Upside beta explained

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 tends to move compared to a benchmark, calculated only on days when the benchmark's return is positive.

Formula

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.^[2] \beta ^{+= (\operatorname{Cov)/((r)} _{i,r} _{m} \mid r _{m>u} _{m)}{\operatorname{Var}(r} _{m} \mid r _{m>u} _{m)},}

with downside beta

\beta ^{-} defined with the inequality directions reversed. Therefore, \beta ^{-} and \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)."^[3] 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.

See also

• Cost of capital
• Downside risk
• Macro risk

External links

• A Study of Sharpe's asymmetric beta model
• Rethinking Valuation and Pricing Models, 1st Edition

Notes and References

1. Web site: The Entrepreneur's Cost of Capital: Incorporating Downside Risk in the Buildup Method. 26 June 2013. James Chong . Yanbo Jin . G. Michael Phillips . 2. April 29, 2013.
2. Bawa. V.. Lindenberg, E.. Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics. 1977. 5. 2. 189–200. 10.1016/0304-405x(77)90017-4.
3. Bawa. V.. Lindenberg, E. . Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics. 1977. 5. 2. 189–200. 10.1016/0304-405x(77)90017-4.