Upside beta

Upside beta measures this upside risk. Defining $r\_i$ and $r\_m$ as the excess returns to security $i$ and market $m$, $u\_m$ as the average market excess return, and Cov and Var as the covariance and variance operators, the CAPM can be modified to incorporate upside (or downside) beta as follows.{{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|issue=2|pages=189–200|doi=10.1016/0304-405x(77)90017-4}}

:$\backslash beta^+=\backslash frac\{\backslash operatorname\{Cov\}(r\_i,r\_m\; \backslash mid\; r\_m>u\_m)\}\{\backslash operatorname\{Var\}(r\_m\; \backslash mid\; r\_m>u\_m)\},$

with downside beta $\backslash beta^-$ defined with the inequality directions reversed. Therefore, $\backslash beta^-$ and $\backslash beta^+$ can be estimated with a regression of excess return of security $i$ on excess return of the market, conditional on excess market return being below the mean (downside beta) and above the mean (upside beta)."{{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|issue=2|pages=189–200|doi=10.1016/0304-405x(77)90017-4}} Upside beta is calculated using asset returns only on those days when the benchmark returns are positive. Upside beta and downside beta are also differentiated in the dual-beta model.

• Cost of capital
• Downside risk
• Macro risk

{{Reflist}}

• [http://www.grin.com/en/e-book/146638/a-study-of-sharpe-s-asymmetric-beta-model A Study of Sharpe's asymmetric beta model]
• [http://store.elsevier.com/Rethinking-Valuation-and-Pricing-Models/isbn-9780124158757/ Rethinking Valuation and Pricing Models, 1st Edition]

Category:Financial risk modeling