As go the global bond markets, so may go German insurer Allianz. Or so some investors fear.

Since the US Federal Reserve signaled in May that it could soon start to scale back its bond-buying activities, shares in the German insurer-up 50% in the past year-have fallen as bond yields have risen and vice versa. A big reason: Allianz's ownership of Pimco, the famed US bond investor founded by Bill Gross.