The gain in the yen followed what was already a significant rally during the last two weeks of July. Salespeople on Wall Street trading desks said the move stemmed from hedge funds cashing out on bets that paid out if the yen weakened to a certain level.

The gains were a turnaround from earlier this year, when the yen depreciated to its weakest point in more than two decades. A soaring dollar, a struggling global economy and worldwide inflation pushed it down.

“The yen has been volatile in recent trading sessions,” said Kamakshya Trivedi, co-head of global foreign exchange, interest rates and emerging-markets strategy research at Goldman Sachs.

The yen is the world’s third-most-traded currency after the dollar and euro, making it an important piece of financial markets. Investors have typically bought it as a haven when financial markets fall apart. Even when an earthquake and tsunami roiled Japan in March 2011, the yen rocketed.

The recent swings are the latest example of how the Federal Reserve’s interest-rate increases are causing tumult in markets around the world. Currency markets were placid for years after the 2008 financial crisis, but over the past year they have sprung back to life.

The exaggerated moves basically amount to a bet on which central banks will deal with inflation fastest and most aggressively. After 2008, central banks across the world slashed interest rates to zero to support the global economy. Now they are lifting interest rates at different paces, making currencies a hot trade again.

In general, investors have rewarded countries whose central banks appear most willing to fight inflation. That is one reason the U.S. dollar has soared this year, as the Fed has aggressively raised interest rates. Wednesday’s inflation report, though, complicates the Fed’s decision on how much to raise interest rates next month. A half-point rate increase in September is on the table, but a 0.75-point rise remains possible.

The Bank of Japan, on the other hand, has stressed that it will continue its easy-money policy. At a news conference in July, Bank of Japan Governor

Haruhiko Kuroda

said it would be unreasonable to tighten borrowing conditions to shore up the currency. He also pushed back against the widely circulated argument that the gap between U.S. and Japanese interest rates is the main driver behind the yen’s weakness against the dollar.

“The U.K. and South Korea, where there is no huge interest-rate gap, have also seen their currencies fall significantly,” Mr. Kuroda said.

A shift in underlying dynamics over the past few decades has made the yen more susceptible to speculation. James Malcolm, head of foreign-exchange strategy at UBS. said the yen used to play a bigger role in global trade.

“Things have changed in terms of how the foreign-exchange market operates,” Mr. Malcolm said. “Japanese banks that used to be big players are now modest players, and there is much more high-frequency trading activity.”

He and others said automated trading had inflated the yen’s moves. Once a trade becomes popular, some algorithms pile in, exaggerating a currency’s moves up or down regardless of economic fundamentals.

The yen has been one of the worst-performing currencies in developed markets this year, making it appealing to investors looking to bet on the dollar rally losing steam.

Keith DeCarlucci, chief investment officer at the London-based hedge fund Melqart KEAL Capital, said the best wager on a falling dollar is buying derivatives that pay out when the yen appreciates. He said that many investors went short on, or sold, the yen, and that it is poised for a reversal.

“I could easily see the yen print ¥125 against the dollar,” said Mr. DeCarlucci. Around ¥133 currently buys one U.S. dollar.

Jeff Yarmouth, head of foreign-exchange options in the Americas at UBS, said gauges used in the derivatives market indicate that investors are closing positions that paid out when the dollar rapidly climbed to more than two-decade highs against the yen.

“We have seen unwinds,” Mr. Yarmouth said. He added that derivatives trades betting on a much weaker dollar aren’t on clients’ radar yet.

Though the dollar is still up significantly for the year, it has been unable to break new highs since mid-July, largely drifting as investors gather more data on the outlook of the U.S. economy and consumer prices. The WSJ Dollar Index, which measures the dollar against a basket of 16 currencies, is up about 8.7% so far this year. In July, it was at times up more than 11%.

—Megumi Fujikawa in Tokyo contributed to this article.

Write to Julia-Ambra Verlaine at julia.verlaine@wsj.com