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Kazakhstan’s $55 billion sovereign-wealth fund helped pull the country through the global financial crisis and offered funding for the country’s bid to host the 2022 Winter Olympics.

But the collapse in oil prices has hit Kazakhstan and its fund, Samruk-Kazyna JSC, hard. In October, the fund borrowed $1.5 billion in its first syndicated loan to help a cash-strapped subsidiary saddled with a troubled oil-field investment.

“Our oil company lost lots of its revenues,” says the fund’s chief executive, Umirzak Shukeyev. “Currently, we are trying to adjust to the situation.”

Funds like Samruk are at a critical juncture. For years, sovereign-wealth funds—financial vehicles owned by governments—swelled in size and number, fueled by rising oil prices and leaders’ aspirations to increase economic growth, invest abroad and boost political influence. A new wave of sovereign funds came from African countries like Ghana and Angola. Asian nations joined in with funds like 1Malaysia Development Bhd., or 1MDB.

The world’s sovereign-wealth funds together have assets of $7.2 trillion, according to the Sovereign Wealth Fund Institute, which studies them. That is twice their size in 2007, and more than is managed by all the world’s hedge funds and private-equity funds combined, according to J.P. Morgan Asset Management. The number of funds tracked by the Institute of International Finance is up 44% to 79 since the end of 2007. Nearly 60% of sovereign-wealth-fund assets are in funds dependent on energy exports.

Now, some funds are shrinking or are being tapped by governments as oil revenues fall. That is forcing them to borrow or sell investments, potentially pressuring global markets just as other investors are pulling back from risk. Saudi Arabia’s central bank, which functions in some ways like a sovereign-wealth fund as it holds significant reserves that are invested widely, has sold billions in assets this year. Norway says it plans to tap its fund, the world’s largest, for the first time in 2016.

The stress from low energy prices comes at a sensitive time. At least two funds are embroiled in controversy. 1MDB, which amassed $11 billion in debt, is the subject of at least nine investigations at home and abroad. One of its main financial backers was an Abu Dhabi fund. The head of South Korea’s fund stepped down in the wake of a public outcry over his plan to invest in the Los Angeles Dodgers baseball team.

Officials at 1MDB declined to comment. Previously, they said they would cooperate with all investigations.

Uncertainty

Adnan Mazarei, deputy director of the International Monetary Fund’s Middle East and Central Asia Department, says the worry is sovereign-wealth funds will be forced to sell during a period of already turbulent markets. “A withdrawal of assets by sovereign-wealth funds against the background of liquidity concerns could lead to large price movements,” he says. “Nobody knows how much or when but the concern is there.”

Uncertainty is stoked by the fact that many of the funds don’t disclose their size, holdings or investment strategies, making it hard to gauge what risk, if any, they pose to the global financial system. While others provide clear disclosure and have good governance, sovereign-wealth funds constitute a large blind spot in the markets, analysts say.

Global financial regulators are investigating “potential vulnerabilities” of sovereign-wealth funds that could affect world markets, the Basel-based Financial Stability Board said in September. An FSB spokesman says it is too soon to comment on the analysis.

Sovereign-wealth funds are largely funded by commodity revenue and foreign-exchange reserves. Their ranks can include government pension plans and economic development funds like Malaysia’s 1MDB and Samruk, which was established in 2008 to hold Kazakhstan’s state companies with an eye to selling them off and investing the proceeds.

As emerging markets grew wealthier, many countries started sovereign-wealth funds. More than three-quarters of assets are in funds from emerging markets, with many of the biggest based in the Middle East and Asia. The latest wave comes from Africa.

“In the old days you built armies,” says Jayne Bok, head of sovereign advisory in Asia for consulting firm Towers Watson. “Now you build a sovereign-wealth fund.”

Many have kept funds in low-risk, highly liquid investments. ​ But as assets grew and global yields tumbled, some invested more in less-liquid assets. They bought real estate, took big stakes in companies and made other hard-to-trade investments.

Government investment funds have borrowed roughly $100 billion since 2007, according to figures reported to Dealogic and analyzed by The Wall Street Journal. About two-thirds of that borrowing has come from net oil exporters such as Bahrain and Kazakhstan.

Selling is picking up. Sovereign-wealth funds yanked roughly $100 billion from asset managers in the six months to Sept. 30, according to Morgan Stanley. “The countries that have accumulated these vast reserves over the last 20 years will be dipping into those reserves,” Martin Gilbert, chief executive of $430 billion Aberdeen Asset Management, told reporters in November. “It could be a difficult 2016.”

The Saudi Arabian Monetary Agency sold​close to $2 billion of European shares this year through November, according to Nasdaq. Its reserves have fallen 13% to $647 billion in the 12 months through the end of October. The agency didn’t respond to inquiries.

In South Korea, where the government tracks foreign ownership of stocks, Saudi state-owned investment funds have sold local stocks for six months straight totaling roughly 3.6 trillion won ($3.1 billion), according to people familiar with the matter and official regulatory data.

The International Monetary Fund, examining the fallout of low oil prices, said in October that a large-scale liquidation of government funds’ extensive bondholdings could drive up interest rates. “A substantial change in the path of asset accumulation by sovereign wealth funds,” it said, “will likely have a direct effect on financial markets.”

U.S. Federal Reserve economists have estimated that five-year Treasury rates would rise by about 0.40 to 0.60 percentage point if foreign official inflows into U.S. Treasurys were to decrease by $100 billion in any given month. That would push rates to their highest level since 2011.

Predicting a sovereign-fund selloff’s impact is difficult because many funds disclose almost nothing. “The problem with sovereign wealth funds is that too often they prove to be ‘black boxes’ into which funds are deposited in a non-transparent fashion,” says Sarah Chayes, a former special adviser to the chairman of the U.S. Joint Chiefs of Staff and a senior associate at the Carnegie Endowment for International Peace, where she researches corruption.

