We report on experiments of simple, repeated asset markets in two risky securities and one risk-free security, set up to test the Capital Asset Pricing Model (CAPM), which embeds the two most essential principles of modern asset pricing theory, namely, (i) financial markets equilibrate, (ii) in equilibrium, risk premia are solely determined by covariance with aggregate risk. Slow, but steady convergence towards the CAPM is discovered. The convergence process, however, halts before reaching the actual equilibrium. There is ample evidence that subjects gradually move up in mean-variance space, in accordance with the CAPM. Yet, adjustment stops as if the remaining trading time was insufficient to complete all the transactions that are needed to guarantee improvements in positions. We conjecture that this is due to subjects' hesitance in the face of market thinness. Because the convergence process halts, statistical tests reject the CAPM.