The impetus for the campaign is a set of simple numbers - a global carbon budget. It's a way of framing the climate crisis that is now uniting student activists and market analysts. The former use the numbers to prosecute a moral case that the fossil fuel industry has gone rogue; the latter, for a cold-blooded calculation that trading away from carbon-heavy assets is in an investor's own interest. The numbers were set out in a report called ''Unburnable Carbon'', which was released last year by the Carbon Tracker Initiative, a group of analysts and environmentalists in the UK. It highlighted the work of the Potsdam Climate Institute, which in 2009 produced a set of emissions scenarios together with their likely influence on global temperatures. These are the numbers: for a low chance - one-in-five - of exceeding 2-degrees warming, we can only emit another 565 gigatonnes of carbon dioxide by mid-century. But proven fossil fuel reserves (held by listed corporations, private companies and nation states) equate to 2795 gigatonnes - five times the carbon budget. In Copenhagen in 2009, the world's governments agreed to limit warming to 2 degrees. To do so, four-fifths of our fuel must stay in the ground. James Leaton, Carbon Tracker's research director, says this ''huge overshoot'' of reserves represents a ''carbon bubble'' in financial markets. We're on track to exceed the budget by 2028. ''Investors need to start questioning the wisdom of companies pouring more capital into developing even more reserves,'' he says.

In its World Energy Outlook for 2012, the International Energy Agency presented a similar case. Using the same research, but choosing a higher, 50-50 threshold for exceeding 2-degrees warming, it stated that two-thirds of proven reserves must stay in the ground, unless carbon capture and storage is widely deployed. (It observed that the pace of deployment of the technology ''remains highly uncertain''.) Bill McKibben, the American author and environmentalist who set up Go Fossil Free in the US, says that despite decades of advocacy, ''the penny dropped'' when he saw those numbers. ''I've followed this all pretty closely - I wrote the first book about climate change - but I'd never really understood in my gut that the end of this story was written. It's utterly clear. There is no room for wishful thinking,'' he says, on the phone from his home in Ripton, Vermont. ''These guys [fossil fuel companies and state owners] have five times as much carbon in their reserves as the most conservative government on Earth says would be safe to burn. Once you understand that, then you understand that this has become a rogue industry. This formerly socially useful thing is now the greatest threat the planet has ever faced.'' Last August, he published an article in Rolling Stone, called ''Global Warming's Terrifying New Math''. Teen heartthrob Justin Bieber was on the cover, but it was McKibben's essay that went viral. Spurred by its unexpected popularity, McKibben hit the road the day after the US election, on his ''Do the Math'' tour. With support from Desmond Tutu, author Naomi Klein and others, he spoke to sold-out concert halls around the country. Just two months on, students on over 250 campuses have started campaigns for their universities to divest from fossil fuel companies. (Together, US colleges command over $US400 billion in endowments.) Already, three have agreed.

''It's actually happening faster than we thought,'' McKibben says. ''These are hard fights. All these kids know that, but they also know that this is their future.'' The campaign is modelled on the anti-apartheid divestment movement. In the 1980s, 155 colleges sold their South African assets, and scores of cities, states and counties joined in economic action against companies connected to the apartheid regime. This time - and with the blessing of Tutu - the call for divestment is about undermining the legitimacy of the fossil fuel industry. ''We're not trying to bankrupt Exxon; colleges selling their stock is probably not going to do that,'' McKibben says. ''We're trying to take away their social licence.'' McKibben is scheduled to visit Australia in June, before his organisation, 350.org, holds its ''Global Power Shift'' conference in Istanbul. But local activists aren't waiting until then. In January, Friends of the Earth began to promote Market Forces, a new campaign that, according to its founder, Julien Vincent, aims ''to stop our money going into projects that would harm the environment and drive global warming''. Likewise, the Australian Student Environment Network has started Lock the Campus, which targets universities' investments, research and partnerships with the fossil fuel industry. They have a precedent: following a brief student campaign in 2011, ANU agreed to sell its million-dollar stake in coal seam gas company Metgasco.

