Downside beta

In investing, downside beta is the beta that measures a stock's association with the overall stock market (risk) only on days when the market’s return is negative. Downside beta was first proposed by Roy 1952^[1] and then popularized in an investment book by Markowitz (1959).

Formula[edit]

It is common to measure ${\displaystyle r_{i}}$ 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, Downside beta is

${\displaystyle \beta ^{-}={\frac {\operatorname {Cov} (r_{i},r_{m}\mid r_{m}<u_{m})}{\operatorname {Var} (r_{m}\mid r_{m}<u_{m})}},}$

while upside beta is given by this expression with the direction of the inequalities reversed. Therefore, ${\displaystyle \beta ^{-}}$ can be estimated with a regression of the excess return of security ${\displaystyle i}$ on the excess return of the market, conditional on (excess) market return being negative.

Downside beta vs. beta[edit]

Downside beta was once hypothesized to have greater explanatory power than standard beta in bearish markets.^[2][3] As such, it would have been a better measure of risk than ordinary beta.

Use in Equilibrium Models of Risk-Reward[edit]

The Capital asset pricing model (CAPM) can be modified to work with dual betas.^[4] Other researchers have attempted to use semi-variance instead of standard deviation to measure risk.^[5]

References[edit]

External links[edit]

• An Investigation of Beta and Downside Beta Based CAPM - Case Study of Karachi Stock Exchange, SSRN. M. Tahir, Q. Abbas, S.M. Sargana, U. Ayub and S.K. Saeed; February 2013
• Estrada (2007). "Mean-semivariance behavior: Downside risk and capital asset pricing". International Review of Economics and Finance. 16 (2): 169. doi:10.1016/j.iref.2005.03.003.