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Swiss business marks two important anniversaries this month. On July 1 last year, Tidjane Thiam, the high-flying boss of the UK’s Prudential, became chief executive of Credit Suisse, a bank struggling to find a sense of strategic direction. Ten days later, Holcim formally merged with France’s Lafarge. New chief Eric Olsen, a French-speaking American, began integrating two very different companies into the world’s largest cement group.

A year on, neither Credit Suisse nor LafargeHolcim has convinced investors that their ambitious plans will work. The companies’ share prices are down 60 per cent and 40 per cent. Both bosses are under pressure.

Less obvious, however, are the behind-the-scenes strains on the two companies’ chairmen. Given the importance of a company’s titular head in Switzerland’s system of corporate governance, they could prove as relevant — if not more so.

At Credit Suisse, Urs Rohner, a former chief operating officer, has been chairman since 2011. As the bank’s woes have mounted, so have the questions: did he wait too long before bringing in Mr Thiam to revamp the bank? Has he chosen the right person?

At LafargeHolcim, Beat Hess, a veteran Swiss corporate lawyer, will have much to explain to shareholders if the merger fails. He was appointed in February after predecessor Wolfgang Reitzle quit to become chairman of Linde, in his native Germany, after apparently deciding he could not commit the time needed to streamline a sprawling portfolio of underperforming cement operations.

As Mr Reitzle discovered, Swiss chairmen have much larger workloads and shoulder more responsibility than in other European countries or the US. They take charge of strategy, risk management, executive compensation, budgets and emergency plans — as well as relations with shareholders.

In fact, “chairman” is a mistranslation if it suggests a neutral or control function. When speaking German or French, the Swiss use “president”, which better reflects the leadership role.

There are rewards: Swiss chairmen are paid a lot more than counterparts in other countries — including the US, the country with the highest-paid chief executives. The median salary of large Swiss company chairmen was €1.2m last year. In the US it was just €448,000, according to HCM International, a corporate governance and compensation consultancy.

The responsibilities of Swiss chairmen have increased in recent years. Under anti “fat cat” measures approved in a referendum three years ago, they face re-election every year at shareholder meetings — so they need to show regularly that they have a grip on strategy and that the right people are in top management posts.

Chairmen frequently call the shots at Switzerland’s biggest companies. That looks likely to be the case, for instance, at Nestlé, the world’s largest food and drink company, which last week announced that Paul Bulcke, its chief executive since 2008, would take over as chairman from next April after a minimum “cooling off” period.

Breaking 94 years of tradition, Nestlé chose an outsider as its new chief executive. Ulf Mark Schneider impressed analysts with his performance at Fresenius, the German healthcare company. But at Nestlé he will be part of the “Nestlé system” and under the tutelage of a company veteran.

LafargeHolcim has a similarly demanding chairman. Mr Hess was a top lawyer at ABB in 2002 when the Swiss engineering group came close to bankruptcy as a result of US asbestos claims. He then was at Royal Dutch Shell from 2004 when the Anglo-Dutch oil group was embroiled in a costly scandal over the overstatement of oil and gas reserves. Now Mr Hess is pressuring LafargeHolcim’s top managers to speed up cost-cutting and centralisation programmes.

At Credit Suisse, much will depend on the success of Mr Thiam’s plans to push into fast-growing Asian markets and to downsize Credit Suisse’s investment bank. If he hits his targets, the pressure would also ease on his chairman.

The Swiss system works when the chairman and chief executive have common interests and form an effective team. The dangers are of personality clashes, of chairmen interfering, and of responsibilities being shirked. When things go badly, there is more than one head that can roll.

ralph.atkins@ft.com