Analysis
By Jeff Randall BBC business editor

What is Vodafone: a boring utility, like a water company, or a racy technology stock?

That is the debate amongst investors after the world's biggest mobile-phone operator announced a surprise 41% increase in its interim pre-tax profits to �4.25bn.

City analysts had been forecasting half-year profits of about �3.5bn. The outcome was more than 20% better than that, yet Vodafone's shares jumped by "only" 10%.

The difference between those figures demonstrates the extent to which the company has to overcome imbedded scepticism.

The bubble image

It is not that Vodafone has made any catastrophic mistakes. Au contraire.

Can Chris Gent once again become the investor's darling

During the boom years of the late 1990s, it was shrewd enough to pay for its acquisition binge in shares not cash (unlike Marconi).

For a while, Vodafone became Britain's biggest company.

Such was the heady euphoria surrounding telecoms companies caught up in the tech bubble that its share price reached 400 pence, valuing it at about �270bn.

On the back of Tuesday's excellent results, the shares jumped from 98.5p to 111p.

Even so, the company's stock market worth is still nearly �200bn below its peak. That's the equivalent of losing the entire net worth of two BPs.

No wonder investors remain wary.

Waiting for the whizz-bang effect

On Monday, the Wall Street Journal expressed the view of many sector professionals when it claimed, "everyone knows that the mobile phone's high-growth decade is over".

If Vodafone's chief executive, Sir Chris Gent, is to regain his status as corporate hero, he must prove the pessimists wrong.

He has bet a big chunk of his chips on rising demand for whizz-bang adaptations to the mobile phone such as video conferencing and picture messaging.

Will it materialise?

That's the killer question.

If the answer is Yes, Vodafone's shares are probably cheap. If No, investors can expect yet more pain.