So, Mr. and Ms. Investor, sick of making next to nothing on your bank savings and money market funds? How would you like to make a nice, round 9% over the next 12 months?

That’s what you might earn in dividends from one of the world’s best-known corporations. And, of course, there’s a chance of making a gain on the stock price as well.

The catch? Well, OK, there is a small one. The company in question is British Petroleum (Stock Quote: BP), owner of the well spewing oil in the Gulf of Mexico. At the moment, BP is a kind of poster child for the dangers of pursuing yield without assessing all the risk.

Dividends are a share of corporate profits paid to shareholders. Dividend yield is the annual dividend divided by the current stock price. Many investors are tempted to see dividend yield the same way they see savings yield, or the interest you could earn on a certificate of deposit or savings account.

But there’s a big difference — risk. Most bank savings are protected from loss by federal insurance, dividends are not. BP’s dividend yield is high because the dividend has so far held steady while the share price has fallen. The stock is trading at around $31 a share, down from more than $60 in the middle of April.

The problem: What you make in dividends can be more than offset by what you lose if the stock price falls. That’s a risk with all dividends, not just BP’s.

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To further complicate the BP situation, President Obama has criticized the dividend payment BP is scheduled to make on June 20. Obama feels BP should conserve its cash to pay for clean up and claims of Gulf Coast residents and businesses that have been hurt by the spill.

Obama said BP should not nickel and dime people and businesses in the Gulf while spending $50 million on image advertising and $10.5 billion on dividends.

BP isn’t likely to cancel the June dividend, which it is obligated to pay to investors who owned the stock before May 5. But in a June 4 conference call with analysts, BP executives did not commit to paying the dividend for the following quarter, saying a decision would be made in July.

Boards of directors have the power to do just about anything they want with the dividend — pay it, raise it, reduce it or cancel it.

BP is an enormous company and has said it can afford the Gulf cleanup and compensation. But analysts say the company’s future profitability could be hurt by lawsuits and regulatory problems. It’s not at all clear, for example, that the company will be able to continue the deep-water drilling it had planned.

Historically, stocks of dividend-paying companies have been safer and more stable than stocks of non-payers. But all stocks have risks, and a dramatic rise in dividend yield can be a red flag.

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