A Note on a New Weighted Idiosyncratic Risk Measure

Abstract

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.

New Risk Measure and Idiosyncratic Risk in Taiwan Stock Market

“…We follow the approach of Daniel and Titman (1998), and use the risk measure developed by Jan and Wang (2012). We find that beta can't explain the expected return in the Taiwan stock market, and that idiosyncratic risk has a positive relation to expected returns for stocks with smaller beta.…”

“…The idiosyncratic risk measure comes from the work of Jan and Wang (2012). Jan and Wang use of the property of martingale to predict return of next period.…”

“…Jan and Wang (2012) have demonstrated why including martingale variance in superior to the ordinary variance.…”

“…To obtain a single objective risk measure, we need an objective risk benchmark. In this study, we apply a new risk measure developed by Jan and Wang (2012) to avoid a benchmark return to compute the investment risk. The new measurement is based on the property of martingale.…”