PARIS—The crux of the Paris climate talks is as simple as this: to ultimately succeed, they must set in motion a swift transformation of the global energy economy away from fossil fuels and toward clean power.

That tipping point presents substantial opportunities, but also ominous risks in the world of finance.

To help the financial industry get prepared, the Financial Stability Board, an international body that coordinates the work of regulators and central banks around the world, is setting up an industry-led task force on the disclosure of climate-related financial risks.

The group will be led by Michael R. Bloomberg, business magnate and former mayor of New York, who appeared in Paris on Friday with Mark Carney, governor of the Bank of England and chairman of the FSB.

The task force is meant to help provide investors the information to assess climate-related risks, which are likely to grow, Bloomberg and Carney said as they announced the project. They emphasized that it is a private and voluntary enterprise, not a regulatory bludgeon.

Climate risks are especially significant for the financial system at a time that experts say trillions of dollars in capital investments need to be rapidly reoriented to meet the proposed treaty’s goals.

With momentum building for investors to back the winners and dump the losers, financial institutions caught on the wrong side could suffer badly. The risks involve not only physical damage from extreme weather, insurance costs, and the like, but also market risks—especially the likelihood that fossil fuels will have to be left in the ground unburned, the so-called stranded assets problem.

In a new financial analysis, the Carbon Tracker Initiative said that around $2 trillion worth of projected coal, oil and gas investments ought to be scrapped in the next 20 years if the Paris treaty goals are to be achieved— “the equivalent of cutting supply and the subsequent emissions by around a quarter.”

It won’t be pain-free for energy producers or the investors who underwrite them.

“All of us must acknowledge what a daunting task lies ahead in making the switch to a low carbon economy,” said former vice president Al Gore at an appearance in Paris.

He warned that investors must be wary “lest they be trapped holding stranded assets.”

Anthony Hobley, chief executive of Carbon Tracker, which has pioneered the financial analysis of risks from stranded assets, said that “we know we are not going to switch off fossil fuels overnight.”

The question for investors, he said, is “How do we stop the projects from going ahead that do not make climate sense as well as financial sense?”

Financial institutions, he said, should be subjected to a “2 degree Celsius stress test.” That would examine the risks of underwriting projects that would fall by the wayside if carbon emissions are cut as much as envisioned in a Paris treaty.

Carney, who spoke alongside Bloomberg at one of the most crowded forums of the first week of the climate talks, said the big risk around transition.

“The question is how smoothly, how quickly and how abruptly will the financial sector adjust?” Carney said. “What we don’t want to see is an abrupt transition, the pulling forward of an adjustment that will happen over time.”

Although the pledges made by almost all the world’s nations in advance of these negotiations fall short of cutting emissions enough to keep warming within the 2 degrees that scientists recommend as a guardrail, that remains the long-term goal of the treaty.

And everyone involved understands the 2 degree goal can only be met if global emissions of carbon dioxide from the burning of fossil fuels drops to essentially zero by the late 21st century. Indeed, as Carney pointed out, even to stabilize temperatures at some higher level would require eventually reducing emissions to zero. So it is reasonable to ask companies, he said, to disclose their plans for a zero-emissions world.

Even traditionally cautious institutions are now saying that the changes are accelerating. Timur Gul, senior energy analyst for the International Energy Agency, said that the share of the world’s energy use met by fossil fuels, roughly 80 percent in recent years, would drop to perhaps 75 percent in the next two decades if all nations live up to their emission pledges. To get on the path to a 2-degree world, he said, that share must drop to 60 percent by 2040.

Some say a shift to carbon-free fuel should come even faster, or that a safer level of warming would be 1 degree C.

Whatever the pace of change, an effective Paris treaty is certain to shift the energy portfolios of big investors over the next few decades.

“Basically this whole exercise that this agreement is part of,” said Todd Stern, the United States’ top negotiator, “is to accelerate the transformation of the energy base of the global economy from high to low carbon. That’s the exercise. That’s what this agreement is about, fundamentally.”

The investment shift is already under way.

The latest signal came on Friday in Paris when New York State Comptroller Thomas P. DiNapoli announced changes to the state’s retirement fund including a $2 billion instrument weighted to avoid carbon-intense companies in favor of investments in companies that are lower emitters.

“Low-carbon, sustainable investments are key to our future,” DiNapoli said. “Our pension fund has long supported climate aware strategies, and this expansion of our commitment offers a sensible solution that will protect the Fund’s investments.”

Janos Pasztor, the United Nations assistant secretary-general for climate change, presented a report on trends in private sector climate finance showing that financial institutions have been meeting and exceeding pledges they made last year at a climate summit in New York.

“This is the first year in history that we have seen more money invested in renewables than in fossil fuels,” said Mindy Lubber of Ceres. “It has switched this year, and we are going to see things going in the opposite direction.”