For one thing, the Fed could buy up most of the companies in the S&P 500. A full 315 individual companies, when counting from the bottom of the list by market capitalization. That includes well-known names like Viacom, Clorox and Expedia.

On the other end, the Fed's spending spree could purchase the top 10 companies: everything from Apple to Wells Fargo. That includes a lot of big outfits like Amazon, Alphabet and Exxon Mobil.

But the Fed maybe should have wound down its balance sheet years ago: A previous CNBC analysis showed that in December 2015, it could have afforded the 14 biggest companies in the index.

"Provided that the economy continued to perform about as expected, most participants anticipated that gradual increases in the federal funds rate would continue and judged that a change to the committee's reinvestment policy would likely be appropriate later this year," the March minutes said.

The Fed's balance sheet is around 24 percent of U.S. GDP, which is far above the historical average of around 6 percent. But other industrialized nations have asset-to-GDP ratios that are much higher. The Fed's total assets have plateaued in recent years while those of other central banks like Japan and the European Union have continued to rise.