This paper proposes using a functional coefficient regression technique to estimate time-varying betas and alpha in the conditional capital asset pricing model (CAPM). Functional coefficient representation relaxes the strict assumptions regarding the structure of betas and alpha by combining the predictors into an index. Appropriate index variables are selected by applying the smoothly clipped absolute deviation penalty. In such a way, estimation and variable selection can be done simultaneously. Based on the empirical studies, the proposed model performs better than the alternatives in explaining asset returns and we find no strong evidence to reject the conditional CAPM.

Sousa (2010a) shows that the residuals from the common trend among consumption, financial wealth, housing wealth and human capital, cday, can predict quarterly stock market returns better than cay from Lettau and Ludvigson (2001), which considers aggregate wealth instead. In this paper, we use a more appropriate proxy of human capital, which alleviates the potential correlation between the residuals and the regressors and makes the estimation more precise. In addition, we extend housing wealth to household capital by taking durable goods into consideration. The new predictor is proposed accordingly. Empirically, we find that our predictor is superior to the other alternatives.