The price of the SNB's 100,000 shares rose from below 2,000 Swiss francs (1,466 pounds) each a year ago to a peak of 9,760 francs this month and was trading at around 7,300 francs on Friday.

"Even though the SNB refrains, in principle, from commenting on its share price performance, I am fully aware that this current movement may raise questions," Jean Studer told shareholders at the SNB's annual general meeting.

"SNB shares are unlike other shares. They are subject to certain restrictions on shareholder rights imposed by law ... the special character of SNB shares means that they are less a conventional investment than a means for shareholders to express their solidarity with our institution," he added.

Some have said buyers are using the shares as a substitute for ultra low-yielding bonds, while others say investors may not understand the SNB's special status, and were buying shares because the central bank made a record profit in 2017.

But since the SNB's dividend is capped at 6 percent of its share capital, even last year's 54 billion franc profit meant it would pay out only 15 francs per share, a total of 1.5 million francs.

Around 40 percent of the shares are owned by Switzerland's cantons, while cantonal banks hold 12 percent. It has 2,192 private shareholders, of whom Theo Siegert, a German businessman, has the largest holding with a 6 percent stake.

SNB shareholders can vote for only five of the 11 members of the bank council, which oversees the SNB's conduct of business, while ordinary shareholders' voting rights are limited to a maximum of 100 shares.

(Editing by Alexander Smith)

By John Revill