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題名：運用隨機矩陣理論探討雜訊交易對投資組合報酬率之影響
作者：許世璋
作者(外文)：Hsu, Shih-Chang
校院名稱：國立臺北大學
系所名稱：企業管理學系
指導教授：古永嘉
王祝三
學位類別：博士
出版日期：2010
主題關鍵詞：雜訊交易理論；投資組合理論；假性相關；隨機矩陣理論；noise trading theory；portfolio theory；spurious correlation；random matrix theory
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本研究以Black (1986) 與 DeLong et al. (1990) 的雜訊交易理論為基礎，首先定義資訊與雜訊的意義，以論證與數學推導的方式，將雜訊交易與投資組合理論 (Markowitz, 1952) 加以結合，並藉由核子物理學的隨機矩陣理論，實證雜訊對於投資組合理論的影響。本研究首先提出4個命題，因為雜訊是由媒體與社群互動交流而產生，具有渲染的特質，是故推論命題1為：雜訊並非公司的個別風險，無法透過多樣化組合完全分散。因為雜訊並非公司的個別風險，在計算投資組合權重時會造成「假性相關」的干擾，又因「假性相關」並不具有持續性，所以推論命題2為：雜訊並非系統風險，無法持續的存在於市場之中。本研究亦發現，投資組合的風險會因為雜訊的存在而有所增加，因此推論命題3為：風險性資產投資組合的風險，將因為雜訊的干擾而提高。此外，雜訊的干擾也會降低投資組合的效率，是故命題4為：雜訊會降低投資組合的效率性。
本研究依據命題的可驗證性，分別將命題2、命題3與命題4，轉化為3個假說。假說1為「隨著持有期間的增加，資訊組合與干擾組合的績效，會逐漸產生顯著的差異」，藉此檢驗雜訊是否為系統風險。假說2為「資訊組合的變異數，會顯著的低於干擾組合的變異數」，以此檢驗雜訊是否會提高投資組合的風險。假說3為「資訊組合的夏普指數，會顯著的高於干擾組合的夏普指數」，以此檢驗雜訊是否會降低投資組合的效率性。再以台灣證券交易所提供的19類類股指數作為研究樣本，取樣期間為2005年初至2009年底，取樣頻率為日，共計1242筆資料。採用Bouchaud和Potters (2000) 發展的方法，濾除隨機矩陣，並分別以30日與60日形成期的移動窗格，對不同的持有期間，進行雜訊交易對投資組合影響的實證。實證研究結果支持假說2，而假說1與假說3則獲得部分的支持。
Based on the noise trading theory proposed by Black (1986) and DeLong et. al. (1990), this study first defines the meanings of information and noise, and then use mathematical deductive method to integrate noise trading and portfolio theory (Markowitz, 1952),and then use random matrix theory which is developed by nuclear physics to get the empirical evidences that impact of portfolio theory with noise trading. The first research proposition of the study is verified that noises are not individual stock risk and therefore, they could not be diversified through investment portfolios. Due to noises, the portfolios correlation matrix might have spurious correlation phenomenon. The second research proposition is that spurious correlation does not have sustainability and therefore, noises could not exist consistently in the stock market. Based on mathematical development, the third proposition is verified that portfolio risk is higher when noises existed. Furthermore, the fourth proposition is verified that due to noises interference, the efficiency of investment portfolios is reduced.
Based on these propositions could be verify, proposition 2, proposition 3, and proposition 4 would be transformed to hypothesis 1, hypothesis 2, and hypothesis 3. “With the increase during the holding period, portfolio performance in information and in interference will gradually produce a significant difference” is hypothesis 1, which could be used to test whether noise is systematic risk or not. “The variance in information portfolio is smaller than in interference portfolio” is hypothesis 2, which is used to test whether risk of the portfolio could be rising by noises. Hypothesis 3 tells that, “the Sharpe ratio of information portfolio is higher than interference one”. Using hypothesis 3 could test possibility the efficiency of portfolio would be reduced by noises. There are 1242 samples of this study which uses 19 sector indices daily rate of returns in Taiwan stock market from the beginning in 2005 to the end in 2009. This Study uses method to filter random matrix which was developed by Bouchaud and Potters (2000), and investigates the empirical evidences of effect in portfolio with noise trading every holding periods which be used method of moving windows with 30 and 60 days’ formation periods. The result supports hypothesis 2, but hypothesis 1 and hypothesis 3 was gat partial support.
中文部分
1.李春安(1999)，後見之明心理與股市反應不足、過度反應理論，中國財務學刊，7期，1卷：頁17-58。
2.劉玉珍，何怡滿(1994)，公司特性與資訊結構－台灣股市之實證研究，國家科學委員會研究彙刊：人文及社會科學，4期，1卷：頁114-132。
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