Shares closed up 9p at 346p on a 26 per cent increase in pre-tax first- half profits to pounds 241m, and an increase in the dividend to 5p from 4p.
"These results exceeded most expectations," said Charles Landa, of SG Strauss Turnbull. "What is particularly impressive was the very strong increase in net asset value, up 23 per cent to 354p."
Analysts' attention focused on the good profits, the expectation that dividend rebuilding will continue, and the recovery in the key US operations.
Richard Gamble, Royal's chief executive, described the dividend increase as a "further step in the process of rebuilding the level of the dividend paid to shareholders", which analysts took as indicating that a further increase was to come.
The toughness of the domestic insurance market, where Royal has decided to let business go rather than underwrite at cut prices, has been balanced out by better performances abroad, which account for over 50 per cent of premium income.
In particular, the move to a pounds 33m profit from a previous pounds 27m loss in the US, Royal's second market, helped the overall performance.
The underwriting profit reflects a repositioning of Royal in the States, taking advantage of a shift by brokers to large companies with international presence.
Royal also revealed it had paid out a $100m settlement this year, the biggest of six large US environmental claims still outstanding at the end of 1994.
In the UK, profits from general insurance dropped to pounds 151m from pounds 180m, with premiums down 4 per cent. "We continue to focus on margins, refusing to write business rather than underprice it," Mr Gamble said.
Motor and household rates in the UK have declined by 6 per cent over the past 12 months, but Mr Gamble said they were showing signs of stabilising.