By Sarah Turner, MarketWatch

SYDNEY (MarketWatch) -- Asia stocks gained on the last trading day of a broadly positive month that nonetheless saw a sharp divergence in performance through the region's major markets.

Friday trading had Japan's Nikkei Stock Average finishing 0.5% higher, and Australia's S&P/ASX 200 index advancing 0.6%, while South Korea's Kospi traded up 0.1%, shaking off early losses.

Chinese markets were also higher, with Hong Kong's Hang Seng Index up 0.6%, and Shanghai Composite Index up 0.3%, although the Shanghai benchmark remained near four-year lows.

Asia's advance followed modest gains for U.S. equity markets on Thursday, with upside there limited by uncertainty that U.S. politicians will succeed in hammering out a deal to prevent more than $600 billion in tax hikes and spending cuts from taking place automatically in January.

Dampening sentiment, Republican U.S. House Speaker John Boehner said Thursday morning there has been "no substantive progress" in negotiations on the so-called fiscal cliff, briefly rattling Wall Street.

IG Index strategist Stan Shamu said the back-and-forth on the fiscal cliff would likely fuel market volatility through the end of December.

"Many [are] now convinced that negotiations will mirror that of last August's debt-ceiling disaster and go right down to the wire. As a result, a choppy last month of the year is probably the most likely scenario, disappointing those hoping for a Santa Claus rally," Shamu said.

The term "Santa Claus rally" refers to a year-end gain for shares that tends to start in December.

Still, U.S. economic data Thursday suggested the recovery continued, and Japanese data out Friday resulted in a set of consumer inflation, unemployment and household spending data that, while remaining relatively weak, either met or exceeded economist expectations.

After the data, the Japanese government announced that it has approved its second stimulus package in a little more than a month, consisting of 880.3 billion yen ($10.7 billion) in spending.

Japanese shares saw choppy trading on Friday, rising, then falling, then rising again. The Nikkei Average gained 5.8% overall in November, helped by speculation that next month's general election will result in the introduction of some radical policies to help the economy.

Exporters have performed particularly well over the past month after the prospect of more monetary-policy easing sent the yen down more than 3% in November.

Yen weakness re-emerged during Friday's stock session, with the dollar rising to  ¥82.41 by the end of trading, up from  ¥82.11 in early action, while the euro hit a seven-month high against the yen.

Some currency-sensitive firms subsequently headed higher, with Nikon Corp. (NINOF) gaining 4.5%, Fujitsu Ltd. (FJTSY) up 2%, and Citizen Holdings Co. (7762.TO) ahead by 2.5%.

Elsewhere, Mitsubishi Heavy Industries Ltd. (7011.TO) climbed 3%, and Hitachi Ltd. (HIT) advanced 4.2%, after the firms said they will merge their thermal-power businesses and related units in a joint venture by 2014.

Hong Kong saw gains in the banking sector, with HSBC Holdings PLC up 1.3%, and Bank of Communications Co. (BCMXY) rising 2%.

Elsewhere in the Hong Kong financial sector, insurer Ping An Insurance Group Co. (PNGAY) climbed 1.8%, while China Life Insurance Co. (LFC) improved by 0.9%.

On a more downbeat note, however, People's Insurance Co. Group of China -- commonly known as PICC -- priced its initial public offering at 3.48 Hong Kong dollars (45 U.S. cents), a level near the low end of its indicative price range of HK$3.42- 4.03.

The firm makes its trading debut on Dec.7, and PICC's listing is set to become the largest IPO -- at a projected $3.1 billion -- for a Chinese state-owned company since 2010.

Hong Kong's blue-chip Hang Seng Index has gained 1.9% so far this month, in contrast to the Shanghai Composite, which has dropped 4.8%, and the Shenzhen Composite, which is down by more than 11% amid concerns over the path of future corporate earnings.

Deutsche Bank cut its view on shares of Hong Kong-listed brokers on Friday, in part due to a challenging outlook for the mainland stock markets. It downgraded Haitong Securities Co. to hold from buy, with the firm's shares losing 1% in Hong Kong.

Hong Kong Exchanges & Clearing Ltd. (HKXCY) fell 1% after announcing a plan to raise HK$7.75 billion via a private placement to fund its acquisition of the London Metal Exchange.

In South Korean trading, auto giant Hyundai Motor Co. (HYMTF) fell 1.5% but heavyweight electronics giant Samsung Electronics Co. (SSNLF) supported the index with a 0.1% advance.

The Kospi is up 1.3% so far in November, while Sydney's S&P/ASX 200 declined 0.2% over the month.

In Australia on Friday, however, the benchmark garnered support from a strong performance in the mining sector, after metals advanced in New York trade on Thursday.

Of the majors, Rio Tinto Ltd. (RIO) climbed 2.8% after announcing cost plans on Thursday, while Fortescue Metals Group Ltd. (FSUMY) rose 1.3%.

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