Both companies are owned by Abu Dhabi, the oil-rich capital of the seven-state Emirates federation, which includes the Gulf commercial hub of Dubai.
The Bloomberg GCC 200 Index, a gauge of the biggest and most liquid stocks in the region, dropped 1.3 percent, the most in a month.
Its more than 700km of shoreline on the Arabian Gulf, in addition to its strategic location on the frontiers of Bahrain, Qatar, UAE, Oman, Kuwait, Iraq and Iran.
Hivelin revived Balmain, which was near bankruptcy in 2004, by hiring gifted designers and turning it into one of France's biggest success stories.
Instead, investors said they planned to use their new property as a “second residence", many of which are unlikely to be lived in at all.
The island is the largest in the Persian Gulf, and has a population of 117,774, mainly occupied in fishing, salt mining and tourism.