Upside beta


In investing, upside beta is the element of traditional beta that investors do not typically associate with the true meaning of risk. 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 positive.

Formula

Upside beta measures this upside risk. Defining and as the excess returns to security and market, as the average market excess return, and Cov and Var as the covariance and variance operators, the CAPM can be modified to incorporate upside beta as follows.
with downside beta defined with the inequality directions reversed. Therefore, and can be estimated with a regression of excess return of security on excess return of the market, conditional on excess market return being below the mean and above the mean." 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.