Here's an eye-opening statistic: older Americans are more afraid of running out of money than of death itself.

And unfortunately, even retirees who have built a nest egg have good reason to be concerned-with the traditional approaches to retirement planning, income may no longer cover expenses. That means retirees are dipping into principal to make ends meet, setting up a race against time between dwindling investment balances and longer lifespans.

In today's economic environment, traditional income investments are not working.

For example, 10-year Treasury bonds in the late 1990s offered a yield of around 6.50%, which translated to an income source you could count on. However, today's yield is much lower and probably not a viable return option to fund typical retirements.

The impact of this rate decline is sizable: over 20 years, the difference in yield for a $1 million investment in 10-year Treasuries is more than $1 million.

In addition to the considerable drop in bond yields, today's retirees are nervous about their future Social Security benefits. Because of certain demographic factors, it's been estimated that the funds that pay the Social Security benefits will run out of money in 2035.

So what's a retiree to do? You could cut your expenses to the bone, and take the risk that your Social Security checks don't shrink. Or you could find an alternative investment that provides a steady, higher-rate income stream to replace dwindling bond yields.

Invest in Dividend Stocks

We feel that these dividend-paying equities-as long as they are from high-quality, low-risk issuers-can give retirement investors a smart option to replace low-yielding Treasury bonds (or other bonds).

Look for stocks that have paid steady, increasing dividends for years (or decades), and have not cut their dividends even during recessions.

One way to identify suitable candidates is to look for stocks with an average dividend yield of 3%, and positive average annual dividend growth. Many stocks increase dividends over time, helping to offset the effects of inflation.

Here are three dividend-paying stocks retirees should consider for their nest egg portfolio.

Amdocs (DOX Quick QuoteDOX - Free Report) is currently shelling out a dividend of $0.57 per share, with a dividend yield of 5.21%. This compares to the Computers - IT Services industry's yield of 0% and the S&P 500's yield of 1.29%. The company's annualized dividend growth in the past year was 10.02%. Check Amdocs dividend history here>>>

First American Financial (FAF) is paying out a dividend of $0.61 per share at the moment, with a dividend yield of 3.61% compared to the Insurance - Property and Casualty industry's yield of 0.68% and the S&P 500's yield. The annualized dividend growth of the company was 1.89% over the past year. Check First American Financial dividend history here>>>

Currently paying a dividend of $0.28 per share, Hanmi Financial (HAFC) has a dividend yield of 3.32%. This is compared to the Banks - West industry's yield of 2.41% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 8%. Check Hanmi Financial dividend history here>>>

But aren't stocks generally more risky than bonds?

Overall, that is true. But stocks are a broad class, and you can reduce the risks significantly by selecting high-quality dividend stocks that can generate regular, predictable income and can also decrease the volatility of your portfolio compared to the overall stock market.

A silver lining to owning dividend stocks for your retirement portfolio is that many companies, especially blue chip stocks, increase their dividends over time, helping offset the effects of inflation on your potential retirement income.

Thinking about dividend-focused mutual funds or ETFs? Watch out for fees.

You may be thinking, "I like this dividend strategy, but instead of investing in individual stocks, I'm going to find a dividend-focused mutual fund or ETF." This approach can make sense, but be aware that some mutual funds and specialized ETFs carry high fees, which may reduce your dividend gains or income, and defeat the goal of this dividend investment approach. If you do wish to invest in a fund, do your research to find the best-quality dividend funds with the lowest fees.

Bottom Line

Regardless of whether you select high-quality, low-fee funds or stocks, looking for a steady stream of income from dividend-paying equities can potentially lead you to a solid and more peaceful retirement.