Elsewhere, during a banking conference at the other end of Interlaken's Hotel Victoria-Jungfrau, National Westminster's chairman, Lord Alexander QC, was his usual gregarious self, chatting with all and sundry about anything - except the recent performance of his bank and its troubled investment banking unit, NatWest Markets.
Both men are closely associated with bold, expensive, attempts to create huge "Made in Britain" investment banking subsidiaries able to compete with well-capitalised foreign competition like Merrill Lynch, Goldman Sachs and Morgan Stanley Dean Witter.
Using their huge balance sheets, NatWest and Barclays planned on reducing their exposure to boring high-street banking to make oodles of money from selling stocks and shares, dealing in bonds and derivatives, and helping companies take each other over and raise money from investors.
There are arguments in favour of the banks cutting their exposure to retail banking. Competition from building societies- turned-banks like Abbey National and food shops turned financiers like Sainsbury's and Tesco threatens to make the mundane business of taking deposits, offering mortgages and lending to smaller businesses less profitable.
Martin Taylor, the intellectual former journalist whom Buxton hired as Barclays' chief executive in 1993, hoped that BZW would be able to produce stable returns throughout the economic cycle.
The idea is to avoid the historical boom and bust scenario in which banks reaped huge profits in good times, splurged on expanding their loans and then wrote off the inevitable duds when the cycle turned down. These notions are compelling. But neither Barclays nor NatWest has successfully transformed theory into practice.
NatWest Markets turned in pre-tax profit last year of pounds 462m, virtually the same as it made in 1993. BZW's operating profits fell 29 per cent in 1996 from 1995. And all this during a raging bull market which should have made for very rich pickings indeed.
What is more embarrassing for the two City titans is the performance of Lloyds TSB. It avoided fancy investment banking and concentrated on the high street and its profits and share price have soared. What was once a relative tiddler is now capitalised at pounds 35.4bn, versus pounds 14.4bn at Natwest, and pounds 18.9bn at Barclays.
The differences are about to be starkly underlined as the big banks report their half year profits in the next 10 days. Lloyds is expected to show a rise in first half pre-tax profit of 33.3 per cent to pounds 1.52bn. EPS is seen rising 42 per cent to 19.5p. Now consider NatWest and Barclays.
"If you strip out exceptionals, both banks show virtually no growth at all," said John Aitken, an analyst with UBS. "We don't expect growth in terms of real, underlying profits. Both, in fact, will be at the bottom end of the range - the weakest of the sector."
NatWest has already said that lower profits at NatWest Markets will pull down overall group profit to no more than pounds 770m - less than it made in the first half two years ago. Analysts are expecting pounds 761m and earnings per share of 26.6p. Barclays is expected to report pre-tax profit down 6.6 per cent to pounds 1.22bn and EPS to fall 1.4 per cent to 54.5p.
Faced with comparisons like this the dilemma for Mr Buxton and Mr Alexander and their respective chief executives, Martin Taylor and Derek Wanless, is whether to jettison the strategy.
"They're in it [investment banking], and the reality now is that it's probably hard to extricate themselves completely," said analyst David Townsend of Goldman Sachs. "That doesn't mean there aren't areas that couldn't be improved. They shouldn't try to be all things to all men, however."
The problem looks particularly acute at NatWest Markets. Alexander and Wanless are currently conducting an operational review following the revelation of a pounds 77m options loss. That prompted the expensive exit of Martin Owen, the investment banking chief executive and six senior colleagues. Analysts have said Wanless and Alexander themselves may be replaced in the next year if investors don't see clear signs of a cogent strategy soon.
But looks aren't everything. Though Wanless will not reveal the real profitability of NatWest Markets, its return on capital last year is estimated to have been around 14 or 15 per cent. That is not something to be proud of.
But consider BZW. It may have avoided scandals but it has not made much money. Last year analysts calculate that BZW made a worrying 9 per cent return on capital. While group profits rose 13 per cent to pounds 2.4bn, BZW's performance was hammered partly because of bonuses paid to attract new executives.
