The relative contribution of conditional mean and volatility in bivariate returns to international stock market indices

Abstract

We compare the relative contribution of conditional mean and conditional volatility terms in vector autoregression–exponential generalized autoregression conditional heteroskedasticity models of bivariate returns to international stock indices. Conditional mean terms are relatively unimportant for bivariate returns to country pairs that trade synchronously such as Australia/Japan, where they account for only 8% of the increase in log-likelihood over an unconditional model, on average. They are more important in nonsynchronous domestic/world-ex-domestic series such as Japan/world-ex-Japan, where they account for 24% of the increase in log-likelihood over an unconditional model, on average. Despite their increased prominence in the domestic/world-ex-domestic series, conditional mean terms detract from residual behaviours in these series. They also detract from some out-of-sample return and volatility predictions in both synchronous and nonsynchronous series.

Notes

¹ Long-horizon (weekly or longer) return predictability has been found using publicly available information variables including lagged returns (Fama and French, 1988a), short-term T-bill rates (Fama and Schwert, 1977), dividend (Fama and French, 1988b) and earnings yields (Campbell and Schiller, 1988; Ang and Bekaert, 2007), term (Campbell, 1987) and default premiums (Fama and French, 1989), aggregate consumption-wealth ratios (Lettau and Ludvigson, 2001), liquidity (Avramov et al., 2006) and aggregate and idiosyncratic volatilities (Ang et al., 2006; Guo and Savickas, 2006). These findings are controversial for several reasons. First, the predictive relation varies across samples and is unstable over time (Goyal and Welch, 2003). This in turn raises concerns about the out-of-sample performance of these predictors, with significant predictive performance being claimed by some authors (Sullivan et al., 1999; Guo, 2006) and refuted by others (Bossaerts and Hillion, 1999; Cooper et al., 2005; Goyal and Welch, 2008). Return predictability is confounded by persistence in the return predictors, which implies persistence in expected returns as well (Paye and Timmermann, 2006; Boudoukh et al., 2008). In contrast to long-horizon return predictions, short-horizon (i.e. daily) volatility predictions typically rely on the historical time series.