Upside beta

Upside beta measures this upside risk. Defining r_i and r_m as the excess returns to security i and market m, u_m as the average market excess return, and Cov and Var as the covariance and variance operators, the CAPM can be modified to incorporate upside (or downside) beta as follows. :\beta^+=\frac{\operatorname{Cov}(r_i,r_m \mid r_m>u_m)}{\operatorname{Var}(r_m \mid r_m>u_m)}, with downside beta \beta^- defined with the inequality directions reversed. 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 (downside beta) and above the mean (upside beta)." Upside beta is calculated using asset returns only on those days when the benchmark returns are positive. Upside beta and downside beta are also differentiated in the dual-beta model. ==See also==