三因子Black資本資產聯立體系之檢定

The Joint Test of the Three-Factor Black CAPM Model

周金福(Chin-Fu Chou)

指導教授 ： 黃河泉

淡江大學/商學院/財務金融學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00387

摘要

資本資產定價理論CAPM模型，為投資學探討資產定價時的基礎理論。該理論是由Sharpe（1964）、 Lintner（1965），利用Markowitz （1952）提出之平均數-變異數投資組合模型（mean-variance portfolio model，MV），推演而成的資本資產定價模型（capital asset princing model，CAPM），Sharpe-Lintner CAPM主要在於描述於投資活動中之報酬率及風險關係。理論假設投資人為趨避者、市場投資人對投資報酬率的期望一致（homogeneous expectation）、而且資產的報酬率為常態分配（normal distribution）、資本市場存在著無風險利率（risk-free or riskless rate）、資本市場為完美市場（perfect market）。
但由於Sharpe-Lintner CAPM該理論假設條件與真實世界存在不符現象，因此，後續實證研究中，許多學者提出不同的見解。例如：Merton（1973）及 Ross （1976）提出多因子架構的理論模型，否認CAPM為單一風險因子解釋報酬。Black, Jenson and Scholes（1972）指出，投資人可創造與市場投資組合無相關而ß為零的投資組合（zero-beta portfolio），以取代CAPM中對無風險利率存在的假設。（以下簡稱Black CAPM）
而Fama and French則以Merton （1973）ICAPM及Ross （1976）APT為理論基礎及 Fama and MacBeth （1973）的CAPM實證迴歸模型，更明確指出影響資產報酬的因素主要有三項，分別是市場因素（market factor），規模因素（size factor）及淨值市價比因素（book-to-market factor），此即所謂Fama and French 三因子模型。因此，可看出就CAPM來說，仍存在許多爭議及可研究空間。
而本文研究範圍期望可結合 Black CAPM對無風險利率的假設及Fama and French 三因子模型，組成 Black三因子CAPM模型，研究方法採用最大概似法（maximum likelihood method ,MLE）及Hansen （1982）一般動差化（generalized method of moments , GMM）計量方法，並分別用概似比率檢定法LR及D統計量檢定作為模型檢定，研究樣本則採用美國股市所有股票三種不同分類方式之投資組合月報酬資料進行模型實證，三種投資組合分別為權益市值比（book to market）、益本比（earnings/price）、市場規模（size）等組成投資組合，研究期間則自1952年1月至2004年12月共636個月資料進行模型實證，期望實證Black三因子模型，在樣本資料範圍內是否存在。
實證結果發現，MLE及GMM計量方法，以風險係數來說，GMM在規模風險係數資料的顯著性來說，較MLE不顯著。而GMM及MLE在三個投資組合中，未受限制式模型的風險係數值完全相同，而就資料的顯著性來說，整體則以MLE計量方法資料較為顯著。
就檢定結果來說，MLE在常態分配假設之下，發覺結果在權益市值比及益本比，拒絕虛無假設。至於在市場規模，則無法拒絕虛無假設；而GMM計量方式在不要求強烈常態分配假設條件下，所得結果與MLE不同，GMM無法拒絕任何投資組合，與MLE在權益市值比及益本比拒絕虛無假設不同。且GMM在權益市值比、益本比及市場規模，皆無法拒絕虛無假設；就兩者計量方法來說，在市場規模，無論是採用MLE或是GMM皆無法拒絕虛無假設，樣本資料符合模型假設。

關鍵字

一般動差化估計 ； 資本資產定價理論 ； 三因子

並列摘要

CAPM model is the essential theory of the research on property price of the investment, capital asset pricing model, CAPM was deduced from mean-variance portfolio model, MV, offered by Markowitz (1952), Sharpe CAPM was main to describe in the relations to invest return rate and risk. the investor was risk-adverse of the hypothesis of theory, market investors were homogeneous expectation on invest return rate, and the return rate of property was normal distribution, risk-free or riskless rate existed in capital market, capital market was a perfect market.
Nevertheless, in virtue of the different conditions between hypothesis term and actual world by Sharpe CAPM, therefore, various opinions were brought up from numerous savants on the experiment evidence research, for instance :Merton (1973) and Ross (1976) offered multi factor structure theory model contradicted CAPM is singular risk factor explanation return. Black (1972) pointed out that zero-beta portfolio could created by the investors which was without related to market portfolio to instead of the hypothesis of risk-free or riskless rate of CAPM. Fama and French exercised by Merton (1973) ICAPM and Ross (1976) APT as the theory foundation and CAMP evidence model by Fama and MacBath (1973),it indicated to the three main factors of influence on property return definitely, market factor, size factor, and book to market factor, accordingly professed Fama and French three factors model, consequently, it can be seen as CAPM, there still existed various disputes and ambit to be researchable.
The range in the research of my thesis, which were expected to composed Black CAPM and Fama and French three factors model evidence from combining the hypothesis of risk-free rate with Black CAPM , Fama and French three factors model, adopted maximum likelihood method ,MLE and Hansen （1982）generalized method of moments, GMM, LR and D test statistic individually, monthly reward data of three kinds of investment combination in American stock market were progressed experiment evidence as the research samplings. The three kinds of investment combination were book to market portfolio, earnings/price portfolio, size portfolio. they were composed by different sorts of combinations, data were proceeded with experiment evidence model as a research duration which was during Jan 1952 ~ Dec 2004, totally 636 months, it was expected to evidence Black CAPM three factors model exist or not in the range of the sampling data.
The consequence of experiment evidence, MLE and GMM ,according to the risk factor，GMM was more unobvious than MLE for the data of the scope risk factor on the conspicuous character. in the three kinds of investment combination ,GMM and MLE were absolute identical with the unlimited model of the value of the risk factor, according to the conspicuous character to the data, the data of MLE was more obvious in the entirety.
As a result of the test of the normal distribution hypothesis of MLE, the consequence was discovered to reject to book to market portfolio and earnings/price portfolio. In the case of size portfolio, they were unable to reject；the result of GMM was different from MLE, when it was not to request to use intense normal distribution hypothesis term for GMM,GMM not rejected to any portfolio, it was different from MLE not rejected anyone portfolio. And GMM was unable to reject to book to market, earnings/price, size; according to the two sorts of estimate method, no matter use MLE or GMM, both of them were unable to reject to size, sampling data was equivalence to hypothesis mode.

並列關鍵字

CAPM ； Balck CAPM ； Fama and French ； FF three factor model

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