In this paper, we introduce a general downside risk measure based on high frequency downward moves below minimum acceptable target in asset prices. Our contribution to the existing literatures is threefold. Firstly, we construct a general downside risk measure, realized semivariance and downward absolute power variation are all special cases of our realized downside risk measure. Secondly, we derive the central limit theorem of this measure. Thirdly, we investigate the distributional properties of this measure in China’s stock market and show the potential of this measure in modeling downside risk.