Image source: The Motley Fool.

Shares of Bank of America (NYSE:BAC) were up Monday after a recent poll showed that people in the United Kingdom were less likely to vote this Thursday in favor of leaving the European Union than had previously been thought.

The U.K.'s Daily Mail published on article yesterday suggesting that more people are now in favor of staying in the European Union than leaving, a turnaround from one week before. The latest poll showed that 45% of those surveyed were in favor of remaining, compared to 42% who favored leaving. It marked a six-point swing in sentiment.

Other polls suggest that the opposite is true. A YouGov survey conducted for Good Morning Britain showed that 44% of voters supported leaving while only 42% would vote in favor of remaining. Meanwhile, an Opinion Poll for the Observer showed that the two sides were equal at 44%.

There are two reasons this matters for Bank of America. The first is that the uncertainty surrounding the U.K.'s potential exit from the European Union seems to have weighed heavily on the broader market over the past week. The Dow Jones Industry Average dropped 1.1% last week, its biggest decline in more than a month, according to The Wall Street Journal.

There's the immediate issue surrounding what will happen when the U.K. leaves, as it would be the first time a country has defected from the European Union. But there's also the question of whether or not it would trigger other member countries to follow suit -- and, relatedly, what that would do to the euro, a major reserve currency.

According to an analysis by Keefe, Bruyette & Woods, an investment bank that specializes in the financial services sector:

A vote for Brexit would lead to macro uncertainty and this would likely result in higher volatility (sometimes unhealthy), but also lower capital markets activity as companies stop transacting due to uncertainty in law and markets. We would also expect the British Pound and Euro to depreciate versus the dollar and this would cause FX headwinds for select companies.

The second reason it matters to Bank of America is more unique to the North Carolina-based bank, as it has investment banking operations in London. While most banks have been reluctant to forecast what would happen in the event that U.K. voters chose to leave, there's little doubt that the impact would be negative.

Jamie Dimon, the chairman and CEO of JPMorgan Chase, for example, has said that up to a quarter of its 16,000 employees in the U.K. would lose their jobs -- though many of these would likely be redeployed to the European continent. And in Bank of America's case, KBW estimates that 1,386 positions would either be eliminated or relocated, equating to 0.7% of the bank's overall workforce.

It remains to be seen, of course, how the actual vote will turn out, the results of which should be known by the end of this week. In the meantime, investors should brace themselves for higher volatility.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.