In investing, downside beta is the
beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...
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 environme ...
) 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
and
as the excess returns to security
and the market
,
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. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the les ...
and
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
operators, Downside beta is
:
while
upside beta In Investment#In finance, investing, upside beta is the element of traditional Beta (finance), beta that investors do not typically associate with the true meaning of Financial risk, risk. It is defined to be the scaled amount by which an asset tend ...
is given by this expression with the direction of the inequalities reversed. Therefore,
can be estimated with a regression of the excess return of security
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
beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...
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 well-diversified portfolio.
The model takes into accou ...
(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 or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
to measure risk.
References
External links
An Investigation of Beta and Downside Beta Based CAPM - Case Study of Karachi Stock Exchange SSRN. M. Tahir, Q. Abbas, S.M. Sargana, U. Ayub and S.K. Saeed; February 2013
*
{{DEFAULTSORT:Downside beta
Financial risk modeling
Finance theories