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.

Upside beta measures this upside risk. Defining ${\displaystyle r_{i}}$ and ${\displaystyle r_{m}}$ as the excess returns to security ${\displaystyle i}$ and market ${\displaystyle m}$, ${\displaystyle u_{m}}$ 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.

...
Wikipedia