“Downside beta”的意思、由来-开放百科全书

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.^[1]

Formula

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.^[2]

Denoting

and

as the excess returns to security

and the market

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.^[3] Downside beta is

while upside beta is given by this expression with the direction of the inequalities reversed. Therefore,

and

can be estimated with a regression of excess return of security

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 has greater explanatory power than standard beta in bearish markets.^[1]^[4] Portfolios that are constructed by minimizing downside beta may be able to maintain more of their value during times of market decline.

References

1. ^¹²{{cite journal|last1=Kaplanski|first1=Guy|title=Traditional beta, downside risk beta and market risk premiums|journal=The Quarterly Review of Economics and Finance|volume=44|issue=5|pages=636–653|doi=10.1016/j.qref.2004.05.008}}
2. ^{{cite journal|last=Hogan|first=W.W.|author2=Warren, J.M.|title=Toward the development of an equilibrium capital-market model based on semi-variance|journal=Journal of Financial and Quantitative Analysis|year=1977|volume=9|issue=1|pages=1–11|doi=10.2307/2329964}}
3. ^{{cite journal|last=Bawa|first=V.|author2=Lindenberg, E.|title=Capital market equilibrium in a mean-lower partial moment framework|journal=Journal of Financial Economics|year=1977|volume=5|pages=189–200|doi=10.1016/0304-405x(77)90017-4}}
4. ^{{cite journal|last=Estrada|title=Mean-semivariance behavior: Downside risk and capital asset pricing|journal=International Review of Economics and Finance|year=2007|volume=16|page=169|doi=10.1016/j.iref.2005.03.003}} Estrada computed standard betas and downside betas for stocks across 23 developed markets and 27 emerging markets. This research showed that downside beta did a better job of explaining variations of cross-section returns in both types of market than did standard beta. In emerging markets, downside beta explained 55% of variations in mean returns.

Formula

Downside beta vs. beta

References

External links