Following Constantinides' (1986) seminal approach and introducing transaction costs in the Pagano (1989) model, conventional CARA investors with heterogeneous endowments trade to construct optimal portfolios. We calibrate to the 1896-1994 equity and bond markets to show that gains from trade are high and, thus, investors require a high illiquidity premium even for a modest transactional charge. Excluding risk premia, exchange of equity and bonds by N strategic investors, as , under a mere 1% round-trip transaction cost induces a 6% illiquidity (equity) premium. Unlike existing literature, our findings are consistent with most stylized empirical facts. We recover the elasticity of trading demand from the excess equity return to confirm a major implication of the model. Among many other, so called, anomalies, we appear to explain the apparent irrational exuberance of equity markets, the 600% price premium for otherwise identical A stock over B stock in China, the low risk-free rate, the 20% letter stock premium and the lower return on the run bonds. Because illiquidity premia do not necessarily imply consumption volatility, variance bounds tests become irrelevant.