Τhis paper examined the relation between stock returns and volatility of these stock returns as far as individual firms are concerned. It examined this relation for firms in both a mature and an emerging financial market, Japan and Korea respectively. The model that used, in order to come to some conclusions, was Duffee’s proposed method (1995). It confirmed his results as for the strong positive contemporaneous relation between firm stock returns and stock return volatility, but it also drew interesting conclusions about firm stocks listed on different indices of market capitalization.