自從Sharpe於1964提出資本資產定價模式(Capital Assets Prining Model; CAPM),以系統風險為CAPM唯一對應期望報酬之風險變數,而Fama and MacBeth於1973將CAPM修正為三因子之模型,試圖去改善原始CAPM估計系統風險之效率。因此,本研究擬將採用灰色預測模型GM(1,1)結合Fama and MacBeth之模型,以台灣50指數成份股為研究對象,以茲改良傳統資本資產訂價實證模式之預測能力。 在beta值之估計方面,觀察能否透過灰色預測模型GM(1,1)之應用,建立更穩定且更精確之預測模式。實證結果發現,採用Theil’s U統計量作為預測精確度之衡量指標,將原始股價報酬率及原始市場報酬率所得之實際beta值進行白化流程,建立之預測模式 ,其在十個預測模式中最為精準,Theil’s U預測誤差值僅11.24%,誤差值比原始之ㄧ因子模式降低了13.53%,此外,在29個研究樣本中, 有23個樣本優於其他預測模式。在二因子部份,雖能提高解釋能力,但其預測值偏離實際值過遠,因此預測績效不如一因子模型。 另外,在穩定度方面,透過兩母體變異數之F檢定亦可發現, 其預測之變異程度最小,顯示 無論在信度及效度皆獲得有力之佐證,也代表著灰色預測模型確實可改良原始CAPM之預測能力。
The Capital Assets Pricing Model (CAPM) developed by Sharpe in 1964 denotes that the systematic risk is only the corresponding variable of the expect returns of the CAPM. Fama and MacBeth adjust CAPM and introduce three-factor model in 1973. Therefore, this research applies both Grey Forecasting Model GM(1,1) and three-factor model sampled from the Taiwan 50 index’ component stocks on improving the forecasting performance of the classical capital asset pricing model. Additionally, for the aspect of estimating the beta, we try to establish a more stable and correct forecasting model by applying the GM(1,1). Using the Theil’s U in the empirical research, the Theil’s U of the is only 11.24%. The declines 13.53% error than the original CAPM. Of 29 samples, 23 forecasting betas from have the smallest errors, which is the most precise one in 10 forecasting models. And though two-factor can raise R-square, the Theil’s U of two-factor model are two time large. So the performance of estimation on two-factor model is less than one-factor model. For aspect of stable, we use F test of two population variance analysis can find the variance of is the smallest one. Consequently, is the best forecasting model in 10 models acquired strong support from empirical result.
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