Here's the simplest way to understand how a Brexit would affect the US

What a Brexit would do to the US economy really boils down to what happens to the dollar.

Britons will vote on Thursday to decide whether the UK should remain a part of the European Union or not.

The UK is one of the region's most important economies. And because of possible negative-growth ripples throughout the region, the prospect of a Brexit has worried traders.

The key channel of any pass through to the US would be the dollar, according to Andrew Milligan, head of global strategy at UK-based Standard Life Investments, which manages $370 billion in assets.

The biggest question, he said, is whether a rise in the dollar would be driven by a flight to safe assets, or by signs that the Federal Reserve is responding more aggressively to economic growth.

"The direction of the currency and the rationale for the currency" are extremely important, he told Business Insider.

Doing the Fed's work

In theory, a stronger dollar would raise the prices of US exports, as dollar-denominated goods become more expensive for buyers with weaker currencies.

At the same time, it would make imports cheaper for US consumers, which is deflationary. Even lower inflationary pressure than we've seen so far this economic cycle would give the Fed more reason to be dovish and delay further interest rate hikes.

"Do we see the Federal Reserve saying yet again 'we don't need to move on interest rates because monetary conditions in the United States have already been tightened and they're being tightened by the move in the dollar?'" Milligan said.

If the answer to that is yes, the Fed could mirror its response to the surge in the dollar from mid-2014 through 2015, when it delayed rate hikes.

Another possible beneficiary of a flight to safety in the wake of a Brexit would be US Treasurys. The recent rally in global bonds including Treasurys sent the 10-year yield to two-year lows. Some analysts attributed this to a flight to safety ahead of the referendum.

However, Milligan argued that Treasurys are instead being driven by major investors, including central banks, who find it difficult to invest in any of the nearly $8 trillion worth of government bonds with negative yields.

And while there might be some treasury buying that's part of a flight to safety, the key thing to watch is the dollar.