The intertemporal relation between risk and return has long been an important topic in asset pricing literature. Most asset pricing models postulate a positive relationship between a stock portfolio's expected returns and risk, which is often modeled by the variance or standard deviation of the portfolio's returns, claiming that idiosyncratic risk has no significant effect on returns. However, no agreement has been met about the existence of such a trade-off for stock market indices. While return volatility is an intuitively appealing measure of risk, the difference approaches used by previous researchers suggest that no clear consensus has emerged regarding its relevance. Yet, whether investors require a larger risk premium on average for investing in a security during times when the security is more risky remains an open question. This paper, therefore, makes a contribution by exploring the relationship between return and risk as proxied by firm-volatility, comprised of both systematic and idiosyncratic volatility. As for the predictability of stock market returns, Goyal and Santa- Clara(2003) propose a new approach to test the presence and significance of a time-series relationship between risk and return for the aggregate stock market. They find a positive relation between the equal-weighted average stock volatility and the value-weighted portfolio returns. They also show that the lagged volatility of market returns has no predictive power for the expected return on the market. Bali, et al.(2005), on the other hand, find that Goyal and Santa-Clara's empirical results based on the equal-weighted average stock risk are not robust across different stock portfolios and sample periods. That is, their conclusions do not hold when either the more natural value-weighted measure of average stock risk or the more robust median stock volatility is used in predictive regressions. Ang, Hodrick, Xing and Zhang(2006) further suggest that volatility of market return is a priced cross-sectional risk factor based on their observation that US stocks with high lagged idiosyncratic volatility earn very low future average returns, and these assets are indeed mispriced when applying the Fama-French model. Their results of the negative relationship between idiosyncratic volatility and expected returns are surprising for two reasons. First, the difference in average returns across stocks with low and high idiosyncratic volatility is rather large. Second, their findings cannot be explained by either exposure to aggregate volatility risk or other existing asset pricing models. On the other hand, in order to capture the time-varying property of idiosyncratic risk, Fu(2009) uses the exponentially generalized autoregressive conditional heteroskedasticity (EGARCH) models and out-of-sample data to estimate expected idiosyncratic volatilities, and find that idiosyncratic risk is positively related to expected returns. Views on the relationship remain divergent: asset pricing theory implies that expected returns should be positively related to model-implied systematic volatility; various theoretical studies suggest that idiosyncratic volatility should be positively related to expected returns; and several empirical studies suggest that idiosyncratic volatility has explanatory power for the cross-section of expected returns. As such, this paper examines the explanatory power of idiosyncratic volatility estimated by three asset pricing models(CAPM, Fama-French 3 factor model, and Alternative 3 factor model suggested in Yun, et al.(2009)), and total volatility, a model-free quantity, for the cross-section of stock returns. Total volatility is the sum of systematic volatility relative to some asset pricing model and idiosyncratic volatility relative to the same model. As a result, no significant link between expected returns and idiosyncratic volatility in Korea stock market (KOSPI) data is traced while some cross-sectional evidence for a negative relationship between total volatility and expected return is detected. In addition, the portfolios of lower volatility stocks achieved a higher expected return than those of higher volatility stocks. We could ascertain that the effect is driven mainly by systematic volatility by applying AHXZ(2006)'s method. We also investigate the implications of the findings above for asset pricing and construct a total volatility factor via the factor mimicking portfolio for total volatility. Following the Fama and French(1992, 1993) model, we construct the factor mimicking portfolio as the zero cost portfolio which is long for the quintile of stock with lowest total volatility and short for the quintile with highest total volatility. We estimate the factor price of total volatility risk using the Fama and MacBeth(1973) procedure for individual stocks in our data. During the research period, the factor price of total volatility risk is positive and significant, indicating that the variation in systematic risk has notable implications for asset pricing. We also conclude based on the multi-factor models of risk that aggregate volatility should be a cross-sectional risk factor. Our finding is that the total volatility has a negative cross-sectional relationship with expected returns of individual stocks. Moreover, when we decompose the total volatility factor into systematic and idiosyncratic components, we find that the factor price of total risk is positive while that for idiosyncratic is insignificant. This negative relationship corroborates the results from the past research in option pricing that has shown a negative price of risk for systematic volatility, by reassuring that stocks with high past exposure to innovations in aggregate market volatility earn low future average returns.