Xstrata has been stalking Anglo American for more than three months. Now a “put up or shut up” ultimatum from the UK’s Takeover Panel means Xstrata’s chief executive Mick Davis has less than three weeks to make his move. He should just walk away.

Xstrata made its offer of a nil-premium merger of equals after its market capitalisation caught up with that of Anglo earlier this year. Davis bet that investors would prefer his management team. But Anglo’s shareholders have so far been willing to give new chairman John Parker, who was parachuted in after Xstrata made its approach, the benefit of the doubt.

Since Xstrata’s interest was made public the two have been neck and neck in terms of market value, with both sides trying to outdo the other with growth forecasts.

Based on Xstrata’s calculations — which exclude Anglo shares held by its investment companies, an employee trust and shares held in treasury — the relative ratio of the two in a nil-premium merger would currently be 52 percent to 48 percent in Xstrata’s favour.

There is no sign the two sides are any nearer to an agreement: Anglo on Friday repeated its view that there is no strategic case for a deal and the terms on offer are unacceptable. But Xstrata simply hasn’t got a lot more it can offer without risking the support of its own investors. Offering Anglo investors a greater share of the combined company would give them most of the benefits of the projected $1 billion in synergies from the deal. Barring a sale of assets such as its 25 percent stake in LonMin, the ambitious mining group, which has net debt of $13.1 billion, is hardly in a position to sweeten its merger proposal with cash.

Xstrata could buy more time by making its offer formal. But Anglo shareholders are unlikely to accept what amounts to a hostile nil-premium bid. Without agreement from Anglo regulatory approval would also be harder to get, particularly in South Africa.

Faced with this situation, the best course for Xstrata is to demonstrate its confidence in the relative growth prospects of the two companies by walking away.

It could then let Anglo’s investors sweat for the obligatory six months it would have to wait before making another approach. After all, there’s nothing to stop shareholders from pushing Anglo’s management to the negotiating table. If Xstrata’s shares continue to outperform while Anglo’s lose some of their bid premium, the balance will move further in Davis’ favour. Given that nobody else appears ready to step forward for Anglo, Davis can afford to bide his time.