The shares have, after all, outperformed the market by 40 per cent over the past year and by 7 per cent in the past month alone.
The reason for the market's enthusiasm centres on Direct Line, the phone-based general insurance business. The expansion of Direct Line has been so rapid that half of RBS's market capital could be attributed to the subsidiary.
Direct Line has two things that make it a winner - critical mass and a cost base roughly a third the size of its orthodox general insurance company competitors.
Direct Line's motor side now has 10 per cent of the British market and the household business is on target for 3 per cent of the market by the end of the year.
There seems to be plenty more potential for growth on the household side, and this sums up RBS's interest as a share - its growth potential in an otherwise mature and fully valued sector.
Assuming that RBS makes about pounds 500m this year and pounds 650m next, its prospective p/e stands at 8.9 compared with 7.5 for Barclays, 9 for Lloyds and 10 for TSB.
While RBS is at the upper end it is not off the scale, and with the growth potential of Direct Line the shares still look cheap.
The only thing to spoil the show would be for RBS to go mad and try to emulate Lloyds by buying a building society.
This is all very well if you have nowhere else to go, as is the case with Lloyds, but RBS is not in this situation.
As RBS already possesses a clutch of growing businesses, it should avoid potentially costly and time-consuming mergers and stick to its successful strategy.
Any 'merger talks' announcement will be a signal to sell.