In investing, downside beta is the

beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...

that measures a stock's association with the overall stock market (

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environ ...

) only on days when the market’s return is negative. Downside beta was first proposed by Roy 1952 and then popularized in an investment book b
Markowitz (1959)

Formula

It is common to measure

r_i

and

r_m

as the excess returns to security

i

and the market

m

u_m

as the average market excess return, and Cov and Var as the

covariance In probability theory and statistics, covariance is a measure of the joint variability of two random variables. The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values of one ...

and

variance In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...

operators, Downside beta is :

\beta^-=\frac,

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

\beta^-

can be estimated with a regression of the excess return of security

i

on the excess return of the market, conditional on (excess) market return being negative.

Downside beta vs. beta

Downside beta was once hypothesized to have greater explanatory power than standard

in bearish markets. As such, it would have been a better measure of risk than ordinary beta.

Use in Equilibrium Models of Risk-Reward

The

Capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (f ...

(CAPM) can be modified to work with dual betas. Other researchers have attempted to use semi-variance instead of

standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...

to measure risk.

References

{{DEFAULTSORT:Downside beta Financial risk modeling Finance theories