# Downside beta

In investing, downside beta is the element of beta that investors associate with risk. It is defined to be the scaled amount by which an asset moves compared to a benchmark, calculated only on days when the benchmark’s return is negative.[1]

## Formula

Downside beta measures downside risk. The CAPM can be modified to use semi-variance instead of standard deviation to measure risk.[2]

Where ${\displaystyle r_{i}}$ and ${\displaystyle r_{m}}$ are the excess returns to security ${\displaystyle i}$ and market ${\displaystyle m}$, and ${\displaystyle u_{m}}$ is the average market excess return, the CAPM can be modified to incorporate downside (or upside) beta as follows,[3]

${\displaystyle \beta ^{-}={\frac {cov(r_{i},r_{m}|r_{m}

Therefore, ${\displaystyle \beta ^{-}}$ and ${\displaystyle \beta ^{+}}$ can be estimated with a regression of excess return of security ${\displaystyle i}$ 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).[1] 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.

## Downside Beta vs. Beta

Downside beta is an effective measure of the risk-return relationship in both developed and growing markets. When companies are grouped according to their two-digit SIC codes, average downside beta is different from standard beta even at the industry average level. Downside market risk can also explain the systematic relative differences in value stocks versus growth stocks, which the CAPM has failed to do, especially in international markets.[4]

Downside beta has greater explanatory power than standard beta in bearish markets.[1][5] Portfolios that are constructed by minimizing downside beta may be able to maintain more of their value during times of market decline.