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Portfolio Optimization Problem for Stock Portfolio Construction

Portfolio Optimization Problem for Stock Portfolio Construction. Student : Lee, Dah-Sheng Professor: Lee, Hahn-Ming Date: 9 July 2004. Outline. Portfolio Definition Property of Portfolio Related work Discussion References. Portfolio Definition 1/2.

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Portfolio Optimization Problem for Stock Portfolio Construction

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  1. Portfolio Optimization Problem for Stock Portfolio Construction Student : Lee, Dah-Sheng Professor: Lee, Hahn-Ming Date: 9 July 2004

  2. Outline • Portfolio Definition • Property of Portfolio • Related work • Discussion • References

  3. Portfolio Definition 1/2 • The investor considers k different stocks S1,... , Sk and wishes to invest some xi dollars in each stock Si for a certain period of time, where and xi > 0 for all i. The vector is called a portfolio. • Effective portfolio optimization involves simultaneously maximizing the portfolio return and minimizing the portfolio risk

  4. Portfolio Definition 2/2

  5. Unique Risk Market Risk Number of Securities Property of Portfolio • NP-Complete Problem Where p is the return of portfolio 1 and 2 are the returns of security 1 and 2 w1 and w2 are the weight of security 1 and 2 in the portfolio 1 and 2 are the Standard Deviation of security 1 and 2

  6. Property of Portfolio • Time Series • Trade-off Problem of risk and return • For a risk-averse investor, minimizing loss is more important than maximizing win, while an aggressive investor has the opposite priority.

  7. Related work 1/4

  8. Related work 2/4

  9. Related work 3/4

  10. Related work 4/4

  11. Discussion 1/2 • Approximate result of NP-Complete Problem can be obtained faster by “pre-process unit” • Dynamic portfolio selection and management policy is proposed recently for time series property of portfolio. We can improve them in “portfolio construction unit”

  12. Discussion 2/2

  13. References 1/3 [1] “Risk Control Over Bankruptcy in Dynamic Portfolio Selection: A Generalized Mean-Variance Formulation” Shu-shang Zhu, Dual Li, and Shou-Yang Wang IEEE TRANSACTIONS ON AUTOMATIC CONTROL Vol. 49, No. 3 MARCH 2004 page(s): 447-457 [2] “Data mining for financial prediction and trading: application to single and multiple markets” Se-Hak Chun and Steven H. Kim Expert System with Application, vol. 26, 2004 page(s): 131-139 [3]”The value of active portfolio management” Ravi Shukla Journal of Economics and Business vol. 56, 2004 page(s): 331-346

  14. References 2/3 [4] “Genetic Algorithms for Use in Financial Problems” Jackson, A. AFIR Vol 2, 1997 page(s): 481-503 [5] “Build Your own GA Efficient Frontier” Wendt, R. Q. Risks and Rewards, December 1995 page(s): 1-5 [6]”Novel Exploitation of Neural Network Methods in Financial Markets” Lowe, D. IEEE International Conference on Neural Networks 6, 27 June-2 July 1994 page(s): 3623-3628

  15. [7]"The Risk Profile Problem for Stock Portfolio Optimization" M.-Y. Kao, A. Nolte, and S. R. Tate. Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC), 2000, page(s): 228-234. References 3/3

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