As it turns out, the students have an unlikely ally - albeit one with a slightly different goal in mind. John Hewson, the former leader of the Liberal Party, now fronts the Asset Owners Disclosure Project (AODP) and its accompanying social media campaign, The Vital Few, which is aimed squarely at superannuation funds. The Vital Few website is set up for battle, rallying the public to ''storm the castle'' and ''rewrite the future''. In practice, that means emailing your fund, requesting transparency about its interests in fossil fuels and calling for a bigger stake in renewables. Hewson says the average pension fund invests about 55 per cent of its portfolio in ''high-carbon intensive industries'' and only 2 per cent in their low carbon counterparts. ''These asset owners have a long-term, not a short-term, horizon,'' he says. ''Their fiduciary responsibility is to maximise the returns to superannuates over time. How are they going to manage the risk of catastrophic climate change going forward? The best way is to put a higher percentage of their funds in low carbon-intensive industries.'' In the finance world, ''climate risk'' translates as the prospect of reduced earnings or devalued assets, caused by climate change. That could come by way of physical impacts - say, a flood that destroys infrastructure - or cheap clean technology, or tough policy measures, such as robust carbon pricing and regulations. Alongside Hewson on the AODP board is Bob Litterman, the former head of risk management for Goldman Sachs in New York. He sees an analogy between the carbon bubble and the sub-prime crisis, in which financial institutions ''piled up mortgages on their balance sheet, assuming they were safe''.

''Similarly, today, we're piling up carbon emissions in the atmosphere. When there's a recognition that it cannot absorb an unlimited amount of carbon, there's risk that people will very quickly revalue all the assets producing those emissions,'' he says. Last year, the AODP - which has connections with The Climate Institute - launched an index of the world's pension funds, insurance companies and sovereign wealth funds. It ranked them on their management and disclosure of climate risk. The highest-rating fund was Local Government Super, based in New South Wales. It estimates that low-carbon assets comprise more than 10 per cent of its total holdings. Members can choose a coal-free shares alternative, which screens out BHP Billiton, Rio Tinto, Wesfarmers and Whitehaven Coal, among others. CEO Peter Lambert insists this attitude to climate risk is pragmatic, not political. ''Increasingly the blowtorch is going to be turned towards these issues and there will be a time when they're priced into assets. ''You can say you'll sit back and wait until that occurs and then start to adjust your portfolio. Our position is that we should be ready for it now, because by then it's too late and it will cost our members money,'' he says. That view is not yet widely shared in the industry. Nathan Fabian is the CEO of the Investor Group on Climate Change, which covers more than sixty institutional investors. ''I'm confident we're heading in the right direction,'' he says. ''But the truth is that the process is going slower than what is necessary to address climate risk.''

For funds and analysts, the risk boils down to the likelihood of widespread carbon pricing. Most are betting against it - that is, they're tipping we'll exceed the budget and press on to a hotter world. Even for the most concerned among them, it is difficult to translate knowledge into action. Typically, super funds invest heavily in ''passive funds'' that track the market - deviating from that benchmark entails a risk of doing worse than everyone else. The very nature of financial modelling is a barrier, Fabian says: a dollar today is worth considerably more than a dollar in a decade. When you factor in deep uncertainty about carbon policy, along with fund managers who are rewarded for meeting short-term targets, a systemic, long-term risk such as climate change slips off the computer screen. ''The risk is there,'' he says. ''It's just hard for us to measure it.'' Nick Robins is the head of the climate change centre at HSBC Bank, in London. Over the past year, his team has tried to measure the risk by estimating the impact in Europe of a deflating carbon bubble. In their scenarios, it could nearly halve the value of coal assets on the London exchange, and knock three-fifths from the value of oil and gas companies. And yet, he says, ''at the moment this risk is not being priced at all''.

While the San Francisco and Seattle divestment proposals received a lot of press, the funds in question haven't yet adopted them. In Seattle, a consultant's report advised the board that doing so would be ''costly''. But just as the current patterns of world finance continue to reinforce the fossil fuel economy, so movements for change - laid out by Carbon Tracker, McKibben and the Vital Few - weaken the walls of the carbon bubble. The more noise they make, the more exposed fossil fuel investments appear. Robins says divestment is ''not on the cards'' for large institutional investors. ''But people are recognising that over the next two years, they will need to come up with investment plans about how they're going to be part of a 2-degree world, rather than the 4- to 6-degree world which they're on at the moment.'' For his part, McKibben expects Go Fossil Free will spread rapidly, precipitated by citizens' experiences of weather extremes. ''If anybody has a good sense of how important this is, it's Australians right now. You guys broke every temperature record you had, day after day in January,'' he says. ''Either we pay attention, or we engage in the most incredible collective denial that human beings have ever engaged in.'' Michael Green is a Melbourne journalist.