Two realities are colliding in business today, and they’re changing the way executives must think about creating new sources of growth.

The first has to do with the ticking time bomb attached to large, conservative businesses. “In the next 10 years, 40 percent of the Fortune 500 companies will be gone,” according to research done at Washington University’s John M. Olin School of Business. Put another way: The pace of change is accelerating, and 40 percent of big companies won’t be able to keep up.

The second reality is people hate change. “Only one in nine people will change their diet and exercise routines even after being told they could prolong their life, reverse diabetes, restore their health,” wrote Alan Deutschman in his book “Change or Die.” In other words, most people won’t change to (literally) save their life.

So as a business leader, you face the challenge that only about 11 percent of your employees will embrace change despite a disruptive future that threatens your company with imminent death.

Insert Jaws soundtrack here.

So what do you do?

You’re a great leader, and great leaders build teams to be competent. Being competent usually means doing the job you were hired to do, just a little better every day. It means understanding and embracing industry best practices. It means being more efficient than your competitors. And, by definition, it means stomping out anything that threatens the status quo or the way you efficiently make money. Indeed, your entire company was created to make radical change difficult.

So while it’s no secret that entrepreneurs are successfully disrupting once untouchable business models, even if an enlightened leader wanted to import, promote or encourage entrepreneurial thought, their competent system would have none of it. After all, entrepreneurs break sacred rules, defy key performance indicators and reimagine the unimaginable. Stuff like that would get any reasonable executive fired.

My friends Susan Robertson and Anne Manning teach creative thinking at Harvard University. Susan and Anne recently conducted a research project to better understand the things keeping large companies from being more creative and able to embrace change. Here are some comments from the people they talked to:

“We are afraid here. We are super conservative and have a ‘can’t-do’ culture. People are terrified of taking risks. It’s built into our DNA. Big ideas flip people out. That has squelched creativity. Even our ad agency said we are cowards.”

— Head of innovation, Fortune 100 financial services firm

“No one ever gets fired for playing it safe, but many have been fired for taking risks. We are incented to not take risks.”

— Innovation manager, construction products company

“We’re focused on short-term results and have been limited to looking in spaces that we’re currently in. We recruit MBAs, which is a narrow subset of the population that is innately risk averse. We’re not getting the scrappiness and creativity.”

— Director of innovation, consumer packaged goods company

And yet big companies need radical change.

What’s the solution? I’d argue you must outsource your crazy.

I’m not talking about outsourcing all innovation. Incremental innovation is possible for most teams. We are all capable of becoming better listeners and responding by modifying our products, services and customer experiences. When we do, evolutionary ideas get to market more quickly. This must be a priority for all companies.

But unless you are a digital company engineered for constant change, revolutionary innovation requires a completely different two-pronged strategy.

First, you must invest in early stage start-ups through a venturing arm, guided by focused industry insights.

Next, you must invest in revolutionary innovation designed to literally put your firm out of business—at least the business it is in today.

This is an idea that many large companies have already embraced. For example, Barclays Bank in the UK has partnered with Techsters to build cobranded incubators. Walmart acquired Kosmix in 2012 for $300 million and turned it into Walmart Labs, a group capable of reimagining the current business model. Conversations I’ve had with Fortune 500 CEOs make me believe that many more will follow.

Needless to say, the idea of a project or team designed to hijack the mother ship is so scary and daunting that it MUST be outsourced, either to outside consultants or an incubator outside of corporate governance. The best incubators have employees with a stake in the outcome and ideally are located in some other state.

I like to tell leaders that it’s easy to make a big idea small but nearly impossible to make a small idea big. Your company needs big ideas designed to disrupt your industry. The way to get them is to hire a team engineered to disrupt or build that team off site.