Beware of sunburn when bathing in reflected glory. There may be no more prestigious perch in global business than a seat on the board of Apple. The company is innovative, huge and beloved. So on the face of it, former Genentech boss Arthur Levinson, just elevated to chairman, and Walt Disney president Robert Iger, newly appointed board member, have received an unmixed blessing.

Apple’s board has been criticised in the recent past for its near silence on the late Steve Jobs’ health and on succession planning. But his death led to an orderly transition, and the shares have not been hit. That may be because the share price already discounted his passing and new chief executive Tim Cook was already running the company day-to-day. The fact is that when a company provides shareholders with 4,500 per cent returns over 10 years, the board looks good, even if its work consists primarily of vigorously agreeing with the brilliant chief executive.

This board, by contrast, is likely to be tested. Apple has ample room to expand (“If iPhone can take 10 per cent of the Chinese market..”), but not even Apple trees grow to the sky. They will have to decide how much freedom to give Mr Cook, who has huge shoes to fill as he manages the transition to slower growth.