High-Voltage Direct Current (HVDC) merchant transmission lines allows trade across separate power markets and often in different countries. The flows on existing cross-border lines are often assessed as suboptimal, which may be due to the light regulation that often prevails in this case. We study the impact of Physical Transmission Rights (PTRs) allocation on the management of an HVDC interconnection between a thermal and a hydroelectricity market, assuming dynamic water management. We use a two-stage game formulated as an Equilibrium Problem with Equilibrium Constraints (EPEC) to model the strategic trade between the New York (US) and Quebec (Canada) systems. The numerical model is calibrated with public data.We find that although the interconnection can create wealth, a high concentration of PTRs can destroy value because of dumping strategies. The impact of trade on local price levels may be of concern and calls for the functional unbundling of traders and generators.