投資組合最適化的數值方法

Portfolio Optimization Using Monte Carlo Method

李泰明(Tai-Ming Lee)

《輔仁管理評論》 15卷2期 (2008/05) Pp. 83-96

https://doi.org/10.29698/FJMR.200805.0005

摘要

雖然近期利率有回升的現象，但是因爲前一陣子面對利率一降再降，把錢放在銀行升息，可以獲得的利息將愈來愈少，不僅對許多要靠定存收入過活的銀髮族是一大警訊，即使是不靠定存維生的普羅大眾也不想讓資產成了呆錢。可是，錢不放在銀行，能往何處去？民眾愈活用資產的理財需求，帶來了新金融商品發展的市場動力。金融商品多樣化之後，投資組合的策略問題就成了很重要的課題。本文利用蒙地卡羅的數值方法去描述投資組合最適化的數值問題，並利用繪圖的技術去傳達重要的思考，如效率前緣等。

關鍵字

投資組合最適化 ； 蒙地卡羅法 ； 效率前緣

並列摘要

The mean variance port folio theory is based on a set of k available risky asset, for example bonds, stocks mutual funds, and derivatives, which rate of return and variance covariance matrix are estimated. The traditional method to maximize an objection function of this problem is computationally troublesome. On this paper the Monte Carlo Method is used to illustrate the Makowitz curve and efficient frontier by generating 10000 portfolio scatter plot. The histogram of objective function is created, and efficient port folios are delineated. The numerical solutions of portfolio optimization are obtained by iterative converged methodology.

並列關鍵字

portfolio optimization ； Monte Carlo Method ； efficient frontier

參考文獻

于趾琴(2003)。新金融商品大觀。台北:聯經出版社。

Alexei A. Gaivoronski,Georg Pflug.Value-at-Risk in Portfolio Optimization: Properties and Computational Approach.Journal of Risk.7(2),1-31.

Edwin J. Elton,Martin J. Gruber(1995).Modern Portfolio Theory and Investment Analysi.New York:John Wiley & Sons.

Matthias Ehrgott,Kathrin Klamroth,Christian Schwehm(2004).European Journal of Operational Research.

Paolo Brandimarte(2002).Numerical Methods in Finance.New York:JOHN WILEY & SONS.