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.

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.

Denoting ${\displaystyle r_{i}}$ and ${\displaystyle r_{m}}$ as the excess returns to security ${\displaystyle i}$ and the 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 downside (or upside) beta as follows. Downside beta is

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