A Note on a New Weighted Idiosyncratic Risk Measure

This note remedies a risk measure, which was proposed by the work of Jan and Wang (2012). They used property of martingale to measure idiosyncratic risk, and illustrated that it is better than the measurements of variance and semivariance. However, their risk measure can¡¯t distinguish between the assets whose return rising firstly and then declining, and the assets whose return declining firstly and then rising. In this note, I propose a remedied method, which puts more weight to the recent return¡¯s variation, and demonstrate that the new weighting risk measure is more close to the investor risk conception.