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위험프리미엄과 위험 간의 시간가변적 관계에 대한 검정

  • 엄영호 연세대학교 경영대학 교수
  • 한재훈 연세대학교 경영대학 교수
  • 박도준 연세대학교 경영대학 연구교수
본 연구의 목적은 우리나라 주식시장 투자자의 시간가변적인 위험회피계수를 소비관 련 거시변수를 사용하여 측정하고, 이러한 실증분석을 통해 위험프리미엄과 위험 간의 시간가변적인 관계(time-varying risk-return trade-off)를 검증하는데 있다. 구 체적으로 본 연구에서는 위험회피계수를 추정하기 위해 Campbell and Cochrane (1999), Santos and Veronesi(2006), Lettau and Ludvigson(2001, 2005) 등이 제시한 잉여소비비율, 소비 대비 소득비율 그리고 총자산 대비 소비비율을 위험회피계 수의 변화를 포착하는 상태변수로 사용하였다. 세가지 소비관련 거시변수는 이론적 근거와 함께 실증분석에서도 위험프리미엄에 대한 유의한 설명력을 가지고 있어 위험 회피계수의 상태변수로 사용하기에 적합하다. 분석결과에서 잉여소비비율의 시간가 변적 위험회피계수에 대한 설명력이 통계적으로 유의하였다. 실증분석의 결과는 분기 및 월 초과수익률 자료를 사용한 경우와 GARCH(1,1)-M과 EGARCH(1,1)-M 모형 을 사용한 경우 그리고 경기변동 관련 변수를 통제변수로 포함한 경우 모두에서 일관 성이 있었다. 소비 대비 소득비율의 설명력은 일부 실증분석에서 유의하였지만, 총자 산 대비 소비비율의 설명력은 유의하지 않았다. 이러한 분석 결과는 Campbell and Cochrane(1999)의 모형을 지지하는 결과로 해석할 수 있으며, 위험회피계수의 변화 로 위험프리미엄과 위험 간의 시간가변적 관계를 설명할 수 있음을 의미한다.
시간가변적 위험회피계수,잉여소비비율,소비 대비 소득비율,총자산 대비 소비비율

Estimating the Conditional Risk-Re turn Re lation Using Consumption-based State Variables : Evidence from the Korean Stock Market

  • Young Ho Eom
  • Jaehoon Hahn
  • Dojoon Park
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.
ICAPM,Time-varying relative risk aversion,ICAPM,Surplus Consumption Ratio,Income to Consumption Ratio,Consumption-Aggregate Wealth Ratio