Stocks in Japan saw sharp declines on Tuesday following an overnight plunge on Wall Street as fears of the economic impact from the coronavirus outbreak spread. Returning from a Monday holiday, the Nikkei 225 closed 3.34% lower at 22,605.41 as shares of index heavyweight Fast Retailing dropped 4.15%. Earlier in the session, the index had plummeted almost 4%. The Topix index also declined 3.33% to end its trading day at 1,618.26. Shares of Fujifilm bucked the overall trend to gain 2.83% after local media reports that the Japanese government was considering the use of an anti-flu drug developed by a unit of the firm to treat the coronavirus.

Shares in mainland China were mixed on the day, with the Shanghai composite shedding 0.6% to around 3,013.05 while the Shenzhen component added 0.71% to 11,856.08. The Shenzhen composite gained 0.507% to about 1,943.17. South Korea's Kospi closed 1.18% higher at 2,103.61, following sharp losses seen on Monday as the country witnessed a spike in the number of coronavirus cases in recent days. On Tuesday, the country reported 60 new cases, bringing the number of infected cases to 893, to become the country with the most cases outside mainland China. Total fatalities now stand at 8. Seoul raised the coronavirus alert to the "highest level" over the weekend. Shares of Korean Air Lines rose 1.58% on Tuesday despite the airline announcing Tuesday that a cabin crew member had tested positive for the coronavirus, according to Reuters. Consumer confidence in South Korea dropped in February to a six-month low, South Korean news agency Yonhap reported Tuesday. The Composite Consumer Sentiment Index for February fell to 96.9, declining 7.3 points from its reading in January, according to data from the Bank of Korea. The Hang Seng index in Hong Kong was about 0.2% higher, as of its final hour of trading. Meanwhile, shares in Australia declined as the S&P/ASX 200 fell 1.6% to close at 6,866.60. Overall, the MSCI Asia ex-Japan index was 0.2% higher.

Political chaos in Malaysia

Elsewhere, markets in Malaysia were watched on Tuesday following recent developments that thrust the country into political uncertainty. The country's Prime Minister Mahathir Mohamad unexpectedly resigned on Monday, but reportedly agreed to stay on as interim leader until a successor is named. In afternoon trade on Tuesday, the FTSE Bursa Malaysia KLCI Index rose about 0.7%, after closing about 2.69% lower on Monday following news of the political upheaval. The country's central bank, Bank Negara Malaysia or BNM, said it was "closely monitoring conditions in the financial markets" after the latest political developments. "While ringgit movements will continue to be market determined, BNM's market operations will ensure sufficient liquidity and orderly financial market conditions," it said in a statement.

Coronavirus economic fears

In China, where the outbreak was first reported, 508 new cases and 71 additional deaths were reported as of Feb. 24. That brings the country's total to 77,658 confirmed cases, and 2,663 deaths. Concerns over the economic impact of disruptions caused by the virus outbreak have sent jitters across markets in recent weeks as some factories in China continue to remain shut due to containment measures. Becky Liu, head of China macro strategy at Standard Chartered Bank, told CNBC's "Street Signs" on Tuesday that China's first quarter GDP is expected to deteriorate "very materially" to only 2.8% while the full-year projection was at 5.5%. "This will be lower than the minimum GDP growth which is required to achieve so-called doubling GDP by 2020 target at 5.7%," Liu said. "From what we have seen so far this year, nothing is growing aside (from) something very small … such as online gaming," she said. "Even if the virus condition start(s) to get contained and we have real activities picking up in March, it's very difficult to see China having any material growth in the foreseeable future."

Even if the virus condition start(s) to get contained and we have real activities picking up in March, it's very difficult to see China having any material growth in the foreseeable future. Becky Liu Head of China Macro Strategy, Standard Chartered Bank

The outbreak in South Korea has also exacerbated concerns, given the country's importance in the global technology and semiconductor supply chains. "We've already seen how the China factory shutdowns have affected industry in the rest of the region as they haven't been able to get the intermediate goods that feed into their … production lines," said Alex Holmes, Asia economist at Capital Economics. While the effect on South Korea won't be as broad, "if they had to shut down factories across the country, then particularly the technology sector across the rest of the region who rely on Korea for things like … liquid crystal displays and semiconducting chips, they would really struggle," Holmes told CNBC's "Squawk Box" on Tuesday. Outside of Asia, Italy has also seen a surge in the number of people infected, with at least 130 reported cases. "The jump in cases outside of China raises the risk of a sharper Q1 2020 global economic slowdown," Kim Mundy, currency strategist at Commonwealth Bank of Australia, wrote in a note. "It also raises the risk that the economic disruption is more prolonged."

Overnight on Wall Street, fears of coronavirus contagion sent the Dow Jones Industrial Average plunging 1,031.61 points to close at 27,960.80. The S&P 500 slipped 3.35% to end its trading day at 3,225.89 while the Nasdaq Composite closed 3.71% lower at 9,221.28. The steep sell-off on Monday left the Dow giving up its gain for 2020, with the index now down 2% for the year. The S&P 500 also had its worst day in two years and wiped out its year-to-date gain as well.

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