This study constructs growth optimal portfolios based on South Korean KOSPI200 sector indices and empirically analyzes their performances compared with the market index during the period July 2010 to March 2019. Sector weights for the growth optimal portfolios are estimated using the geometric mean maximization formula suggested by Markowitz. Main results of our empirical analysis are as follows. Firstly we find that the periods of 9 months for sector weights’ estimation and 2 months for holding with those estimated weights are selected as optimal for the growth optimal portfolios which provide the highest return in excess of KOSI200 index. Secondly, we show that the excess returns of these growth optimal portfolios are significantly positive even after controlling for the Fama-French three factors and the market momentum effects through the in- and out-of-sample tests. Thirdly, we find that the excess return on the growth optimal portfolio increases as the ratio of short selling increases but decreases above a certain level of leverage ratio. This result supports that the Security Market Line does not increase linearly but tends downward after a certain level of leverage ratio.