# Upside beta

In investing, upside beta is the element of traditional beta that investors do not typically associate with the true meaning of risk.[1] 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 positive.

## Formula

The equation for upside beta, which measures this upside risk is below, “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.

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 (downside beta) and above the mean (upside beta)."[2] Upside beta is calculated using asset returns only on those days when the benchmark returns are positive.

Though rarely the case, an investor facing two hypothetical stocks with same downside betas would be better off selecting the stock with higher upside beta, since upside beta can be thought of as a representative of potential returns.