論文中，我們針對共同基金提出了兩個以基因規劃法為基礎以改進交易策略的模型。
這兩個交易模型可幫助投資人增加投資報酬率並減少投資風險。第一個交易模型使用
索丁諾比率（Sortino ratio）來選取基金，並且平均分配資金至被選取的基金以增加
投資報酬率，此模型在實驗中有最好的年化報酬率。第二個交易模型同樣使用索丁諾比
率來選取基金，但改以平均數變異數模型為基礎，分配資金至被選取的基金以降低風險。
最重要的是我們的交易模型使用了基因規劃法建構交易策略，基因規劃法所得出的交易
策略相當適合用在瞬息萬變的交易市場當中，以增加投資報酬率。
為了驗證交易模型，從1999年1月至2009年12月（共11年），我們以基金為對象，
使用交易模型模擬交易的過程。從實驗的結果中，第一個交易模型可在2004年1月1日
至2008年12月31日當中獲得9.11%的年化報酬率，相對於已存在的方法得到的6.89%的年
化報酬率，有更佳的結果。此外，第二個交易模型可得到與已存在的方法近似的年化報酬
率，但是相對第一個交易模型有較小的下跌風險。

In this thesis, we propose two genetic-programming-based models that improve the
trading strategies for mutual funds. These two models can help investors get returns
and reduce risks. The first model increases the return by selecting funds with high
Sortino ratios and allocates the capital equally, achieving the best annualized return.
The second model also selects funds with high Sortino ratios, but reduces the risk
by allocating the capital with the mean variance model.
Most importantly, our model utilizes the genetic programming to generate
feasible trading strategies to gain return, which is suitable for the market that
changes anytime. To verify our models, we simulate the investment for mutual
funds from January 1999 to December 2009 (11 years in total). The experimental
results show that our first model can gain return from 2004/1/1 to 2008/12/31,
achieving the best annualized return 9.11%, which is better than the annualized
return 6.89% of previous approaches. In addition, our second model with smaller
downside volatility can achieve almost the same return as previous results.

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Portfolio Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Mean Variance Model . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Sortino Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Genetic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Tsai’s Method for the Investment of Mutual Funds . . . . . . 17
Chapter 3. Fund Investments with Genetic Programming . . . . . . 19
3.1 The Flow Chart of Investment . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Selecting Funds with the Sortino ratio . . . . . . . . . . . . . . . . . 20
3.3 Allocating the Capital with the Mean Variance Model . . . . . . . . . 24
3.4 Determining the Timing with the Genetic Programming . . . . . . . 25
Chapter 4. Experimental Results . . . . . . . . . . . . . . . . . . . . . . 27
4.1 Data Collection and Preprocessing . . . . . . . . . . . . . . . . . . . 27
4.2 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.1 The Performance of the 4433 Rule . . . . . . . . . . . . . . . . 29
4.2.2 The Performance of the MSCI World Price Index . . . . . . . 33
4.2.3 The Performance of the S&P 500 Composite Price Index . . . 35
4.3 Our Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 Experimental Results with the Sortino Ratio on the Buy and
Hold Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.2 Experimental Results with Sortino Ratio on the Genetic Programming
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.4 Performance Comparison of Various Models . . . . . . . . . . . . . . 70
Chapter 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Appendixes
A. The Global Trend Indicator (GTI) Index Values . . . . . . . . . . 75
B. The First Tradable Date of Our Funds . . . . . . . . . . . . . . . . . 83
C. The Transaction Details of the Buy and Hold Strategy . . . . . . 90
D. The Transaction Details of Strategy 1 Generated by Genetic
Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

