We analyse the empirical relationships between firm fundamentals and the dependence structure between individual REIT and stock market returns. In contrast to previous studies, we distinguish between the average systematic risk of REITs and their asymmetric risk in the sense of a disproportionate likelihood of joint negative return clusters between REITs and the stock market. We find that REITs with low systematic risk are typically small, with low short-term momentum, low turnover, high growth opportunities and strong long-term momentum. Holding systematic risk constant, the main driving forces of asymmetric risk are leverage and, to some extent, short-term momentum. Specifically, we find that leverage has an asymmetric effect on REIT return dependence that outweighs the extent to which it increases the average sensitivity of REIT equity to market fluctuations, explaining the strong negative impact of leverage on firm performance especially during crisis periods that has been documented in recent empirical work.