Ilaria Resta has bad news. Rumours keep swirling that Audemars Piguet, of which she is chief executive officer, is set to open its first Australian boutique, a development that should make the possibility of securing one of its sought-after watches slightly more achievable. Resta sends her apologies. “We don’t have any concrete plans,” she concedes in her heavy Italian accent. “But our distribution network is extremely tight.”

I’m speaking with Resta in Le Brassus, a small village in Switzerland’s Vallée de Joux that’s home to AP’s headquarters, museum and manufacturing. Dressed head-to-toe in black, she’s sitting in a heated cubicle outside Hôtel des Horlogers, a 50-room boutique establishment designed by Danish starchitect Bjarke Ingels that represents AP’s first foray into luxury hospitality. Such extracurricular ventures are possible when Morgan Stanley proclaims you to be the world’s fourth-biggest watch brand with an annual turnover of 2.38 billion Swiss francs ($4.27 billion).