An examination of conditional effect on cross-sectional returns: Singapore evidence

This article empirically examines the usefulness of beta, firm size, book-to-market equity ratio (B/M) and earnings-to-price ratio (E/P), as risk proxies in explaining the cross-sectional returns in the Singapore stock market under both unconditional and conditional frameworks based on up and down markets. Consistent with previous studies, though beta plays no role under unconditional framework, there is evidence of a significantly positive (negative) risk premium on beta during periods of up (down) markets, supporting for the continuous use of beta as a risk measure. Interestingly, our results show that firm size is the only significant variable in explaining average returns under the unconditional framework but its impact becomes much less under the up and down market conditions. However, significant conditional effect of E/P is found. Although, B/M alone is not significantly conditionally related to returns, in various combinations with beta, it becomes significant and the joint role of beta and B/M, due to an interaction effect between them, has an 'amplified' gain in the explanatory power. Our study suggests that beta does not suffice to explain the cross-sectional variations of returns, but it is possible that the joint effect of beta and B/M may be a surrogate as an underlying and more fundamental factor that is missing in the conditional SLB model. We also find evidence that investors in the Singapore stock market react virtually the same to these firm-specific factors and to beta during up and down markets. Our results are robust for both beta-size and size-beta sorting procedures and for both value- and equally weighted market proxies.