Competition is also increasing in the region.

Li's China-ASEAN Investment Cooperation Fund invests primarily in ASEAN markets, some of which present more opportunities than developed markets.

The fund's first two investments were in last October and in January.

"Investment in Southeast Asia will still focus on infrastructure, resource and consumer products," says Li.

"As long as the economy is stable, there are good investment opportunities. But the challenges in this market remain, such as information asymmetry and foreign exchange control."

TPG provides a clear example of the learning process that funds have gone through. The TPG Newbridge Asia III fund that invested before 2005 reported internal rates of return of 31 percent.

But the TPG Asia V fund, which invested before 2012, returned just 2 percent because of failures at companies such as Li Ning Co Ltd, a Chinese sportswear firm, and PT Delta Dunia Makmur Tbk, an Indonesian mining group.

The environments in the other large markets in the region have a variety of outcomes.

South Korean companies, for example, were hit hard by capital flight in recent years. The government has intervened through various means, including the use of the State-owned Korea Development Bank (KDB) to invest in companies.

Of course, the KDB is a competitor to the PE outfits, but even with government help, there are plenty of companies looking to shore up their balance sheet.

Another developed market, Japan, remains a hard nut to crack.

"Japanese private equity is almost non-existent. It is a very underdeveloped area," says Haig Oghigian, partner at international law firm Baker & McKenzie. "There are few players compared with private equity in the US, for example, or Europe."

Developing markets in the region offer the greatest opportunities, but need to persuade funds. Some have done so, but the investments are relatively low.

Last May, a consortium led by Warburg Pincus made the largest PE investment yet in Vietnam — a $200 million deal with Vingroup, to build shopping malls. It is the first investment in Vietnam by the company that has been in Asia since 1994. Lower inflation since mid-2012 is once again attracting investors.

But that is dwarfed by the investment that KKR made in China last October. The US firm bought a 10 percent stake in Haier Group, China's largest maker of white goods, for $550 million. It was one of a number of deals of that size.

ASEAN countries such as Malaysia and Singapore are doing well, say investors, but Thailand is less stable because of the political turmoil. Other markets are too small.

China remains the single largest market for PE investors, as well as the most attractive.

Temasek Holdings, Singapore's State investment company, has about 23 percent of its portfolio in China deals.

But a long suspension of initial public offerings made it impossible for funds to exit out of their China investments.

The ban on new A-shares (shares in companies on Chinese stock markets and denominated in yuan) was only recently lifted. But Li from the China-ASEAN Investment Cooperation Fund says it is hard to predict whether investors are ready to part with their cash in China.

"Chinese PE is shifting its focus from the domestic market to the international market. This is part of the bigger trend of Chinese companies going out."

Limited partners (LPs) of the actual fund, as opposed to those who invest in the funds, take a very small proportion of the international market.

"Although they are growing very fast, there is still a lack of mature LPs. There is no mature LP culture," says Li.

However, change is underway. Last May, financier Fang Fenglei, chairman of Hopu Investment Management, started raising more than $2 billion for the Hopu Master Fund II, to invest in China and abroad.

As they expand internationally, Chinese funds have to compete with established international partners.

KKR, for example, is one of the most committed to the region. The company has made other investments, including small deals in Indonesia.

Haier wants to expand internationally to build on its position as a leading white goods maker by sales, but its market share is still in single digits. KKR has the know-how and, hopefully, the connections, to make that happen.

"We believe KKR's sufficient capital and rich experience in international mergers and acquisitions will accelerate the integration of Haier's white electric platform," said Tan Lixia, the company's vice-chairman.