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標題: | 一般化之Treynor比率 Beyond the Treynor ratio |
作者: | Ya-Yen Wu 吳雅岩 |
指導教授: | 曾郁仁 |
關鍵字: | 風險指標,績效指標,崔諾比率,資本資產定價模型,隨機優越,偏態,峰態, Risk Index,Performannce mearurment,Treynor ratio,Capital Asset Pricing Model,Riskiness,skewness,kurtosis, |
出版年 : | 2017 |
學位: | 碩士 |
摘要: | 本研究提出了一般化崔諾比率(Riskiness based Treynor ratio),此績效指標以Riskiness CAPM beta來衡量系統性風險,滿足單調性和隨機優越性等良好性質,且除了平均數和變異數,更考量了報酬率分配的偏態和峰態對於績效衡量的影響。
一般化崔諾指標衡量投資人承擔一單位系統性風險所得之超額報酬,相較於傳統的Treynor ratio,該指標係以Mean-Riskiness架構下估計所得之Riskiness CAPM beta,即投資組合報酬率與市場投資組合報酬率之非線性函數的共變數,和市場投資組合報酬率與市場投資組合報酬率之非線性函數的共變數之比值,取代傳統Mean-Variance架構下的CAPM beta來衡量系統性風險。 本研究以Fama and French 25個由不同公司規模與淨值市價比所形成之投資組合的月報酬率進行實證研究,比較各績效指標的排序結果。實證結果顯示,傳統CAPM傾向因低估了系統性風險,而高估了正的異常超額報酬和負的異常超額報酬,即傳統CAPM beta傾向被低估而傳統Treynor ratio傾向被高估,此現象與Chen et al.(2017)的實證結果一致。同時也發現,當投資組合超額報酬率分配接近常態分配時,若以Aumann and Serrano (2008)的定義估計Riskiness,則Risiness based Treynor ratio 與Treynor ratio排序相近但不全然相同。一般化崔諾比率為在經濟意涵及數學上更為嚴謹的績效指標,使得當資料樣態偏離古典假設時,仍能夠較正確地衡量投資組合的績效。 This paper proposed a Riskiness based Treynor ratio, which generalized Treynor ratio under Mean-Riskiness instead of Mean-Variance framework. This performance measure satisfies monotonicity with respect to second degree of stochastic dominance, moreover, it considers not only mean and variance but also skewness and kurtosis of the excess return distribution. Compare to Treynor ratio, Riskiness based Treynor ratio estimate Riskiness-CAPM beta instead of traditional CAPM beta to capture systematic risk under Mean-Riskiness reward-risk framework. To explain more, Riskiness-CAPM beta depends on the covariance of portfolio return and a non-linear function constructed by market portfolio return and market portfolio’s Riskiness index. Treynor ratio is a commonly used performance index which measures how much excess return a portfolio can earn by taking one unit of systematic risk. In this paper, consistent to findings in Chen et al. (2017), we found that traditional CAPM beta tends to underestimate systematic risk and overestimate abnormal excess return of the portfolio; it also implies that traditional Treynor ratio could be overestimated. Furthermore, when we establish Riskiness Treynor ratio based on Aumann and Serrano (2008), Riskiness Treynor ratio performance ranking is close to traditional Treynor ratio if the excess return distribution of portfolios is normally distributed. Using 25 Fama & French Size and Book to Market ratio portfolios, we suggest Riskiness Treynor ratio is a more rigorous performance indicator in terms of economic and mathematic and it can still measure the performance of portfolio accurately when the distribution of excess return is not normally distributed. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/59755 |
DOI: | 10.6342/NTU201700510 |
全文授權: | 有償授權 |
顯示於系所單位: | 財務金融學系 |
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