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downside beta : ウィキペディア英語版
downside beta
In investing, downside beta is the element of beta that investors associate with risk in the sense of the uncertain potential for loss. It is defined to be the scaled amount by which an asset tends to move compared to a benchmark, calculated only on days when the benchmark’s return is negative.
==Formula==
Downside beta measures downside risk. The Capital asset pricing model (CAPM) can be modified to use semi-variance instead of standard deviation to measure risk.
Where r_i and r_m are the excess returns to security i and market m, and u_m is the average market excess return, and Cov and Var are the covariance and variance operators, the CAPM can be modified to incorporate downside (or upside) beta as follows.
:\beta^-=\frac
Therefore, \beta^- and \beta^+ can be estimated with a regression of excess return of security i on excess return of the market, conditional on excess market return being below the mean for downside beta (or above the mean for upside beta).〔 Downside beta is calculated from data points of the asset or portfolio return using only those days when the benchmark return is negative. Downside beta and upside beta are also differentiated in the dual-beta model.

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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