Finance theory suggests that there should be a positive relationship between risk and the risk premium. Investors demand compensation for holding risky assets, and how much compensation they demand is related to both the degree of risk aversion and the amount of risk. Extensive empirical evidence in the past several decades also suggests that risk premium varies over time with strong association with business cycle, which implies that the relation between risk and the risk premium is also likely to vary over time. Motivated by these theory and empirical evidence, we examine time-varying risk-return relationship by estimating the relative risk aversion coefficient using consumption-based measures as state variables, aiming to capture the conditional relation between risk and the risk premium. A number of consumption-based measures have been proposed as forecasting variables for asset returns such as the surplus consumption ratio (Campbell and Cochrane, 1999; Wachter 2006), the labor income to consumption ratio (Santos and Veronesi, 2006), and the consumption-aggregate wealth ratio (Lettau and Ludvgison, 2001). Campbell and Cochrane (1999) introduce habit persistence to their asset pricing model and use the surplus consumption ratio as a proxy for time-varying relative risk aversion and Wachter (2006) uses a proxy for the surplus consumption ratio to extend the model to the bond market. The model of Santos and Veronesi (2003) implies that the ratio of labor income to consumption is inversely related to the conditional covariance between asset return and consumption. Therefore, the ratio is also inversely related to the risk premium. Lettau and Ludvigson (2001, 2005) introduce CAY, which measures deviation of consumption from its stable relationship with wealth. As consumers' trading of financial assets is motivated by a desire to smooth consumption both over time and across states, CAY has the predictive power for the risk premium. Park, Eom, and Hahn (2019) constructs three consumption-based measures using Korean data and shows that these measures have predictive ability for the equity, bond, and housing risk premia in Korea. Their findings suggest that the consumption-based measures capture the information relevant for time-varying risk premium in Korea and can be used as state variables for empirical analysis. We estimate the relative risk aversion coefficient in the framework of Merton (1973)'s ICAPM by using three consumption-based measures as state-variables for the risk aversion. In constructing four proxies for the surplus consumption ratio, we use two estimation procedures based on Campbell and Cochrane (1999) and Wachter (2006) with two persistency parameter estimates. We follow Park, Eom, and Hahn (2019) to calculate the labor income to consumption ratio and CAY. We use both monthly and quarterly excess return data from April 1988 to March 2016. Two conditional variance models (GARCH(1,1)-M and EGARCH(1,1)-M) are estimated by the overlapping data inference (ODIN) method suggested by Hedegaard and Hodrick (2016). We also include five control variables which are the relative risk free rate, term premium, default premium, business cycle indicator, and industrial production. The main findings are as follows. First, when we use the proxy for the surplus consumption ratio as a state variable, we find a positive relationship between risk and the risk premium. The surplus consumption ratio has the statistically significant explanatory power of the relative risk aversion coefficient. Second, the main results are consistent across various cases of using monthly and quarterly excess return data, using GARCH(1,1)-M and EGARCH(1,1)-M models, and including control variables which are related to business cycle. Third, the explanatory power of the surplus consumption ratio is robust to using four alternative proxies used in this study. Finally, when we use the labor income to consumption ratio by Santos and Veronesi (2003) as a state variable, we also obtain some significantly positive time-varying risk-return relationship. However, we fail to obtain significant results when we use the consumption-aggregate wealth ratio by Lettau and Ludvigson (2001, 2005) as a state variable. Taken together, our empirical findings suggest that the relationship between risk and the risk premium should be investigated in a conditional setting, one of which is the model of Campbell and Cochrane (1999) with time-varying risk aversion.