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Alpha (finance) : ウィキペディア英語版
Alpha (finance)

Alpha is a measure of the so-called active return on an investment, the performance of that investment compared to a suitable market index. An alpha of 1 means the investment's return on investment over a selected period of time was 1% better than the market during that same period, an alpha of -1 means the investment underperformed the market. Alpha is one of the five key measures in modern portfolio theory.
In modern financial markets, where index funds are widely available for purchase, alpha is commonly used to judge the performance of mutual funds and similar investments. As these funds include various fees normally expressed in percent terms, the fund has to maintain an alpha greater than its fees in order to provide positive gains compared to an index fund. Historically, the vast majority of traditional funds have had negative alphas, which has led to a flight of capital to index funds and non-traditional hedge funds.
It is also possible to analyze a portfolio of investments and calculate a theoretical performance, most commonly using the capital asset pricing model (CAPM). Returns on that portfolio can be compared to the theoretical returns, in which case the measure is known as Jensen's alpha. This is useful for non-traditional or highly focused funds, where a single stock index might not be representative of the investment's holdings.
==Definition==
The alpha coefficient (\alpha_i) is a parameter in the capital asset pricing model (CAPM). It is the intercept of the security characteristic line (SCL), that is, the coefficient of the constant in a market model regression.
:\mathrm : R_ - R_ = \alpha_i + \beta_i\, ( R_ - R_ ) + \epsilon_ \frac{}{}
It can be shown that in an efficient market, the expected value of the alpha coefficient is zero. Therefore the alpha coefficient indicates how an investment has performed after accounting for the risk it involved:
*\alpha_i < 0 : the investment has earned too little for its risk (or, was too risky for the return)
*\alpha_i = 0 : the investment has earned a return adequate for the risk taken
*\alpha_i > 0 : the investment has a return in excess of the reward for the assumed risk
For instance, although a return of 20% may appear good, the investment can still have a negative alpha if it's involved in an excessively risky position.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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