臺灣博碩士論文加值系統

近年來，重大的金融危機事件層出不窮，使得風險管理的議題也逐漸受到重視。一般而言，風險管理均利用風險值(Value-at-Risk)作為衡量指標，但是在常態分配的假設下可能會低估下端風險。因此本研究中使用極值理論估計風險值，但是將風險值應用在投資組合時，由於不具備風險測度的特性，目前僅能以窮舉法進行求解，不符合實務上的需要。然而，近年來已被廣泛運用在各種組合問題上的蟻群系統演算法是模仿自然界螞蟻覓食的現象所提出的啟發演算法。本研究使用蟻群系統演算法取代傳統的窮舉法，並以Safety-First模式為基礎求解投資組合最佳化問題。
在本研究中，我們選取摩根台灣股價指數（MSCI Taiwan Index）中的20支股票作為投資標的，並且與大盤指數比較績效。最後結果證實，藉由Safety-First模式所選取的投資組合優於市場。

In recent years, there have been more and more critical financial market crises,
which have caused the subject of risk management to be taken a great deal more
seriously. In general, Value-at-Risk is a tool to measure risk management, but the
downside is that the risk may be underestimated under normal distribution. Therefore,
we use Extreme Value Theory to estimate the Value-at-Risk. Unfortunately,
this does not conform to the characteristic of risk measure when we apply the Valueat-
Risk to a portfolio problem. The current method can only be resolved by an
exhaustive search, but this does not meet practical requirements. However, the Ant
Colony System has been widely used in various combined issues, and is based upon
the natural ants’ phenomenon of Heuristic Algorithms.
In this study, we use Ant
Colony System to replace the traditional method of exhaustive search.
We chose 20 stocks from the MSCI Taiwan Index as investment targets, and
examined their performance with the market index. The results verify that the portfolio
selected by means of the Safety-First mode is better than the market.

摘要. . . . . . . . . . . . . . . . . . . . . . I
Abstract. . . . . . . . . . . . . . . . . . . II
誌謝. . . . . . . . . . . . . . . . . . . . . .III
List of Tables . . . . . . . . . . . . . . . . . . . VI
List of Figures . . . . . . . . . . . . . . . . . . VIII
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Organizations of The Thesis . . . . . . . . . . . . . . . . . . . . . . . 3
2 Preliminary and Literature Review 4
2.1 Safety-First PortfolioModels . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Theoretical Background of Extreme Value Theory . . . . . . . . . . . . . 8
2.2.1 Peak-Over-Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Ant Colony System . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Portfolio Optimization Model 19
3.1 Estimation of Downside Risk Based on GPDModel . . . . . . . . . . . . . 19
3.1.1 Selection of Threshold . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2 VaR Estimation of Fitted GPDModel . . . . . . . . . . . . . . . . . . 22
3.2 Portfolio Optimization Using the Ant Colony System . . . . . . . . . . 23
4 Numerical Analysis 28
4.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Conclusion 35
Bibliography 37
Appendices 40
A The Twenty Stocks of Our Investment Strategy from The MSCI
Taiwan Stock Index 40
B Weekly Portfolio of Our Investment Strategy 42
C Return Rates of All Models and Market 63

