A Risk Return Relation in Stock Markets: Evidence from a New Semi-Parametric GARCH-in-Mean Model

Abstract

In this paper, I propose a new semi-parametric GARCH-in-Mean model. Since many empirical papers have the mix results on the risk-return relation, the cause of problem may come from the misspecification of conditional mean equation or conditional variance equation or both of them. My model uses non-parametric estimation in conditional mean equation and semi-parametric estimation in conditional variance equation which allows the non-linear risk return relation in conditional mean equation and allows the non-linear relation between the volatility and the cumulative sum of exponentially weighted past returns. Three parameters on my model are GARCH parameter, the leverage effect parameter and leptokurtic parameter. I also extend my model to include four exogenous variables, dividend yield, term spread, default spread and momentum into conditional mean equation by using additive model which allows each variable to have non-linear relation with the return. An empirical study on S&P 500 suggests that risk has a small affect on market return. However, when four exogenous variables are added to the model, my model shows that the risk-return relation has a positive hump shape.