Overnight returns of stock indexes: Evidence from ETFs and futures

During the period 1999–2014, overnight returns of US exchange-traded index funds and most international index futures are significantly positive, while returns during trading hours are negative. The overnight volatility is lower than the trading volatility. Estimating the value at risk and expected shortfall by incorporating the daytime and overnight returns into a joint distribution with a copula method, we find that the risk contribution of trading hours is substantially higher than that of nontrading hours. The results are not consistent with the usual risk-return tradeoff. For US ETF and futures markets, we also show that overnight returns can forecast both the in-sample and out-of-sample returns during the first half-hour (with a negative relation) and last half-hour (with a positive relation) of trading hours.