Asian stock markets presented a varied picture on Tuesday, as the initial optimism following the ninety-day cessation of hostilities in the trade dispute between the United States and China diminished, with experts cautioning that President Donald Trump's policy stances remained subject to swift alteration.

In a joint statement, the United States and China announced significant reductions in reciprocal tariffs. The US will decrease tariffs on Chinese imports from a peak of 145% to 30%, while China will lower its tariffs on US goods from 125% to 10%. This measure provides additional time for further discussions following the weekend's negotiations in Geneva, Switzerland, which the US characterized as having achieved "substantial progress."

The outcome considerably exceeded most expectations, providing investors with renewed confidence, stated Stephen Innes of SPI Asset Management.

He said in a commentary, "It's clear this diplomacy was carefully planned. But it looks good, and the results are important. It shows that even this government understands how constant tariffs hurt the economy."

Significant obstacles persist in the ongoing negotiations between Beijing and Washington, and numerous Asian nations have yet to secure their own agreements to mitigate tariffs.

Beijing’s continued frustration regarding the trade dispute is evident, with President Xi Jinping asserting that trade wars are mutually detrimental and that “Coercion or dominance inevitably results in self-imposed isolation.”

The Nikkei 225 index in Tokyo experienced a significant surge, rising 1.6% to reach 38,232.21, with prominent gains observed within the automotive sector, notably Toyota Motor Corp. and Suzuki Motor Corp., which saw increases of 3.7% and 4.3% respectively.

Nissan Motor Co.'s shares rose by 3.4% following a report from Japan's national broadcaster, NHK, indicating the company intends to dismiss over 10,000 employees, bringing the total job cuts to 20,000 as part of its restructuring initiatives. The corporation was scheduled to release its financial performance for the previous fiscal year later that Tuesday.

South Korea's Kospi remained largely stable, closing at 2,606.46.

Following a 3% surge the previous day spurred by the announced agreement between Chinese and U.S. officials to suspend and decrease tariffs, Hong Kong's Hang Seng index experienced a 1.5% decline, reaching 23,189.15 amidst substantial divestment in technology stocks.

The Shanghai Composite index advanced marginally by 0.2% to reach 3,376.22, while Taiwan's Taiex experienced a significant gain of 1%.

Australia’s S&P/ASX 200 index rose by 0.5%, reaching 8,274.70.

On Monday, the two biggest economies in the world agreed to cut most of the taxes on goods traded between them.

This surge propelled the S&P 500 upward by 3.3%, bringing it within 5% of the peak reached in February. Having previously declined by almost 20% from this zenith, the index rebounded last month, buoyed by expectations that President Donald Trump may reduce tariffs following the conclusion of trade agreements with other nations.

The main index for many 401(k) accounts is now higher than it was on April 2, which Trump called "Liberation Day." On that day, he put in place big tariffs around the world, which made people worry about a possible recession caused by the country itself.

Both the Dow Jones Industrial Average and the Nasdaq composite experienced significant increases, rising 2.8% and 4.3% respectively.

Following a rally on Monday, oil prices retreated, with U.S. benchmark crude declining by 22 cents to $61.73 a barrel and Brent crude, the international standard, falling by 25 cents to $64.72 a barrel.

The U.S. dollar appreciated against various currencies, including the euro, Japanese yen, and Swiss franc, on Monday. However, by early Tuesday, its value had declined against the Japanese yen, trading at 147.98 yen compared to 148.47 yen, while concurrently strengthening against the euro, reaching $1.1113 from $1.1088.

The U.S.-China trade dispute was temporarily suspended following an agreement the United States unveiled last week with the United Kingdom, which is set to reduce tariffs on numerous U.K. imports to 10%, though its full implementation is still weeks away.

Forthcoming economic data, notably reports on inflation and American consumer confidence, may reveal the extent of the economic damage inflicted by uncertainty surrounding tariffs.

A significant number of retailers saw their stock rise, primarily due to sourcing a large proportion of their merchandise from China and other parts of Asia; notable gains included Best Buy, which saw a 6.6% increase, and Amazon, which experienced an 8.1% rally.

U.S. smaller companies, whose prosperity is more closely tied to the domestic economy's health than that of their larger competitors, experienced substantial increases, as evidenced by the Russell 2000 index's 3.4% rise.

Clothing companies that procure a significant portion of their materials from China also saw gains. Lululemon's stock surged by 8.7%, and Nike's increased by 7.3%.