Smaller portfolio returns and the risk-return trade-off for the whole market

Abstract

Empirical evidence on the risk-return trade-off in stocks has been conflicting. Several studies estimate a positive risk-return trade-off (see French et al., 1987; Campbell and Hentschel, 1992) but other researchers find the opposite (see Nelson, 1991; Glosten et al., 1993) and most of the results have been statistically insignificant regardless of the sign of the risk-return trade-off. Using bivariate GARCH-M models, we investigate (1) the risk-return trade-off for the market portfolio and (2) the relation between the expected return of individual portfolios and time-varying covariance with the market portfolio. Our bivariate models using individual portfolios yield results with positive, significant estimated risk-return trade-offs for the market portfolio and strong evidence of a positive relation between expected return and the time-varying covariance for individual portfolios. We also construct a robust estimate for the risk-return trade-off across model specifications using Bayesian model averaging and the resultant risk-return trade-off is estimated to be positive with high posterior probability.

Keywords:

• asset pricing
• Bayesian econometrics
• bivariate GARCH-M
• risk-return trade-off

JEL Classification:

• C11
• C22
• G12

Notes

¹ The results of , and from MLE are mostly statistically insignificant.