“THE STONE age did not end for lack of stone, and the oil age will end long before the world runs out of petroleum.” That battle cry has long animated critics of Big Oil, who dream of a phase-out of hydrocarbons in favour of cleaner fuels and technologies. Their bête noire is ExxonMobil, long the richest and mightiest of Western oil supermajors—and the most unrepentant in its defence of crude. Lee Raymond, a formidable former boss of the Texan titan, once told your correspondent to get out of his office after being challenged over his flagrant denial of climate science.

How the times have changed. Darren Woods, who currently does Mr Raymond’s old job, does not deny that climate change is real. And he is about to confront the stiffest challenge posed to the firm’s management in living memory. At his company’s shareholder meeting on May 26th a coalition of activist investors led by Engine No.1, a small hedge fund, will try to put four green-tinged directors on the board to promote a lower-carbon strategy of the sort espoused by European supermajors such as BP, Royal Dutch Shell and Total. Proxy advisers, who counsel shareholders on such votes, have backed some of Engine No.1’s demands.

Unlike earlier foiled attempts to contest ExxonMobil’s carbon-addiction, this one is not a foregone conclusion. The voting could be a close-run thing, with a mixed outcome. Huge institutional investors must square their climate-friendly rhetoric with the desire for healthy returns, which have outperformed those at the European rivals as the oil price has rebounded from its pandemic-induced collapse (see chart). But even if the dissidents do not win outright, there are reasons to think that Mr Woods is unlikely to emerge from the proxy battle as brashly self-confident as he and his predecessors have from previous dust-ups.

The activists have enlisted powerful allies. CalPERS and CalSTRS, pension funds representing, respectively, California’s public employees and its teachers, have between them over $700bn in assets under management. Two giant funds representing New York’s state and city employees, with another $300bn or so in assets, have joined them in supporting Engine No.1’s effort. Together they hold less than 1% of ExxonMobil’s shares. But as large asset managers, their actions send a strong signal to the broader market. “The links between climate change, business and financial investments are undeniable,” says Aeisha Mastagni of CalSTRS. She argues that the election of the four activist directors will “prepare the oil giant for the global energy transition”.

Institutional Shareholder Services (ISS) and Glass Lewis, the proxy-advisory duopoly, recommend the election of three and two of Engine No.1’s directors, respectively. But even one dissident director could make a big difference, says Charles Elson, a corporate-governance expert at the University of Delaware who has served as a courteous rebel on various boards. In a report published on May 14th ISS declared that the hedge fund “made a compelling case that additional board change is needed to provide shareholders with sufficient confidence” in ExxonMobil’s prospects.

Outside pressure for the oil business to embrace the transition to a low-carbon future is growing intense. On May 18th the International Energy Agency (IEA), an international forecaster not known for alarmism, warned that investments in all new fossil-fuel projects must stop now if the global energy sector is to achieve carbon neutrality by 2050. President Joe Biden wants America’s power sector to stop adding greenhouse gases to the atmosphere 15 years earlier than that.

So far it has been Europe’s oil giants that were pushed harder to go greener—by activists, consumers, regulators and some investors. Last year BP vowed to slash the carbon intensity of the products it sells by 50% in the next 30 years. This month Shell won shareholder approval for its plan to create a carbon-neutral business, including emissions from the fuel burned by end-users, by mid-century.

The activists would like to push ExxonMobil down a similar path. In response to their badgering, earlier this year it already unveiled plans for a new “low carbon solutions” division, which will develop technologies to capture carbon and store it underground. It has also pledged to cut the carbon intensity of its own exploration and production operations by 15-20% by 2025.

Not good enough, Engine No.1 and its backers retort. They point to ExxonMobil’s plans to spend only about $3bn in total over the next five years on its low-carbon effort, compared with around $20bn a year on dirtier traditional investments. Unlike Shell, the company has promised only to reduce emissions from its own operations, not the vastly greater ones produced when its products are used by consumers.

The big reason such arguments are no longer falling on deaf ears is that ExxonMobil’s once mighty reputation for being tightly run has slipped. Historically prudent capital spending has been replaced by indiscipline. The company has torched billions in shareholder value in the past few years. The most eye-popping chart in Engine No.1’s 80-page manifesto shows its return on capital languishing at or well below its weighted-average cost of capital since 2015.

ExxonMobil has splashed out nearly $100bn on capital expenditure in total over the past five years even as world oil prices swooned. Chevron, its biggest American rival that is similarly bullish on oil, spent less than $70bn in that period. ExxonMobil’s net debt has nearly doubled since 2015 to over $60bn. Its mistimed and overpriced acquisition of XTO Energy, a gas firm, led it last November to write off $17bn-20bn—and S&P Global, a rating agency, to entitle a scathing analysis of the incident “How not to do M&A”. “Additional board refreshment is necessary due to the long-term financial underperformance at ExxonMobil,” concludes Anne Samson of CalPERS.

Last summer, as ExxonMobil’s share price headed to a two-decade low and the company was knocked out of the Dow Jones Industrial Average after nearly a century in the blue-chip index, Ms Samson’s argument would have sounded incontrovertible. To many it remains compelling. But many investors in energy firms appear to be getting cold feet about a green shift. Thanks to dearer oil ExxonMobil has clawed back $110bn in market capitalisation since October, handily besting the European giants whose promised wind and solar projects are years away from profitability and could meanwhile eat into their dividends. This puts huge asset managers such as BlackRock, the world’s biggest, in a bind. Its boss, Larry Fink, who rarely misses a chance to talk up the importance of curbing global warming, also has a fiduciary duty to guarantee optimal returns to investors in his firm’s funds.

Crude prices are, of course, cyclical by nature. They will fall again at some point, unlike the carbon dioxide relentlessly accumulating in the air as more oil is burned. Mainstream investors now view climate risk as “a core component of long-term value”, insists Timothy Youmans of EOS, which offers stewardship services to owners of $1.5trn in assets and supports Engine No.1. This week’s shareholder battle will not be the last one Mr Woods and his successors will face.