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 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. The Capital asset pricing model (CAPM) can be modified to use semi-variance instead of standard deviation to measure risk.^[2]

Where $r_{i}$ and $r_m$ are the excess returns to security $i$ and market $m$, and $u_{m}$ is the average market excess return, and Cov and Var are the covariance and variance operators, the CAPM can be modified to incorporate upside (or downside) beta as follows.^[3]

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

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)."^[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.

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

See also

• Cost of capital
• Downside risk
• Macro risk

References

1. James Chong, Ph.D.; Yanbo Jin, Ph.D.; G. Michael Phillips, Ph.D (April 29, 2013). "The Entrepreneur's Cost of Capital: Incorporating Downside Risk in the Buildup Method" (PDF). p. 2. Retrieved 26 June 2013. Cite uses deprecated parameter |coauthors= (help)
2. Hogan, W.W.; Warren, J.M. (1977). "Toward the development of an equilibrium capital-market model based on semi-variance". Journal of Financial and Quantitative Analysis. 9 (1): 1–11. doi:10.2307/2329964.
3. Bawa, V.; Lindenberg, E. (1977). "Capital market equilibrium in a mean-lower partial moment framework". Journal of Financial Economics. 5: 189–200. doi:10.1016/0304-405x(77)90017-4.
4. Bawa, V.; Lindenberg, E. (1977). "Capital market equilibrium in a mean-lower partial moment framework". Journal of Financial Economics. 5: 189–200. doi:10.1016/0304-405x(77)90017-4.

External links

• MacroRisk Analytics “Patented and proprietary macro risk measurements and tools for investors since 1999”.
• buyupside "free information for the serious investor".
• Raymond James "Independent Financial Advisors, Financial Planning, Investment Banking and Asset Management".
• A Study of Sharpe's asymmetric beta model
• Rethinking Valuation and Pricing Models, 1st Edition