[1] A. Chaudhry and H. L. Johnson, “The efficacy of the Sortino ratio and other
benchmarked performance measures under skewed return distributions,” Australian
Journal of Management, Vol. 32, No. 3, pp. 485–502, 2008.
[2] J. S. Chen, J. L. Hou, S. M. Wu, and Y. W. Chang-Chien, “Constructing investment
strategy portfolio by combination genetic algorithms,” Expert Systems
with Application, Vol. 36, pp. 3824–3828, 2009.
[3] Y. Chen, S. Mabu, K. Shimada, and K. Hirasawa, “A genetic network programming
with learning approach for enhanced trading model,” Expert Systems with
Application, Vol. 36, pp. 12537–12546, 2009.
[4] Y. Chen, E. Ohkawa, S. Mabu, K. Shimada, and K. Hirasawa, “A portfolio
optimization model using genetic network programming with control nodes,”
Expert Systems with Application, Vol. 36, pp. 10735–10745, 2009.
[5] E. J. Elton, M. J. Gruber, S. J. Brown, and W. N. Goetzmann, Modern Portfolio
Theory and Investment Analysis. Wiley, 2006.
[6] FundDJ Co., Ltd., “FundDJ.” http://www.funddj.com/, 2000.
[7] W. Huang, Y. Nakamori, and S.-Y.Wang, “Forecasting stock market movement
direction with support vector machine,” Computers & Operations Research,
Vol. 32, pp. 2513–2522, 2005.
[8] H. Ince and T. B. Trafalis, “Kernel principal component analysis and support
vector machines for stock price prediction,” IEEE International Joint Conference
on Neural Networks, Vol. 3, Budapest, Hungary, pp. 2053–2058, July
2004.
[9] K.-J. Kim and I. Han, “Genetic algorithms approach to feature discretization
in artificial neural networks for the prediction of stock price index,” Expert
Systems with Application, Vol. 19, pp. 125–132, 2000.
[10] T. Kimoto and K. Asakawa, “Stock market prediction system with modular
neural networks,” Proceedings of the International Joint Conference on Neural
Networks, Vol. 1, Washington, USA, pp. 1–6, June 1990.
[11] J. Koza, Genetic Programming: On the Programming of Computers by Means
of Natural Selection. MIT Press, 1992.
[12] J. Koza, Genetic programming II: Automatic discovery of reusable programs.
MIT Press, 1994.
[13] H. M. Markowitz, “Portfolio selection,” Journal of Finance, Vol. 7, pp. 77–91,
1952.
[14] H. M. Markowitz, Portfolio selection: Efficient Diversification of Investments.
John Wiley and Sons, 1959.
[15] P.-F. Pai and C.-S. Lin, “A hybrid ARIMA and support vector machines model
in stock price forecasting,” OMEGA: The International Journal of Management
Science, Vol. 33, pp. 497–505, 2005.
[16] J.-Y. Potvin, P. Soriano, and M. Vallee, “Generating trading rules on the
stock markets with genetic programming,” Computers & Operations Research,
Vol. 31, pp. 1033–1047, 2004.
[17] W. F. Sharpe, “The Sharpe ratio,” Journal of Portfolio Management, Vol. 21,
pp. 49–58, 1994.
[18] H. Soleimani, H. R. Golmakani, and M. H. Salimi, “Markowitz-based portfolio
selection with minimum transaction lots, cardinality constraints and regarding
sector capitalization using genetic algorithm,” Expert Systems with Application,
Vol. 36, pp. 5058–5063, 2009.
[19] F. A. Sortino and L. N. Price, “Performance measurement in a downside risk
framework,” The Jounal Of Investing, Vol. 3, pp. 59–64, 1994.
[20] T. J. Tsai, C. B. Yang, and Y. H. Peng, “Genetic algorithms for the investment
of the mutual fund with global trend indicator,” Proceedings of the 8th Conference
on Information Technology and Applications in Outlying Islands, Kinmen,
Taiwan, pp. 471–476, May 2009.
[21] Q. Wen, Z. Yang, Y. Song, and P. Jia, “Automatic stock decision support
system based on box theory and SVM algorithm,” Expert Systems with Application,
Vol. 37, pp. 1015–1022, 2010.