List of Tables
3.1 Upper-Tail Asymptotic Percentage Points forW2. P-value is Pr(W2 ≥ z) . . 21
4.1 Performance of AllModels and theMarket . . . . . . . . . . . . . . . . . 30
4.2 Number of Weeks with Negative Return of All Models and the Market . . . 30
B.1 Weekly Portfolio of Our Investment Strategy In January 2008 . . . . . . 43
B.2 Weekly Portfolio of Our Investment Strategy In February 2008 . . . . . . 44
B.3 Weekly Portfolio of Our Investment Strategy In March 2008 . . . . . . . 45
B.4 Weekly Portfolio of Our Investment Strategy In April 2008 . . . . . . . 46
B.5 Weekly Portfolio of Our Investment Strategy In May 2008 . . . . . . . . 47
B.6 Weekly Portfolio of Our Investment Strategy In May 2008 . . . . . . . . 48
B.7 Weekly Portfolio of Our Investment Strategy In June 2008 . . . . . . . . 49
B.8 Weekly Portfolio of Our Investment Strategy In July 2008 . . . . . . . . 50
B.9 Weekly Portfolio of Our Investment Strategy In August 2008 . . . . . . . 51
B.10 Weekly Portfolio of Our Investment Strategy In September 2008 . . . . . 52
B.11 Weekly Portfolio of Our Investment Strategy In October 2008 . . . . . . 53
B.12 Weekly Portfolio of Our Investment Strategy In October 2008 . . . . . . 54
B.13 Weekly Portfolio of Our Investment Strategy In November 2008 . . . . . 55
B.14 Weekly Portfolio of Our Investment Strategy In December 2008 . . . . . 56
B.15 Weekly Portfolio of Our Investment Strategy In January 2009 . . . . . . 57
B.16 Weekly Portfolio of Our Investment Strategy In February 2009 . . . . . 58
B.17 Weekly Portfolio of Our Investment Strategy In March 2009 . . . . . . . 59
B.18 Weekly Portfolio of Our Investment Strategy In April 2009 . . . . . . . 60
B.19 Weekly Portfolio of Our Investment Strategy In April 2009 . . . . . . . 61
B.20 Weekly Portfolio of Our Investment Strategy In May 2009 . . . . . . . . 62
C.1 Return Rates of All Models and Market(from 2008-Jan. to 2008-Sep.) . . . 64
C.2 Return Rates of All Models and Market(from 2008-Oct. to 2009-May.) . . . 65

List of Figures
2.1 Portfolio Loss Distribution with VaR . . . . . . . . . . . . . . . . . . 12
2.2 Foraging behavior of ants . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Diagramof the exploitation and exploration . . . . . . . . . . . . . . . 17
2.4 Flow chart of algorithm . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 Diagramof systemarchitecture . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Flow chart of ourmodel . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Number of Weeks with Negative Returns of All Models and the Market . . . 31
4.2 Comparisons of the return rates of the Model and the Safety-firstModel
Using Original Data and theMarket . . . . . . . . . . . . . . . . . . . . . 32
4.3 Comparisons of the return rates of the Model and the Safety-firstModel
Using Original Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Comparisons of the return rates of the Model and the Market during
the Financial Tsunami period . . . . . . . . . . . . . . . . . . . . . . . . 33
4.5 Cumulative returns for Model and Safety-first Model using original
data and the Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

