In this paper, we estimate generalized autoregressive conditional heteroskedasticity (GARCH) and vector autoregressive (VAR) models to examine whether investor sentiment impacts the returns and volatility of various U.S. Dow Jones Islamic equity indices. The results from GARCH estimations show that changes in investor sentiment are positively correlated with the returns of the Shari'ah-compliant market portfolio. In addition, we find similar results for the three Shari'ah-compliant firm-size portfolios (i.e., large-, medium-, and small-cap). However, this relationship is stronger for harder to arbitrage Shari'ah-compliant stocks; that is, investor sentiment has a greater influence on small-cap equities. Additionally, estimations from the vector autoregressive model confirm the aforementioned results. In terms of volatility, GARCH estimations suggest that bullish shifts in investor sentiment in the current period are accompanied by lower conditional volatility in the ensuing period. In general, our findings suggest that as noise traders create more risk the market seems to reward them with higher expected returns.

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