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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Treynor-Black model ： ウィキペディア英語版 Treynor–Black model In Finance the Treynor–Black model is a mathematical model for security selection published by Fischer Black and Jack Treynor in 1973. The model assumes an investor who considers that most securities are priced efficiently, but who believes he has information that can be used to predict the abnormal performance (Alpha) of a few of them; the model finds the optimum portfolio to hold under such conditions. In essence the optimal portfolio consists of two parts: a passively invested index fund containing all securities in proportion to their market value and an 'active portfolio' containing the securities for which the investor has made a prediction about alpha. In the active portfolio the weight of each stock is proportional to the alpha value divided by the variance of the residual risk. == The Model == Assume that the risk free rate is ''RF'' and the expected market return is ''RM'' with standard deviation $\backslash sigma\_M$. There are ''N'' securities that have been analyzed and are thought to be mispriced, with expected returns given by: :$r\_i\; =\; R\_F\; +\backslash beta\_i(R\_M-R\_F)+\backslash alpha\_i+\backslash epsilon\_i$ where the random terms $\backslash epsilon\_i$ are normally distributed with mean 0, standard deviation $\backslash sigma\_i$, and are mutually uncorrelated. (This is the so-called Diagonal Model of Stock Returns, or Single-index model due to William F. Sharpe). Then〔Kane et al.〕 it was shown by Treynor and Black that the active portfolio ''A'' is constructed using the weights :$w\_i\; =\; \backslash frac$ (Note that if an alpha is negative the corresponding portfolio weight will also be negative, i.e. the active portfolio is in general a long-short portfolio). The overall risky portfolio for the investor consists of a fraction ''wA'' invested in the active portfolio and the remainder (i.e. $w\_M=1-w\_A$) invested in the market portfolio. This fraction is found as follows: :$w\_A\; =\; \backslash frac$ :$w\_0\; =\; \backslash frac$ where the alpha, beta and residual risk of ''A'' are found using the previously computed weights ''wi'' in the obvious way :$\backslash alpha\_A=\backslash sum\; w\_i\; \backslash alpha\_i$ :$\backslash beta\_A=\backslash sum\; w\_i\; \backslash beta\_i$ :$\backslash sigma\_A^2=\backslash sum\; w\_i^2\; \backslash sigma\_i^2$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Treynor–Black model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.