Dual-beta
In investing, dual-beta is a concept that states that a regular, market beta can be divided into downside beta and upside beta. Thus, dual stands for two betas, upside and downside. The fundamental principle behind dual-beta is that upside and downside betas are not the same. This is in contrast to what the Capital Asset Pricing Model assumes, which is that upside and downside betas are identical. Moreover, Fama and French (1992) demonstrated that beta is an imperfect measure of investment risk.

Formula
The dual-beta model allows investors to differentiate downside risk – risk of loss – from upside risk, or gain. Regular beta fails to acknowledge, and thus to permit, this distinction. The dual-beta model does not assume that upside beta and downside betas are the same but actually calculates what the values are for the two betas, thus allowing investors to make better-informed investing decisions. “The dual-beta model can thus be expressed as:

,

where the dependent variable,  is “the asset return in excess of the riskless rate, the two intercepts are  and , for the ‘up-market’ and ‘down-market’ regime respectively, and  is the product of the ‘up-market beta’ and the up-market excess return, and similarly  is the product of the ‘down-market beta’ and the down-market excess return. , , , and  are the estimated parameters for up-market and down-market days, respectively;  on days the market index did not decline and   on days it did;  is a dummy variable, which takes the value of 1 when the market index daily return is non-negative and zero otherwise.” “The final term, , reflects the idiosyncratic information not proportional to either the up-market or down-market excess returns.”

Dual-beta vs. beta
Dual-beta can be a useful and  an effective extension to traditional beta, which “underestimates equity risk about half the time, compared with the dual-beta estimate…which can translate into large differences in present value computations.” The dual-beta model is particularly useful because CAPM beta “consistently lags the dual-betas, in terms of average daily returns and return-to-standard deviation ratio.”  While the dual-beta model has many benefits in terms of accuracy and usefulness, it might not be cost-effective for individual investors and is more suitable for financial planners due to transaction costs.