If you are a shareholder in a so-called socially responsible or sustainable mutual fund, you may also be an owner of BP, the company responsible for the environmental catastrophe in the Gulf of Mexico.

When BP's oil rig in the Gulf of Mexico exploded on April 20, the company was a major holding of the Dow Jones Sustainability Index, which calls itself an index of "the leading sustainability-driven companies worldwide."

BP was also held by Pax World Funds ("sustainable investing is a better, smarter way to invest"), by the MMA International Fund, which is part of a fund group that is "guided by Christian values," and by the Legg Mason Social Awareness Fund, which, as of March 31, had BP as its single biggest holding.

These are not anomalies. When Cary Krosinsky, an editor of a book called "Sustainable Investing: The Art of Long Term Performance," tallied up the holdings of about 350 socially responsible investment (SRI) funds from around the world, he found that at the end of 2008, BP was the second biggest holding, in terms of how much money the funds had collectively invested. The five biggest holdings were Royal Dutch Shell, BP, Nokia, Vodafone and HSBC Holdings.

What's more, BP and Shell aren't the only oil companies held by the social funds. The biggest holding of a mutual fund called the Sentinel Sustainable Core Opportunities Fund, which says it "screens for fundamentally strong, well-managed companies with sustainable business models and a commitment to corporate responsibility," was, as of March 31, believe it or not ... Transocean, the world's largest offshore drilling contractor, which operated the Deepwater Horizon rig for BP.

While no mutual fund manager could have foreseen the oil rig explosion, you've got to wonder how a fund with the word sustainable in its name could have as its biggest holding an offshore oil drilling company. I emailed Sentinel to try to probe their reasoning a bit. You won't be surprised to hear that they declined to be interviewed.

So what does the BP-SRI connection tell you? At the very minimum, it suggests that any investor in a mutual fund that calls itself socially responsible, sustainable, green, blue or any other color would do well to dig deep beneath the magazine ads and website fluff to understand what the fund is really all about. (Disclosure: I'm a small investor in Calvert and Domini Funds, and a believer in the SRI idea.) Some SRI funds still focus on feel-good, negative screens that shield investors from weapons, tobacco and alcohol, and don't get much more analytical than that. (See Socially Responsible Investing's Silly Screens)

As Cary Krosinsky, who now works for Trucost, a research firm that focuses on environmental risks, told me: "The SRI world in the U.S. developed largely around social issues, and it's still largely focused on values. Some funds don't look as closely at the environment."

The other reason why many SRI funds bought BP is that they want to track stock-market indices, and so they seek exposure to the oil and gas sector. Otherwise, when oil company stocks boom, the performance of these funds will suffer.

For social funds that want to buy oil-and-gas stocks, BP and Shell were the obvious choices because they have had more progressive policy positions on climate change and they invested in renewable energy.

Bennett Freeman, senior vice president for sustainability research and policy at Calvert, says that BP under its former CEO, Sir John Browne, in the late 1990s and early 2000s, was a pioneer in its approach to corporate responsibility. "It's easy and appropriate and necessary to criticize them now," Freeman says, "but these were the guys who broke the crockery in the industry on climate change. The same on human rights."

Interestingly, Calvert never held BP in its traditional mutual funds, which invest only in companies that meet all of its environmental, social and government standards. But Calvert did own BP in a large-cap value fund which is one of its SAGE funds. SAGE stands for "Sustainability Achieved Through Greater Engagement." The theory is that by engaging in shareholder advocacy, Calvert will try to to improve the social, environmental and financial performance of its SAGE holdings, which include ExxonMobil, Walmart and Duke Energy. Shareholders in SAGE funds, in other words, cannot expect purity or anything close. Even so, Calvert sold BP in June, explaining its reasoning in this thoughtful and strongly-worded statement.