風險控制投資組合最佳化:使用粒子群演算法

Safety-First Portfolio Optimization： Using Particle Swarm Optimization Method

李玟蒂(Wen-Di Li)

指導教授 ： 張國華

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2010年)

https://doi.org/10.6840/cycu201000621

摘要

隨著金融國際化、自由化風潮及市場環境快速變遷，同業競爭日趨激烈，各 類創新的金融商品與業務相繼開發，使得金融相關業者承受較以往更為複雜的風 險型態，因此風險管理成為了金融業刻不容緩的首要課題。 風險值(Value-at-Risk, VaR)為財金分析者用來量化市場風險的標準衡量指 標。然而，風險值的計算是以常態分配為基礎，如此將導致下端風險被低估。有 鑑於此，本研究使用極值理論來計算風險值，其計算不需進行常態性假設。 為了最佳化投資組合，傳統的做法是利用窮舉法評估所有可能的方案以找出 最佳組合，此作法在實際應用上將耗費大量時間而不切實際，近年來基因演算 法、蟻群系統演算法、退火演算法及粒子群演算等方法已被廣泛地應用在最佳化 投資組合的問題上。本研究應用粒子群演算法並配合Safety-First 模式以選取最 佳投資組合，其中，粒子群演算法為模仿自然界群鳥覓食的現象所提出的啟發式 演算法；Safety-First 模式則會將較差股票的機率值限制在事先所定義的水準之 下。 在本研究中，選取摩根台灣股價指數 (MSCI Taiwan Index)中的前20 支股票 作為投資標的，並透過本研究所提出之研究方法，最後可獲得優於市場的投資組 合。

關鍵字

極值理論 ； 投資組合 ； 粒子群演算法 ； Safety-First 模式 ； 蟻群系統演算

並列摘要

In recent years, hash competition and introducing of new financial derivatives
have let the financial institutions to bare higher risk. Due to those reasons, risk
management has become a serious issue for all financial institutions.
Value-at-Risk (VaR) has become the standard measure that financial analysts
use to quantify market risk. However, the VaR estimators based on the normal
distribution thus lead to the underestimation of the true value of the risk. To solve
this problem this paper applied the Extreme Value Theory (EVT) to calculate the
Value-at-Risk (VaR), it does not rely on the normality assumption.
A traditional method to optimize the portfolio is by exhaustive search method
(ESM) which would evaluate all alternatives to find the optimal, but it will be timeconsuming
and unrealistic in practical applications. In recent years, Genetic Algorithms,
Ant Colony System Algorithm, Simulate Annealing Algorithm and Particle
Swarm Optimization have been applied on portfolio optimization problem. In this paper,
Particle Swarm Optimization (PSO) was incorporate with Safety-First model for
portfolio optimization is presented. In which, Particle Swarm Optimization (PSO)
is inspired by social behavior of bird flocking or fish schooling; Safety-First model
restricted the probability of worse case to be less than a predetermined value.
In the research, top 20 stocks from the MSCI Taiwan Index are chosen as the
investment targets. The experimental results show that with the proposed method,
better than market average’s portfolio can be achieved.

並列關鍵字

Portfolio Optimization ； Ant Colony System ； Safety-First ； Extreme Value

參考文獻

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