* Annual net profit falls 46 pct to 1.21 bln euros
* Sales down 4 pct, watches down 15 pct at constant currency
* Announces new share buyback programme, higher dividend
* Chairman Rupert's son Anton to join board
* Shares fall 6 pct (Adds chairman, CFO, analyst comment, shares)
By Silke Koltrowitz
ZURICH, May 12 (Reuters) - Cartier owner Richemont expects trading to remain volatile after net profit slid more than the market expected and watch sales fell 15 percent in its latest financial year, sending its shares sharply lower.
Luxury watchmakers have been grappling with dwindling demand in their biggest markets, Hong Kong and the United States, but sales had improved of late thanks to easier comparisons and what appears to be a sustainable recovery in mainland China.
However, Richemont struck a cautious note on Friday.
"Volatility and uncertainty in the geopolitical and trading environments are likely to prevail," the world's second-biggest luxury goods group said in a statement on Friday.
Chairman and controlling shareholder Johann Rupert opted against committing to specific targets for trading.
"Why should we stick our necks out with so many moving variables?" Rupert asked reporters on a call, adding any kind of prediction would put pressure on the group's brands.
Rupert said he was confident of the longer-term potential for luxury goods because the Chinese -- crucial consumers -- would keep traveling and help revive European markets that suffered in the aftermath of militant attacks.
But outgoing Chief Financial Officer Gary Saage said it was too early to say the worst was over in the important Hong Kong market that has collapsed over the last two to three years.
LVMH, the world's biggest luxury goods group, last month reported underlying sales growth of 11 percent in its watch and jewellery business in the first quarter of 2017, helped by a recovery in Europe and Asia.
Sales at Richemont fell 4 percent to 10.65 billion euros ($11.58 billion) in the year to the end of March, missing expectations, but with a clear improvement in the second half thanks to a recovery in the United States and strong growth in mainland China.
Despite a 46 percent drop in net profit after a one-off gain a year ago, the company announced a new share buyback and a 6 percent higher dividend, but shareholders were unimpressed.
Shares, up nearly 30 percent this year, were down 5.3 percent at 0929 GMT, also dragging down rival Swatch Group by more than 4 percent.
"Future revenue growth and margin profile remain uncertain given the lack of visibility on the watch inventory cycle recovery and structural challenges," said Citi analyst Thomas Chauvet, who has a "neutral" rating on the stock.
Jewellery sales, which represent 39 percent of group sales mainly under Cartier and Van Cleef & Arpels brands, posted robust growth of 7 percent at constant currency. Watches, which represent 41 percent and include IWC and Piaget timepieces, declined 15 percent, hit by inventory buybacks.
Richemont is trying to boost profitability by saving costs and rejuvenating its management team and board.
Nine new board members will stand for election in September, including former Google executive Nikesh Arora and Rupert's son Anton.
Rupert, 66, said Arora would help tackle digital challenges while his son would ensure continuity by acting as a link between management and controlling shareholders but was not, at this point, his designated successor as chairman. ($1 = 0.9200 euros)
Editing by Michael Shields