[1] Arzac, E. R., and Bawa, V. S., (1977), ”Portfolio choice and Equilibrium in
Capital Markets with Safety-First Investors.” Journal of Financial Economics,
Vol. 4, pp. 277-288.
[2] Bucay, N., and Rosen, D., (1999), ”Credit Risk of an International Bond Portfolio:
a Case Study.” ALGO Research Quarterly, Vol. 2, pp. 9-29.
[3] Choulakian, M. A., and Stephens, V., (2001), ”Goodness-Of-Fit Tests for The
Generalized Pareto Distribution.” Technometrics, Vol. 43, pp. 478-485.
[4] Davison, A. C., and Smith, R. L., (1990), ”Models for Exceedances Over High
Thresholds.” Journal of the Royal Statictical Society, Vol. 52, pp. 393-442.
[5] Danielsson, J., and de Vries, G. G., (1997), ”Tail Index and Quantile Estimation
with Very High Frequency Data.” Journal of Empirical Finance, Vol. 4, pp.
241-257.
[6] Dorigo, M., and Gambardella, L. M., (1997), ”Ant Colony System: A Cooperative
Learning Approach to the Traveling Salesman Problem.” IEEE Transactions
on Evolutionary Computation, Vol. 1, pp. 53-66.
[7] Dorigo, M., and Gambardella, L. M., (1997), ”Ant Colonies for The Traveling
Salesman Problem.” BioSystem, Vol. 43, pp. 73-81.
38
[8] Dorigo, M., Di Caro, G., and Gambardella, L. M., (1999), ”Ant Algorithms for
Discrete Optimization.” Artificial Life, Vol. 5, pp. 137-172.
[9] Dorigo, M., (1992), ”Optimization, learning and Natural Algorithm.” Ph.D. Thesis,
DEI, Politecnico di Milano, Italy.
[10] Fisher, R., and Tippett, L., (1928), ”Limiting Forms of The Frequency Distribution
of The Largest or Smallest Member of a Sample.” Proceedings of the
Cambridge Philosophical Society, Vol. 24, pp. 180-190.
[11] Fernandez, V., (2005), ”Risk Management Under Exteme Events.” International
Review of Financial Analysis, Vol. 14, pp. 113-148.
[12] Gencay, R., and Selcuk, F., (2004), ”Extreme Value Theory and Value-at-Risk:
Relative Performance in Emerging Markets.” International Journal of Forecasting,
Vol. 20, pp. 287-303.
[13] Gnedenko, B. V., (1943), ”A Test of the Efficiency of a Given Portfolio.” Econometrica,
Vol. 57, pp. 1121-1152.
[14] Gumbel, E. J., (1958), statistics of Extremes, Dover Publications.
[15] Hall, P., (1990), ”Using The Bootstrap to Estimate Mean Squared Error and Select
Smoothing Parameter in Nonparametric Problems.” Journal of Multivariate
Analysis, Vol. 32, pp. 177-203.
[16] Haque, M., Hassan, M. K., and Varela, O., (2004), ”Safety-First Portfolio Optimization
for US Investors in Emerging Global, Asian and Latin American Markets.”
Pacific-Basin Finance Journal, Vol. 12, pp. 91-116.
[17] Jorion, P., (1996), ”Risk-Measuring the Risk in Value-at-Risk.” Financial Analysis
Journal, Vol. 52, pp. 47-56.
39
[18] Jansen, D., Koedijk, K., and de Vries, C., (2000), ”portfolio Selection with Limited
Downside Risk.” Journal of Empirical Finance, Vol. 7, pp. 247-269.
[19] Jorion, and Philippe, (2000), Value at Risk: The New Benchmark for Controlling
market Risk, McGraw-Hill, New York.
[20] Kataoka, S., (1963), ”A Stochastic Programming Model.” Econometrica, Vol. 31,
pp. 181-196.
[21] Markowitz, H., (1952), ”Portfolio Selection.” Journal of Finance, Vol. 7, No. 2,
pp. 77-91.
[22] Mausser, H., and D.Rosen, (1991), ”Beyond VaR: From Measuring Risk to Managing
Risk.” ALGO Research Quarterly, Vol.1, 2, pp. 5-20.
[23] McNeil, A., and Frey, R., (2000), ”Estimation of Tail-Related Risk Measures for
Heteroscedastic Financial Time Series: An Exteme Value Approach.” Journal of
Empirical Finance, Vol. 7, pp. 271-300.
[24] Roy, A. D., (1952), ”Safety-First and The Holding of Assets.” Econmetrica, Vol.
20, pp. 431-449.
[25] RiskMetricsTM, (1996), Technical Document, 4-th Edition, New York, NY,
J.P.Morgan Inc., December.
[26] Simons, K., (1996), ”Value-at-Risk New Approaches to Risk Management.”, New
England Economic Review, Sept/Oct, pp. 3-13.
[27] Stambaugh, F., (1996), ”Risk and Value-at-Risk.” European Management Journal,
Vol. 14, pp. 612-621.
[28] Telser, L. G., (1995), ”Safety-First and hedging.” Review of Economic Studies,
Vol. 23, No. 1, pp. 60.