資本資產定價模型之分量迴歸分析

資產價格的均衡結構(equilibrium structure)建立了所謂的資本資產評價模型(Capital Asset Pricing Model, CAPM)，在過去相關的文獻中，大多數是以線性型態作為探討風險與報酬率之依據，並且假設其風險與報酬率之間呈現顯著之正相關，然而，也有不少的實證指出，CAPM之高風險高報酬特性以及完美線性模型假設之正確性是有待加以檢測的。因此，本文特別提出在考量市場之實際情形可能不為高風險高報酬，以及假設模型為非線性之狀態下，做一實證分析與檢測，我們選取自1926年7月至2005年8月之月資料，嘗試以Fama and MacBeth (1973)的模型設定為本文研究之基礎，輔以分量迴歸之方法(Quantile Regression)探討投資組合市場風險與報酬率間之關係表現以及完美線性模型假設之是否正確，此外，亦可對於不同分量下模型之表現加以討論及分析，進而了解CAPM實際適用之可能性。由本實證研究之結果發現，於較低程度之條件分量水準下，與CAPM正斜率之假設及傳統最小平方法之結果，發生互為矛盾之情形，亦即系統風險與投資組資報酬率之間關係，非恆為正相關；此外，在不設定模型參數，以無母數方法估計之情形下，實證之結果，皆與CAPM之線性假設，產生矛盾之情形，亦即，使用分量迴歸方法之實證研究發現，CAPM之正斜率以及完美線性之兩假設，不一定恆為成立。

關鍵字

非線性；資本資產定價模型；分量迴歸

並列摘要

This paper proposes that if we consider the real circumstance of market which may not be the high risky high return and the assumed model is under the non-linear state, how we can do the analysis and measurement for the CAPM? We select the monthly data from July of 1926 to August of 2005, and try to use the model of Fama and MacBeth (1973) as the basis in this text. We also use the method of Quantile Regression to discuss the relationship between the market risk of investment portfolio and the rate of return, in addition, we can identify the assumption of the perfect linear model is whether or not correct. Furthermore, we also can analyze the behavior of the model under different quantiles, and then understand the possibility of practical applications in CAPM. From the result of this research, under the lower degree of the quantile level, the assumption of the positive slope of CAPM and the result of the traditional least square method are contradictive, that is, the relationship between systematic risk and the rate of portfolio returns are not be the positive correlation permanently. Moreover, under the situation of not set the parameter of model and use the nonparametric method to calculate and estimate, the result is also present a contradiction to the linear assumption of CAPM, that is, using the method of quantile regression to make a demonstration that the two assumptions of CAPM which are positive slop and perfect linear are not always correct.

並列關鍵字

Nonlinear ； CAPM ； Quantile Regression

參考文獻

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資本資產定價模型之分量迴歸分析

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