The U.S. Federal Reserve is set on Wednesday to announce the start of a plan to trim its $4.5-trillion portfolio of assets, much of it amassed in response to the 2007-2009 financial collapse, marking another milestone in bringing to an end the crisis-era measures.

If Fed Chair Janet Yellen gets her way, financial markets that had swung wildly with past shifts to the policy will barely shrug when the asset reduction begins, probably in October.

The plan is for the Fed to stop buying bonds so gradually that it will take years for its holdings to shrink to $3 trillion, around where some policymakers and economists estimate it will settle.

The Fed’s asset holdings stood at about $900 billion in mid-2008, before it began buying bonds to spur hiring and economic growth.

Years of planning and months of careful public messaging should make the asset-unwinding process about as riveting as