And because CAPM uses variance in its calculation of Beta, it too gives equal weight to both upside and downside movements.
Since at least the late 1950s the idea of semivariance has been tossed around and discussed occasionally (with some papers on it--see the introduction), but has never really been pushed very hard.
That may change. A new paper by Post, Van Vliet, and Lansdrop tests a downside beta (essentially how the returns move in down markets) and finds that the downside beta adds explanatory power to the model even when the other usual stuff (size, momentum, value) are included.
SSRN-Sorting Out Downside Beta by Thierry Post, Pim Van Vliet, Simon Lansdorp:
"Downside risk, when properly defined and estimated, helps to explain the cross-section of US stock returns. Sorting stocks by a proper estimate of downside market beta leads to a substantially larger cross-sectional spread in average returns than sorting on regular market beta. This result arises despite the fact that downside beta is based on fewer return observations and therefore is more difficult to estimate and predict. The explanatory power of downside risk remains after controlling for other stock characteristics, including firm-level size, value and momentum."How do they do this? Much like testing beta, they create portfolios based on the downside beta (thus hopefully accounting for any firm specific noise) and then test "out-of sample" using "data from 1926 to the present".
Post, Thierry, Van Vliet, Pim and Lansdorp, Simon D.,Sorting Out Downside Beta(March 2009). ERIM Report Series Reference No. ERS-2009-006-F&A. Available at SSRN: http://ssrn.com/abstract=1360708