Coming off a terrible May, the stock market started out June with its worst day of the year. After a first quarter of 2012 in which stocks could do no wrong, investors are seeing the flip side of the risk-reward equation as concerns about trouble spots throughout the global economy are rising to a fevered pitch.

When risk levels start to increase overall, it's helpful to know which stocks could see some of the wildest moves. With that goal in mind, let's take a closer look at the 30 stocks of the Dow Jones Industrial Average (INDEX: ^DJI) to look at one measure of how vulnerable they are to further big market declines.

You'd beta know about volatility
The measure I'm using to assess risk among the Dow 30 is known as beta. Beta measures volatility in relation to the overall stock market, so a stock that has a beta value of 1 is just as volatile as the market. Betas less than 1 indicate a smoother ride for shareholders, while stocks that have betas higher than 1 have given their shareholders a lot more bounces along the way.

You can look at beta values over different time frames. When I looked at both five-year and one-year betas, the three stocks at the top of the list were the same. Let's take a closer look at these three volatile stocks.

Bank of America (NYSE: BAC)
Bank of America had the highest betas over both periods, with the bank stock coming in with more than double the volatility of the overall market during the past five years and a 1.82 beta over the past year. Since the five-year period covers the entire financial crisis, the figure may actually seem pretty low.

B of A remains a volatile stock, with shares having run from $5.56 per share at the end of 2011 to climb above $10 briefly during March before falling back to today's levels around $7. Although it passed the Federal Reserve's latest stress tests, it still hasn't started paying more than a token $0.01-per-share dividend, and many still fear that B of A is on rocky ground. As a speculative play, it could soar in a recovery or plunge again in another systemic crisis.

Alcoa (NYSE: AA)
The aluminum maker has also seen extreme volatility in recent years, with a five-year beta of 2.14 and a one-year figure of 1.64. Because of its sensitivity to global economic activity, Alcoa has moved sharply in both directions as issues arise, apparently get resolved, and then come back again to threaten overall growth.

Alcoa is unquestionably a cyclical stock, and so it's at a delicate point right now. It has been reducing capacity because of low prices and weak demand, but if the market recovers, Alcoa's stock could jump just as fast as it's fallen over the past year.

Caterpillar (NYSE: CAT)
Like Alcoa, Caterpillar's stock is closely tied to the health of the economy. With its construction and mining equipment businesses, Caterpillar needs to see economic strength around the globe to drive purchases of its equipment.

With betas of 1.85 for the past five years and 1.52 for the past year, Caterpillar's recent stock action gives hints about both possible outcomes for the company. If the economy returns to an upward track, then the stock could rise as strongly as it did during its 60%-plus jump from last October to February. If it starts slumping, then the stock's 25% drop since 2012's highs could be the tip of the iceberg.

Honorable mention
Which stock comes in at No. 4 depends on which timeframe you look at. Over the past five years, American Express is the surprising winner with a beta of 1.84. It's important to remember that AmEx suffered more than other credit card network companies during the financial crisis because it also retains the credit risk of its cardholders.

More recently, JPMorgan Chase (NYSE: JPM) has the fourth-highest one-year beta of 1.46. Clearly, much of that volatility stems from its recent trading debacle, but the episode also underscores the inherent riskiness of financial institutions generally in the current economic environment.

Looking for safety
Before you put too much stock in beta, keep in mind that it's purely a backward-looking measure. Just because a stock has a low beta value over the past year or five years doesn't mean it will continue to be safe, and what was a volatile stock can turn calm when conditions change. Still, knowing how a stock has behaved in the past is of some value in trying to figure out what may come next.

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