This paper classified the Korean stock market into 7 industrial groups, and assumed that investors make portfolio decision over these stocks and a risk-free bill. Various forms of the Mean-Variance Optimization model with a multivariate-ARCH, even with a time-varying relative risk aversion coefficient were applied to explain the Korean stock market movement. We found that investors hedge against inflation, which means they are more concerned with the real return, rather than the nominal. Regarding to the risk aversion coefficient, we were able to obtain an appropriate size of the estimates. They were very stable over the time, but decreasing over a year around the 1997 financial crisis. This result suggests a critical point in asset pricing model that more variety of investment instruments should be considered in investor's portfolio.