引導式隨機搜尋在多變數股票投資組合的應用

Adaptive Random Search in Multifactor Equity Portfolio Management

賴忠成(Chung-Chain Lai)

指導教授 ： 盧以詮

元智大學/管理學院/管理研究所/碩士(1997年)

摘要

「透過多變數超額報酬模式的建立來形成投資組合」已逐漸成為股票投資組合管理經常使用的工具，這些模式自變因子的選擇將因研究者的不同而有所差異，但是這類模式還是有規則可循的，那就是它們大都是利用迴歸來針對自變因子間的兩兩相互關係去說明每個變數對報酬的影響能力，但是這些研究通常是以個股為主，使用迴歸方法將所有個股做排序之後再找出排名最好的一部份做為投資的參考。當投資組合數目不多，而且報酬率只受到公司本身因素影響時，適合採用這類方法，不會受到多變數相關性複雜化的影響，但是相對的，這類研究將無法兼顧投資組合風險。除了投資組合風險之外，迴歸分析也無法考慮自變因子權重限制、投資組合結構、交易成本及周轉率等影響報酬的變項。因此本研究認為投資組合的建立不只是curve fitting問題，而應該是全域最佳化問題。在對於最佳化方程式複雜度沒有先前的假設及方程式可能擁有多個區域極值的前提下，本研究為了在模式的建構過程能有效的控制風險，使用報酬除以風險-也就是Sharpe ratio為目標，運用引導式隨機搜尋、套利理論及"moving window"M最佳化問題，預期本模式的建議將可以作為投資組合經理人的決策參考。

關鍵字

投資組合管理 ； 引導式隨機搜尋 ； 套利理論 ； 全域最佳化

並列摘要

Building a multifactor excess return model to select a portfolio stocks has become a widely used tool for portfolio management. The decision of which return factors should be included in such model vary widely from practitioners to practitioners. The common characteristic in most models is that the factor weightings are determined by linear regression. Linear regression approach is to rank stocks by expected future return and then select a portfolio from among the highest ranked stocks. The critical characteristics of regression model related to portfolio construction are that regression produces a model that is a "best" historic fit to the returns of every stock. No measure of portfolio return or risk can be considered in determining the regression coefficients. In addition to the portfolio risk, restrictions on factor weights, portfolio structure, transaction costs, or turnover cannot be easily incorporated in determining the regression model. In this thesis, we consider the portfolio construction model as a global optimization problem, rather than a curve fitting problem. No assumptions about convexity of optimization function F(q) are made and, therefore, it may have several local maxima. To control risk throughout a portfolio construction process, we consider the model's objective function as to maximize return divided by risk - the Sharpe ratio. The model is constructed using a ten-year "moving window" of stock market information. The model is then tested on the next year. We then examine the performance of adaptive random search and arbitrage pricing theorem to solve this global optimization problem.

並列關鍵字

Portfolio Management ； Adaptive Random Search ； Arbitrage Pricing Theorem ； Global Optimization