It’s a conundrum: Despite Japan being a likely target of freshly erupting North Korean ire, traders still see the yen as a safe-haven play, and they’re pushing the currency higher.

The yen has surged, with the dollar fetching as little as 109.71 yen in Asia trade, down from 110.82 overnight. The dollar/yen was at 109.88 at 11:21 a.m. HK/SIN.

That’s in stark contrast to another country likely on the North’s target list, South Korea, which saw its currency, the won, markedly drop. The dollar was worth as much as 1,137.10 won in Asia trade on Wednesday, up from as little as 1,125.37 won earlier.

That came in the wake of the North Korean army saying in a statement carried by Pyongyang’s state news agency that it was “carefully examining an operational plan” for targeting the U.S. island territory of Guam with “enveloping fire.”

If Washington wished to avoid military action, it should stop “recklessly” provoking Pyongyang, a separate statement from another military spokesperson said, according to the stat-run outlet.

North Korea’s threats followed a blunt warning from President Donald Trump, which used language similar to the North’s own frequent saber-rattling: Pyongyang “will be met with fire, fury, and frankly, power, the likes of which this world has never seen before,” Trump said.

The president’s warning followed a Washington Post report, citing a confidential U.S. intelligence assessment, that claimed the pariah state had successfully produced a miniaturized nuclear warhead which could fit inside its missiles.

The current war of words appears so far confined between Pyongyang and Trump, but if the situation escalates, Japan could become a target.

But instead of outflows, the yen has seen safe-haven inflows.

Takuji Okubo, chief economist at Japan Macro Advisors, said that’s because Japan is a net overseas investor, both on the retail and institutional levels.

“For those Japanese investors who are invested overseas, having their assets in non-yen is a risk because they are exposed to foreign-exchange volatility,” he said on Wednesday. “So when these geopolitical risks, or any risks, get heightened, they want to reduce risk and that means unwinding overseas investments.”

The size of Japan’s overseas investments has been fairly large: At the end of 2016, Japan had around 159.195 trillion yen ($1.448 trillion) in overseas direct investment and 452.917 trillion yen in portfolio investment, according to data from Japan’s Ministry of Finance.

But South Korea’s won doesn’t have the same support. Okubo noted that South Korea is a net creditor with its financial institutions dependent on foreign credit.

Still, pulling funds back into yen amid a heightened possibility that Japan could be a military target may not be the most logical move.

“People with trigger fingers do a knee-jerk response. Never underestimate that factor,” Michael Every, head of financial markets research at Rabobank, said on Wednesday.

But he added, “It’s a traditional response, but personally I don’t see it as in any way rational.”

Indeed, he noted that the U.S. dollar also rose overnight, as another likely safe-haven play on the North Korea tensions.

But with both Japan and the U.S. likely drawn into any potential conflict, he pointed to the euro and the Swiss franc as better safe-haven choices.

Not everyone was on board, however, with pinning the yen’s climb on the tensions over North Korea.

Ed Rogers, CEO of Rogers Investment Advisors, said he doesn’t think the missile crisis had anything to do with the dollar/yen moves.

“Japan is one of the two primary targets for North Korean missiles, so why is it a safe-haven?” he asked, noting the U.S. would be the other target. “I’m quite dubious that because North Korea has marginally improved its missile capability, that’s having an impact.”

Rogers said the yen’s move wasn’t huge and he expected other news, such as fresh developments in the U.S. Department of Justice’s investigation of the Trump campaign’s Russia ties may be more relevant to any safe-haven move toward the yen.

“From an economic point of view, [Japan’s] economic data continues to be OK. Nothing’s fallen apart here,” he said. “If it continues on a moderate improvement, and wondering what’s going to go on for political troubles in the U.S., that’s a more reasonable answer for why the [yen] might start to strengthen.”

—Nyshka Chandran contributed to this article.