Long-term investors like companies with strong fundamentals. In the words of investing guru Warren Buffett, you want to find "a wonderful company at a fair price," then hold on for the long term as this wonderful company simply executes on its rock-solid business model. Share prices and dividends will eventually follow suit and reward investors for finding the true gems on the market. Most of the 30 stocks in the Dow Jones Industrial Average (DJINDICES:^DJI) fit this description to a "T" and should be suitable vehicles for investors with long time horizons.

The opposite of this ideal long-term holding would be a so-called "story stock" -- you know, the kind of stock that sways back and forth like a candle in the wind. The kind whose price can swing dramatically in response to unimportant or irrelevant news items. The kind where solid balance sheets, generous cash flows, and high-quality execution of the core strategy don't seem to matter.

And you'll find a few of these on the Dow as well. That's no knock on the Dow itself, or on any of the stocks I'm about to discuss. Story stocks are a vital part of the market, and it makes sense to find a few on the most elite of index rosters. The question is: What should a traditional Dow investor do with these often uncomfortable stocks?

Bank of America (NYSE:BAC) has become one surprising example of story-driven investing. The megabank took the 2008 crisis on the chin, nearly wiping out its formerly rock-solid dividend policy. Share prices plunged as the drama developed and remained more than 90% below peak pricing as recently as 2011.

The bank's shares have soared recently, rising 88% over the last year. You can certainly argue that some of this surge comes from improved fundamentals, but reading financial statements will not tell you the whole story. One major catalyst here is the idea that Bank of America might be allowed to increase its dividends again after regulators nixed that strategy for half a decade. Yes, the final outcome here rests on B of A getting its fundamental house in order -- but one headline could change the entire investment thesis for a ton of investors, and any hint of moving toward a stronger dividend (or not!) will move the stock by several percentage points.

This uncertainty and story-focused action have turned a boring bank stock into the most volatile ticker on the Dow. It sports a five-year beta value of 2.4, far ahead of the market average of one. The Dow's second- and third-highest beta values belong to Alcoa (NYSE:AA) and Caterpillar (NYSE:CAT), at 2.1 and 1.9, respectively.

These runners-up follow the same economic trends as Bank of America. When the global economy seems primed for fresh infrastructure investments, Alcoa will supply materials while Caterpillar sells construction machinery to support the building boom. And Bank of America will pump capital into the same projects. This volatile trio is waiting for the same macro-level catalyst.

BAC Dividend Chart

BAC Dividend data by YCharts.

Alcoa slashed its dividends at the ankles in 2009, just like Bank of America, and investors are still waiting for a sign of stronger payouts. Caterpillar is different because, thanks to its healthy cash flows, it never cut its dividends, and it shows in the stock price. Alcoa and Bank of America are still looking for that magic turn of phrase that would restore their share prices to pre-crisis levels, while the Cat never stopped more or less pacing the Dow.

BAC Total Return Price Chart

BAC Total Return Price data by YCharts.

Story stocks versus fundamental fortresses
When it comes to these two types of investments, buy the former if they're cheap and you foresee their stories reaching a happy ending; buy the latter if you just want rock-solid returns and a good night's sleep.

Fool contributor Anders Bylund holds no position in any company mentioned. Check out Anders' bio and holdings or follow him on Twitter and Google+.

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