BZW is shortly to reveal, say brokers Credit Lyonnais Laing, that first half profit fell again by 36 per cent to pounds 100m though this at least reflects an upturn on the miserable pounds 47m in the second half of last year. NatWest Markets profits, it forecasts, will be down 48 per cent at pounds 135m. Both, in short, are suffering. A poorly performing BZW may be improving. A relatively stronger NatWest markets is now weakening.
Both banks have spent heavily to make their investment banking dreams come true. When BZW recruited new chief executive Bill Harrison last year, after the untimely death of David Band, he was paid pounds 2.9m, much of it to compensate him for the bonus he would have lost from leaving his previous job.
Time will tell whether that was money well spent. Within days of arriving last year Harrison put in train a wholesale reorganisation which has proved testing on morale inside. He in turn recruited Bob Diamond, a highly paid American investment banker as global markets chief.
Diamond said recently BZW's strategy assumes a single European currency will lead to the creation of a pan-European corporate bond market. BZW could lead this market since it is already a leader in the UK corporate bond market, the largest in Europe.
Perhaps. What is certain is that Taylor will continue to "invest" heavily through 1997, particularly on IT and a disruptive move for BZW to new premises in London's Docklands.
"This year the costs are more constructive, however, in the sense that we are already seeing income coming through," said Buxton. "We see the performance of BZW certainly improving." To do that BZW will have to avoid slip-ups like NatWest's options problem at the same time as it expands in proprietary trading, using its own money to make profits.
Wanless at NatWest has chosen to travel an even more expensive route. He has bought entire companies, people businesses whose assets walk out of the door each night, loaded with expensive goodwill. In 18 months the bank has made four major acquisitions in the US and at home, costing pounds 1bn.
One major similarity between the two banks is in their approach to fund management. No sooner was Gartmore bought by NatWest Markets than it was placed directly under the ownership of the parent bank. Here Wanless was playing copycat to BZW. The latter purchased the huge Wells Fargo fund management business, but it soon became part of the parent bank.
These are both attractive operations and removing them from investment banking operations makes the latter easier to reshape - or maybe even sell if the right offer came along. Speculation that Barclays may try to sell BZW was, however, recently dismissed by Buxton as "purely a press- inspired rumour".
Meanwhile, NatWest is expected to announce next week that the corporate lending and treasury businesses will be removed back to the main bank from NatWest Markets - a move that will cut NatWest Market's capital from pounds 3.1bn to about pounds 2bn, or 25 per cent of the total capital in the group. That does little to solve a more fundamental problem with NatWest Markets: some of the acquisitions are still working as independent empires rather than working with and passing on each other's clients. NatWest has moved to reduce this problem by handing more operations inside Markets to the Hambro Magan's corporate financiers.
"The City would be much happier if they stripped it down quite dramatically," said Aitken.
The NatWest announcement on 5 August may also reveal whether the bank intends to acquire or merge with another financial institution. Abbey National executives say NatWest approached them with a merger offer and was rebuffed, and more recently NatWest was said to be in failed talks with Prudential Corp.
NatWest lags Barclays in the race to cut costs by closing branches, although it is beginning to catch up. Last year, Wanless said NatWest would reduce the number of branches to 1,750, from 2,046.
"But that's what all the banks will have to continue doing, all banks have to improve their cost-income [ratio]," said Townsend.
NatWest's cost-income ratio was 68 per cent for 1996, while Lloyds was 56 per cent. Barclays doesn't release a cost-income ratio because Taylor believes it is a misleading figure.
Barclays' strength is its credit card business, which is the market leader in Britain, although analysts say it has been losing market share to, among others, NatWest.
Barclays' dividend will show a 15 to 20 per cent increase, while NatWest's will be half that level, said UBS's Aitken. "That might disappoint the market, and Barclays may seem to have the better set of results."