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.

The tried - and - true retirement investing approach of yesterday doesn't work today.

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.

While this yield reduction may not seem drastic, it adds up: for a $1 million investment in 10-year Treasuries, the rate drop means a difference in yield of more than $1 million.

Today's retirees are getting hit hard by reduced bond yields-and the Social Security picture isn't too rosy either. Right now and for the near future, Social Security benefits are still being paid, but it has been estimated that the Social Security funds will be depleted as soon as 2035.

So what can retirees do? You could dramatically reduce your expenses, and go out on a limb hoping your Social Security benefits don't diminish. On the other hand, you could opt for an alternative investment that gives a steady, higher-rate income stream to supplant lessening 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.

Going beyond those familiar names, you can find excellent dividend-paying stocks by following a few guidelines. Look for companies that pay a dividend yield of around 3%, with positive annual dividend growth. The growth rate is key to help combat 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 3.97%. This compares to the Computers - IT Services industry's yield of 0% and the S&P 500's yield of 1.31%. The company's annualized dividend growth in the past year was 10.02%. Check Amdocs dividend history here>>>

H&R Block (HRB) is paying out a dividend of $0.46 per share at the moment, with a dividend yield of 3.10% compared to the Consumer Services - Miscellaneous industry's yield of 0% and the S&P 500's yield. The annualized dividend growth of the company was 17.19% over the past year. Check H&R Block dividend history here>>>

Currently paying a dividend of $0.68 per share, ONE Gas (OGS) has a dividend yield of 3.38%. This is compared to the Utility - Gas Distribution industry's yield of 3.43% and the S&P 500's current yield. Annualized dividend growth for the company in the past year was 1.52%. Check ONE Gas dividend history here>>>

But aren't stocks generally more risky than bonds?

It is true that stocks, as an asset class, carry more risk than bonds, but high-quality dividend stocks not only have the ability to produce income growth over time but more importantly, can also reduce your overall portfolio volatility relative to the broader stock market.

Combating the impact of inflation is one advantage of owning these dividend-paying stocks. Here's why: many of these stable, high-quality companies increase their dividends over time, which translates to rising dividend income that offsets the effects of inflation.

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

If you prefer investing in funds or ETFs compared to individual stocks, you can still pursue a dividend income strategy. However, it's important to know the fees charged by each fund or ETF, which can ultimately reduce your dividend income, working against your strategy. Do your homework and make sure you know the fees charged by any fund before you invest.

Bottom Line

Seeking steady, consistent income through dividends can be a smart option for financial security in retirement, whether you invest in mutual funds, ETFs, or in dividend-paying stocks.