There is a push to get funds to adhere to a voluntary code of conduct known as the Santiago Principles, which calls for annual reporting, clear governance rules and effective risk management, among other things. The chairman of the International Forum of Sovereign Wealth Funds, Adrian Orr, has said he wants members to adopt the highest standards of transparency and governance.

“Not doing so bankrupts the principles, leaving them worthless for all,” Mr. Orr said in September. He also runs New Zealand’s Super Fund, which invests government money to fund future pension payments.

But Mr. Orr has little power to get funds to comply, as membership in the forum doesn’t require funds to implement the high standards he is urging. At least five of the 29 forum members don’t publish public annual reports. At least four don’t disclose their asset size.

Singapore’s GIC and the Qatar Investment Authority were named to the forum’s board in September. While both have signed up to the Santiago Principles, GIC is only partially compliant and Qatar is noncompliant, according to analysis by GeoEconomica, a Swiss political-risk advisory firm. Neither discloses how much money it manages. Qatar doesn’t publish an annual report.

“We do not report on investment specifics, to safeguard our competitive edge,” says a GIC spokeswoman. The GIC takes the Santiago Principles seriously, she says. The Qatar fund said last year it would publish an annual report, which its website says is “coming soon.” A fund spokesman declined to comment. “It is not part of IFSWF’s mandate to comment on member practices,” Mr. Orr says in an interview.

The case of 1MDB

The situations at Malaysia’s 1MDB and Abu Dhabi’s International Petroleum Investment Co., or IPIC, are examples of exploitation of weak oversight at government investment funds, says Ms. Chayes, the former U.S. special adviser.

Executives at 1MDB are selling assets to repay debt. The new management at IPIC is now trying to determine how the fund guaranteed bonds and investments by 1MDB valued at more than $7 billion, say people familiar with the matter.

IPIC and U.A.E. spokesmen declined to comment for this article.

The deals between IPIC and 1MDB began in 2009 with a public promise by Abu Dhabi to invest $1 billion in projects alongside the newly formed 1MDB. It is unclear how the commitment transformed into guarantees for 1MDB. Those include $3.5 billion of bonds, about $1.5 billion of interest on those loans over their lifetime and $2.3 billion of investments with a Cayman Islands-registered fund, according to company documents and people familiar with the deals.

The transactions occurred under IPIC’s managing director, Khadem Al Qubaisi, who took over in 2007. Under Mr. Al Qubaisi, the fund’s net debt grew almost tenfold to $24.6 billion.

Executives now digging into IPIC’s operations also found a subsidiary of the fund bought shares of a publicly listed construction company from an associate of Mr. Al Qubaisi’s and bought large amounts of land from the private investment vehicle of the fund’s chairman, Sheikh Mansour Bin Zayed Al Nahyan, say people familiar with the matter. Sheikh Mansour didn’t respond to inquiries.

In a rare presidential decree in April, Mr. Al Qubaisi was replaced at IPIC. A London-based representative of Mr. Al Qubaisi says he declined to comment. The new managing director, Suhail Al Mazrouei—he is also the country’s energy minister—ordered a review of the company with a view to returning to its original mandate of investing in oil and gas projects. Mr. Al Mazrouei didn’t respond to inquiries.

Long-running concerns about sovereign-wealth funds have centered on the idea that they don’t behave like traditional institutional investors, which typically invest only to produce returns. Sovereign funds often answer to top government officials and may invest not only to produce returns but also to further government initiatives, usually focused on economic development or diplomacy.

Those concerns peaked before the financial crisis when the funds were seen as “agents of the state executing ‘checkbook’ foreign policy strategies,” said the sovereign-wealth forum’s Mr. Orr in September.

But after the financial crisis hit, political concerns faded, says Jukka Pihlman, head of central banks and sovereign-wealth funds at Standard Chartered PLC. “Many countries just wanted the capital,” Mr. Pihlman says. “The tables turned quite significantly.”

Other countries’ sovereign-wealth funds quickly came to the aid of the Russian Direct Investment Fund, or RDIF, when U.S. and European sanctions restricted business between the fund and Western companies. The fund is on the U.S. sanctions list drawn up to punish Moscow for annexing Crimea last year.

In June, Russian President Vladimir Putin hosted his annual dinner for foreign investors in a seaside palace built for Peter the Great. Around the table were officials of sovereign-wealth funds who together manage trillions in assets, according to RDIF, which organized the gathering. Representatives of funds from China, Abu Dhabi, Qatar, Bahrain, South Korea, Iran, France and Italy attended the conference during which the meeting was held, according to a Russian-language statement on the Kremlin’s website.

Korea Investment Corp., the Abu Dhabi Investment Authority and Bahrain’s Mumtalakat fund confirmed their officials attended the conference. The Qatari and Kuwaiti funds declined to comment. The Chinese, Italian and French funds didn’t respond to inquiries.

One important new guest: Prince Mohammed bin Salman, the 30-year-old Saudi Arabian defense minister and second in line to the throne. He agreed the next month to invest $10 billion in Russia. A few months later, a Kuwaiti sovereign fund pledged $500 million, raising its total commitment to $1 billion.

“The headline may seem political, but, in fact, it is not a blank check,” a Saudi official says, adding that Russian investments offer among the highest yields in the world. Kuwait Investment Authority executive director Ahmad Bastaki declined to comment.

​“For us, it’s about finding additional money to invest in Russia,” says Kirill Dmitriev, the Russian fund’s chief executive. The fund is “nonpolitical” and focused on returns, he says. “Those sanctions really do not affect our work much.” ​​