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

The equation for upside beta, which measures this upside risk is below, “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.

\beta^+=\frac{cov(r_i,r_m |r_m>u_m)}{var(r_m |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)."[2] Upside beta is calculated using asset returns only on those days when the benchmark returns are positive.

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

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". p. 2. Retrieved 26 June 2013.
  2. ↑ 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