Asian stock markets fell sharply Tuesday, building on the heavy selling in the U.S. a day earlier.

But the picture brightened a bit by late-session trading.

Japan’s Nikkei Stock Average for a time was on pace for its biggest one-day point drop since 1990. Instead, it merely logged its largest such decline since the U.K.’s vote to leave the European Union in June 2016. The index closed down 4.7% to 21,610.24.

Meanwhile, S&P 500 futures US:ESH8 rose nearly 60 points in an hour, pulling off their lows. They were recently down just 1.1%, compared with a loss of almost 3% earlier.

More declines loom for U.S. equities. After the S&P 500 slid 4.1%, the most in 6 1/2 years, futures US:ESH8 were recently down 2.8%, raising the specter of the index’s first drop of at least 10% in two years.

Overall, “it’s pretty crazy,” said Chris Weston, chief market strategist at IG in Melbourne, Australia. “There has been a large portion of people who don’t quite understand why things have happened.”

Some explanations for the heavy selling in recent days include the sharp start-of-year gains in bond yields, prospects of faster-than-expected interest-rate increases, particularly in the U.S., and some downbeat quarterly reports.

Some of those rate concerns have been dialed back as Monday’s global stock selloff sent Treasurys into a rally after a rough start to 2018. The 10-year yield TMUBMUSD10Y, 0.701% fell to 2.65% during Asian trading, from 2.85% late Friday in New York, and was recently at 2.69%.

That risk-off sentiment also bled into expectations for how quickly the Federal Reserve will raise interest rates this year.

Fed-fund futures show a 26% chance for three quarter-point rate increases this year, versus 35.5% on Friday, according to CME data. Meanwhile, the probability for two increases has risen to 35% from 27% and odds for four increases have slumped to 9% from 21%.

Also seeing safe-haven gains were gold US:GCJ8 and the Japanese yen. U.S. gold futures have risen 0.8% while the dollar USDJPY, -0.15% has dropped to ¥108.80 from ¥110 at the close of local stock trading Monday.

Taiwan’s Taiex XX:Y9999 slumped 4.9% to 10,404, the biggest fall in 6 1/2 years, while other indexes in the region fell 3% to 4%. Korea’s Kospi 180721, +0.25% closed down 1.5% to 2,443.31, with heavyweight Samsung 005930, -0.33% shedding 1% following the release of the company’s de-facto leader from prison.

Investors following strict rules-based approaches, such as risk-parity funds that attempt to maintain a constant level of volatility, were forced to sell because of the increased market fluctuations, Mr. Weston said.

The tumult has been exacerbated by sales of exchange-traded notes tracking implied volatility, which had become a popular way of betting on whether the recent calm in global equities would continue.

Many institutional investors were pausing to see where markets settled before taking big positions, said Lee Porter, managing director for Asia Pacific at brokerage Liquidnet.

“We’ve been through such a prolonged period of low volatility, and it was a question of when, not if, it would end,” he said.

With that lull shattered, many ETFs betting that volatility would remain low have suffered wrenching declines.

Japanese investment bank Nomura said Tuesday it would close one such fund early after the underlying index plunged 80% Monday, hitting a condition for early redemptions.

“We apologize from the bottom of our hearts for causing great inconvenience for the holders,” the fund said in a statement.

In Hong Kong, money flooded in from mainland China through the Shanghai Stock Connect, which allows reciprocal investment of stocks between the two cities. Net inflows hit the highest level since April 2015, when the link’s daily trading limit was last triggered. The Hong Kong Hang Seng HSI, +0.47% dropped 4.5% to 30,802.51, while the Shanghai Composite Index SHCOMP, +2.06% closed down 3.4% to 3,370.65.

Elsewhere, Australia’s S&P ASX 200 index XJO, -0.31% finished down 3.2% to 5,833.30.

Ric Spooner, chief market strategist at CMC Markets, said the writing has been on the wall for a retreat for weeks. All markets needed was for sentiment to turn, he said.

The S&P 500’s average forward price-to-earnings ratio from 2013 to 2017 was 16.1, with the 10-year Treasury yield averaging 2.17%. But both have been rising lately, “suggesting something might give,” Spooner said.

Even with the S&P 500 down 8% from its latest record closing set a week and a half ago, it is still above average at 16.75 after recently peaking at 18.5, he added.

Oil futures US:CLH8 fell 1% in Asian trading, putting Brent futures UK:LCOJ8 below $67 a barrel. Bitcoin BTCUSD, +0.79% briefly slumped below $6,000, after sitting at $10,000 on Thursday.

By Gregor Stuart Hunter and Kevin Kingsbury