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研究生:張惠渝
研究生(外文):Hui-Yu Chang
論文名稱:VaR限制下的最適投資組合
論文名稱(外文):Optimal asset allocation under VaR constraint
指導教授:王明隆王明隆引用關係
指導教授(外文):Ming-Long Wang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:財務金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:48
外文關鍵詞:Student-t distributionFat tailOptimal asset allocationVaR(Value at Risk)
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VaR is defined as the expected maximum loss (or worst loss) over a target horizon within a given confident level. In this paper, we use a portfolio selection model suggested by Telser [1955], which allocates financial assets by maximizing expected return subject to the VaR constraint set by the fund manager. We show that the optimal asset allocation under VaR constraint provide the identical result to the mean-variance decision. Furthermore, our analysis reveals that the degree of the shortfall probability plays a crucial role in determining the effects of the choice between fat-tailed and a normal distribution. The results highlight the influence of non-normal characteristics of the expected return distribution.
ABSTRACT…………………………………………………………………Ⅰ
TABLE OF CONTENTS……………………………………………………Ⅱ
LIST OF FIGURES………………………………………………………Ⅳ
LIST OF TABLES…………………………………………………………Ⅴ
CHAPTER 1 INTRODUCTION…………………………………………1
1.1 Motivation and Background…………………………………………1
1.2 Objective……………………………………………………………2
1.3 Organization…………………………………………………………3
CHAPTER 2 LITERATURE REVIEW………………………….………..4
2.1 Introduction of VaR……………………………………………………4
2.1.1 Definition………………………….…………………………..4
2.1.2 VaR for general distributions………………………….………..6
2.1.3 VaR for normal distribution………………………….……….…7
2.2 Literature Review……………………….……………………………..7
2.2.1 The distribution of asset returns………………………….……8
2.2.2 Portfolio theory………………………….…………………...8
2.2.3 Assts allocation model considering downside risk……………...9
CHAPTER 3 MODEL SPECIFICATIONS AND METHODOLOGY…14
3.1 The Model………………………….………………………….…......14
3.2 Probability distribution.………………………………………………15
3.2.1 Normal distributed returns…………………………………...15
3.2.2 Unknown distribution………………………………………..18
3.2.3 Symmetric distribution………………………………………20
3.2.4 Student-t distribution………………………………………...21
3.3 Empirical Methodology……….……………………………………...25
3.3.1 The VaR constraint and Student-t distribution with various v….26
3.3.2 The parameter estimation and empirical process……………...27
CHAPTER 4 EMPIRICAL RESULT…………….………………………29
4.1 Data Collections……………………….…………………………...….29
4.2 Empirical Results……………………….……………………………..30
4.2.1 Optimal asset allocation…………………………………..…30
4.2.2 The effect of misspecification v……………………………...32
CHAPTER 5 CONCLUSIONS…………….……………………………44
5.1 Conclusions………………………….…………………….………...44
5.2 Further Research………………...……….…………………………..45
REFERENCE…………….…………………………………………….….…46
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André Lucas and Pieter Klaassen, “Extreme returns, downside risk, and optimal asset allocation.” Journal of Portfolio Management, Fall 1998, pp. 71-79.

Blattberg, R.C. and N.J. Gonedes. “A comparison of the stable and student distribution as statistical models for stock prices.” Journal of Business, 1974, pp. 244-280.

Chia-chih Chien “Controlling downside risk in asset allocation.” Master thesis (Department of Finance, NTU, Taiwan, ROC), 2001.

Chopra, V. K., and W.T. Ziemba. “The effect of errors in means, variances, and covariances on optimal portfolio choice.” Journal of Portfolio Management, Date Winter 1993, Volume 19, Issue 2, pp. 6-11.

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Leibowitz, M.L., and S. Kogelman, “Assets allocation under shortfall constraints.” Journal of Portfolio Management, Winter 1991, pp. 18-23.

Peter Ritchken, “ Derivative market: Theory, strategy, and applications.” Harper Collions,1996.

Philippe Jorion, “Risk2: Measuring the risk in value at risk.” Financial Analysts Journal, November/December 1996, pp. 47-56.

Philippe Jorion, “Value at risk : The new benchmark for managing financial risk.” McGraw-Hill, 2000. (2nd ed.)

Praetz, P.D. “The distribution of share price changes.” Journal of Business 45,1972, pp. 45-55.

Rachel Campbell, Ronald Huisman, Kees Koedijk, “Optimal portfolio selection in a Value-at-Risk framework.” Journal of Banking and Finance, 2001, pp. 1789-1804.

Roy, A. D. “Safety-first and the holding of assets.” Econometrics, July 1952, pp. 431-449.

Telser, L.G. “Safety first and hedging.” Rev. of Econ. Stud. 6, 1955, 410-9.
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