NEW YORK (TheStreet) -- With markets sinking in Asia and Latin America, investors have been dumping emerging-market bonds.

During the past year, emerging-market bond mutual funds lost 9.3%, according to Morningstar. In the fourth quarter of 2013, unhappy shareholders withdrew $4 billion from the funds, a sizable outflow for a category that has $69 billion in assets.

At a time when some economies are slowing, the emerging markets face clear headwinds. But there are good reasons to think that the bond funds can deliver single-digit returns this year. Many countries still have solid balance sheets. And after the recent downturn, plenty of bonds sell at bargain prices and offer compelling yields.

"There is tremendous value in some emerging-markets bonds vs. what you can get in the U.S.," says David Robbins, portfolio manager of TCW Emerging Markets Income (TGEIX - Get Report).

Robbins says that yields are 4.5% on U.S. corporate bonds that are rated double-B, the highest level in the below-investment grade universe. In contrast, some investment-grade corporate bonds in Brazil yield 6.4% or more.

As recently as a year ago, emerging-market bonds were recording steady gains. At a time when developed markets struggled with sluggish economies and huge debt burdens, many countries in Latin America and Asia recorded solid growth.

Then last May, Federal Reserve Chairman Ben Bernanke mentioned the idea of tapering the central bank's bond purchases. In response, most bonds sank. Losses were particularly severe for emerging markets. Investors worried that interest rates in the U.S. would rise, making yields in emerging markets less competitive.

Since then, other problems have plagued emerging markets. Reports suggested that growth in China was slowing. That signaled trouble for Chile and other countries that rely on exports to Asia. In countries such Turkey and Venezuela, government policies appeared to be weakening balance sheets. With investors pulling cash out of Latin America and Asia, emerging-market currencies slipped against the dollar. When foreign currencies fall, overseas bonds can lose their value for U.S. investors.

For all the problems, the outlook for many countries remains bright. In countries such as Mexico and Indonesia, the economies are growing and balance sheets remain strong. To take advantage of the higher yields of the emerging markets, consider a mutual fund with a record of delivering steady returns. Solid performers include Goldman Sachs Emerging Market Debt (GSDAX - Get Report), JPMorgan Emerging Markets Debt (JEDAX - Get Report), and TCW Emerging Markets Income.

TCW ranks as one of the top performers. During the past five years, the fund returned 15% annually, outdoing its average peer by 4 percentage points. The portfolio managers can keep up to one-third of their assets in bonds that pay interest in local currencies. But these days the fund only has 6% of assets in local currencies.

The portfolio managers worry that currencies can continue sinking. When that happens, dollar investors can record losses. For protection, the fund has most of its assets in emerging-market bonds that are denominated in dollars. Those can hold their value when local currencies fall. The big position in dollar bonds has helped the TCW fund outdo competitors in the past year.

TCW portfolio manager David Robbins is particularly keen on Russian bonds. Although the economy is sluggish, the country has a rock-solid balance sheet that has been propped up by oil revenues. "Russia can afford to buy back all its debt tomorrow," says Robbins.

During the past five years, JPMorgan Emerging Markets Debt returned 13% annually. Portfolio manager Pierre-Yves Bareau is sticking with dollar bonds. He is keen on bonds from Indonesia, which yield around 7%. The country's debt is equal to about 26% of the gross domestic product.

In contrast, many developed countries are burdened by debt levels equal to more than 70% of GDP. Indonesia's currency has been weakening, a development that has troubled investors. But a cheaper currency will boost many Indonesian companies by lowering the cost of exports.

"The weaker currency will make the economy more competitive," Bareau says.

Goldman Sachs Emerging Market Debt returned 13% annually during the past five years. The fund has most of its assets in government bonds. The portfolio managers have a big weighting in Mexico. As labor costs increase in China, more U.S. companies are shifting production to Mexico.

"The U.S. direct investment should help the Mexican economy and the currency," says portfolio manager Yacov Arnopolin.

At the time of publication, Luxenberg had no positions in funds mentioned.

This article represents the opinion of a contributor and not necessarily that of TheStreet or its editorial staff.