Previous experimental research has shown that thin financial markets fail to fully equilibrate, in contrast with thick markets. A specific type of market risk is conjectured to be the reason, namely, the risk of partial execution of desired portfolio rearrangements in a system of parallel, unconnected double auction markets. This market risk causes liquidity to dry up before equilibrium is reached. To verify the conjecture, we organized markets directly as a portfolio trading mechanism, allowing agents to better coordinate their orders across securities. The mechanism is an implementation of the combined-value trading (CVT) system. We present evidence that our portfolio trading mechanism facilitates equilibration to the same extent as thick markets do. Like in thick markets, the emergence of equilibrium pricing cannot be attributed to chance. Inspection of order submission and trade activity reveals that subjects manage to exploit the direct linkages between markets presented by the CVT system.