policies and assets prices, The Review of Finance Studies 14, 371-405 (2001).
Beasley, J. E., N. Meade and T. J. Chang, Index tracking technical report, Imperial College, (1999).
Beasley, J. E., N. Meade and T. J. Chang, An evolutionary heuristic for the index tracking problem, European Journal of Operational Research 148, 621-643 (2003).
Bellman, R. and L. A. Zadeh, Decision making in a fuzzy environment, Management Science 17, 141–164 (1970).
Blake, A. and A. Zisserman, Visual Reconstruction, MIT Press, Cambridge, MA (1987).
Brooke, A., D. Kendrick and A. Meeraus, GAMS-A User’s Guide, The Scientific Press, Redwood City, CA (1988).
Campbell, R., R. Huisman and K. Koedijk, Optimal portfolio selection in a Value-at-Risk framework, Journal of Banking and Finance 25, 1789–1804 (2001).
Coleman, T. F., J. Henninger and Y. Li, Minimizing tracking error while restricting the number of assets, Journal of Risk 8, 33-56 (2006).
Fang, Y. and S. Y. Wang, A fuzzy index tracking portfolio selection model, Lecture Notes in Computer Science 3516, 554-561 (2005).
Feinstein, C. D. and M. N. Thapa, A reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39, 1552-1553 (1993).
Fernholz, R., R. Garvy and J. Hannon, Diversity-weighted indexing, Journal of Portfolio Management 24, 74-82 (1998).
Gaivoronski, A. and G. Pflug, Value-at-Risk in portfolio optimization: properties and computational approach, The Journal of Risk 7, 1-31 (2005).
Gourieroux, C., J. P. Laurent and O. Scaillet, Sensitivity analysis of Values-at-Risk, Journal of Empirical Finance 7, 225-245 (2000).
Grootweld, H. and W. G. Hallerbach, Upgrading VaR from diagnostic metric to decision variable: a wise thing to do?, Report 2003 Erasmus Center for Financial Research, June (2000).
Jansen R. and R. van Dijk, Optimal benchmark tracking with small portfolios, Journal of Portfolio Management 28, 33-39 (2002).
Jorion, P., Value-at-Risk: the new benchmark for controlling market risk, McGraw-Hill, New York (2000).
Kast, R., E. Luciano and L. Peccati, VaR and optimization, 2nd International Workshop on Preferences and Decisions, Trento, July 1–3 (1998).
Konno, H. and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37, 519-531 (1991).
Konno, H. and R. Yamamoto, Minimal concave cost rebalance of a portfolio to the efficient frontier, Mathematical Programming, Series B 97, 571-585 (2003).
Krokhmal, P., J. Palmquist and S. Uryasev, Portfolio optimization with conditional Value-at-Risk objective and constraints, The Journal of Risk 4, 11-27 (2002).
Mansini, R., W. Ogryczak and M. Speranza, Conditional Value-at-Risk and related linear programming models for portfolio optimization, Annals of Operations Research 152, 227–256 (2007).
Markowitz, H., Portfolio selection, Journal of Finance 7, 77-91 (1952).
Markowitz, H., Portfolio selection: efficient diversification of investments, John Wiley & Sons, New York (1959).
Meade, N. and G. R. Salkin, Index funds-construction and performance measurement, Journal of the Operational Research Society 40, 871-879 (1989).
Rockafellar, R.T. and S. Uryasev, Optimization of conditional Value-at-Risk, The Journal of Risk 2, 21-41 (2000).
Rong, X. and J. Xia, Index portfolio optimization model with CVaR constraints and a practical analysis, Application of Statistics and Management 26, 621-628 (2007).
Speranza, M. G., Linear programming models for portfolio optimization, Finance 14, 107-123 (1993).
Uryasev, S., Conditional Value-at-Risk: optimization algorithms and applications, Financial Engineering News 14, 1-5 (2000).
Watada, J., Fuzzy portfolio model for decision making in investment, Dynamical Asspects in Fuzzy Decision Making, 141–162, Physica-Verlag, Heidelberg (2001).
Wu, L.-C., S.-C. Chou, C.-C. Yang and C.-S. Ong, Enhanced index investing based on goal programming, Journal of Portfolio Management 33, 59-56 (2007).
Yitzhaki, S., Stochastic dominance, mean variance and Gini’s mean difference, American Economic Revue 72, 178-185 (1982).
Young, M. R., A minimax portfolio selection rule with linear programming solution, Management Science 44, 673-683 (1998).
莊智祥，使用目標規劃建立指數基金，國立政治大學應用數學研究所碩士論文 （民87）。
白惠琦，指數基金追蹤模型的最佳化，國立政治大學應用數學研究所碩士論文 （民91）。
蘇代利，調整指數基金的最小成本模型，國立政治大學應用數學研究所碩士論文 （民93）。 |
| Description: | 碩士
國立政治大學
應用數學研究所
96751002
99 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0096751002 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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