臺灣博碩士論文加值系統

自從1952年Markowitz發表了Portfolio Selection 的論文後，投資組合在財務金融領域中已是一個非常重要的議題，諸多專家學者接續著Markowitz的腳步提出了許多的研究及論文。這些研究及論文以Markowitz的論文為基礎，提出了許多看法及修正，可惜的是至今只有少許的文獻針對投資組合的風險性資產的跳躍性進行模型推導、分析及實證討論，但在金融市場全球化的環境下，金融危機發生的頻率及影響力相對地提高，例如:1997年亞洲金融危機、2008年全球金融海嘯等，這些金融危機的發生顯示了金融市場是存在著跳躍且其重要性越來越不可忽略，因此本論文在風險性資產服從跳躍分配以及投資人之效用符合固定絕對風險趨避效用函（CARA）的前提下，建構一個多維度的投資組合模型及效用函數，並推導出其相關結構及偏態結構，最後本論文運用以上之推導並採用三檔指數型基金(ETF)分別為；iShares MSCI 德國指數型基金 (EWG), SPDR 美國S&P 500 指數型基金(SPY) and the iShares MSCI加拿大指數型基金(EWC)，2001年一月至2010年九月之資料進行投資組合策略及績效評比之實證。本論文的貢獻是我們將原本單維度的投資組合績效指標推廣至多維度，且我們的多維度績效指標是有考慮到跳躍效果且具有類似Sharpe ratio 指標之意義，但本研究的績效指標更具一般性。

Portfolio selection proposed by Markowitz (1952) is one of the most important issues in finance. Many researchers propose numerous extensions, but few researches consider the impacts of idiosyncratic jump and co-jump shocks on optimal portfolio selection. Due to the global financial crisis, such as the Asia economy crisis in 1997 and subprime crisis in 2008, the jump and co-jump shocks exist in the financial market and are quite important for the global portfolio selection. Therefore, this paper constructs a multivariate portfolio model, which the asset returns follow a multivariate Lévy processes proposed by Luciano and Semeraro (2010) with idiosyncratic jump and co-jump shocks, we derive an expected utility function with constant absolute risk aversion (CARA) form and the corresponding generalized sharp ratio (GSR). Using the data of iShares MSCI Germany Index Fund (EWG), SPDR USA S&P 500 (SPY) and the iShares MSCI Canada Index Fund (EWC) from Jan. 1, 2001 to Sep. 30, 2010, we do some empirical analysis for our multivariate Lévy portfolio model. Above all we extend the performance measure to the multivariate case by the multivariate Lévy processes,and our performance measure has some propositions similar as the sharpe ratio ,however, our performance is more general . It is the contribution of this thesis.

摘要 i
Abstract ii
致謝 iii
Contents iv
Table Contents vi
Figure Contents vii
1. Introduction 1
2. Literature Review 4
3. Methodology 8
3.1 Portfolio wealth process 9
3.2 The performance measure 10
3.3 Multivariate Alpha (α) Lévy processes 13
3.4 Dependence and skewness structures 21
3.5 Portfolio strategy decisions and Portfolio performance index 24
3.6 Relationship between Sharpe ratios 26
4. Parameters Estimation and Analysis 31
4.1 Data analysis 31
4.2 Estimations 32
4.3 Model selection 34
4.4 Parameters analysis 38
5. Applications 43
5.1 The strategy 44
5.2 Portfolio expected utility and wealth accumulation analysis 46
6. Conclusion 52
REFERENCES 54
Appendix A 57
Appendix B 64
Appendix C 67
Appendix D 73
Appendix E 75

1.Athayde, G. and Flôres, R. (1997), A CAPM with Higher Moments: Theory and Econometrics, Discussion Paper EPGE-FGV, 23.

2.Cont P.,Tankov P. (2004), Financial Modeling with Jump Process ,CRC press company .

3.Diacogiannis ,G., (1994) ,Three-parameter Asset Pricing, Managerial and Decision Economics 15,149–158.

4.Farinelli, S., Ferreira, M., Rossello, D., Thoeny, M., Tibiletti, L. (2008), Beyond Sharpe ratio: Optimal asset allocation using different performance ratios. Journal of Banking and Finance 32, 2057–2063.

5.Hodges, S. (1998), A generalization of the Sharpe ratio and its applications to valuation bounds and risk measures. Working Paper, Financial Options Research Centre, University of Warwick.

6.Jurczenko, E., Maillet, B. edited (2006), Muti-moment Asset Allocation and Pricing Model. John Wiley & Sons Ltd.

7.Levy, H. (1969), A Utility Function Depending on the First Three Moments, Journal of Finance 24,715–719.

8.Luciano, E.and Schoutens, W. (2006), A Multivariate Jump-Driven , Quantitative
Finance, 385–402.

9.Luciano, E. Semeraro,P. (2007), Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators Working Paper.

10.Luciano, E., Semeraro, P. (2010), A Generalized Normal Mean Variance Mixture for Return Processes in Finance, International Journal of Theoretical and Applied Finance, 415–440.

11.Luciano, E. Semeraro,P. (2007), Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators Working Paper.

12.Luciano, E., Semeraro, P.(2010), Multivariate Time Changes for Lévy Asset Models: Characterization and Calibration, Journal of Computational and Applied Mathematics, 1937–1953.

13.Madan , D.,B. and McPhail, G.S. (2000), Investing in skews. Journal of Risk Finance 2, 10–18.

14.Madan, D., B. and Seneta,E. (1990), The Variance Gamma (VG) Model for Stock Market Returns , Journal of Business, Vol. 63, 4,511–524.

15.Markowitz,H.(1952), Portfolio Selection , Journal of Finance 7 , 77–91.

16.Matsuda,K.(2004), Introduction to Option Pricing with Fourier Transform: Option Pricing with Exponential Lévy Models, The Graduate Center, The City University of New York.

17.O. E., Barndorff-Nielsen, J.,Pedersen and K. I. Sato (2001), Multivariate Subordination Self- Decomposability and Stability, Advance Application Probability. 33, 160–187.

18.Rubinstein, M. (1973), The Fundamental Theorem of Parameter-preference Security Valuation, Journal of Financial and Quantitative Analysis 8, 61–69.

19.Samuelson, P. (1970), The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments, Review of Economic Studies, 37,537–543.

20.Schoutens,W.(2003), Lévy Processes in Finance, John Wiley & Sons Ltd.

21.Semeraro,P. (2008), A Multivariate Variance Gamma Model For Financial Applications, International Journal of Theoretical and Applied Finance 11, 1–18.

22.Sharpe, W. (1964), Capital Asset Prices: A Theory of Market Equilibrium under conditions of Risk, Journal of Financial 19,425-442.

23.Sharpe, W. (1967), A Linear Programming Algorithm for Mutual Fund Portfolio , Management Science, Vol. 13, No. 7,. 499-510.

24.Wang, J. (2009), The Multivariate Variance Gamma Process and It`s Application in Multi-Asset Option Pricing, PhD dissertation, University of Maryland.

25.Zakamouline, V., Koekebakker, S. (2009), Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance, Journal of Banking and Finance 33, 1242–1254.