Ever since J. Pierpont Morgan was simultaneously reviled and celebrated a century ago, the titans of banking have enjoyed a special place in the popular imagination.

Their economic clout, political influence and sheer wealth have inspired justified awe; the alumni of a single firm, Goldman Sachs, include the current Treasury secretary, the White House chief of staff, New Jersey’s last governor, the World Bank boss, the head of Italy’s central bank, and the Nature Conservancy’s incoming president.

Yet there are questions about what modern investment banks do — and last week’s ructions at Lehman Brothers only make these questions trickier.

Until about a year ago, the main complaints about investment banks concerned conflicts of interest. By collecting all kinds of financial business under one roof, they created all kinds of opportunities to take advantage of customers.

Investment-bank brokerage departments execute buy and sell orders on behalf of outside clients, supposedly at the best price possible. But the proprietary trading desks make money by trading the banks’ own capital; the temptation to use knowledge of outside clients’ strategies to boost prop-desk profits is, shall we say, considerable.

Long-Term Capital Management, the hedge fund that blew up in 1998, was partly a victim of brokers who were copying its trades, making them impossible to exit in a crisis.

In 2000, the tech and telecom bubble burst, showing further conflicts of interest. Investment-bank research departments, which advise fund managers on what to buy, were caught pushing stocks that they knew to be worthless — because the banks collected fees from those worthless companies.

The banks also were capable of tilting the playing field the other way. Initial public offerings were underpriced, meaning that the firms issuing stock were cheated while the banks got to distribute cheap IPO shares to their favorite fund managers.

These conflicts smelled bad but fell short of real scandal. The customers were grown-ups who understood the game; if they chose to patronize the banks, they were presumably benefiting from their services. But the bursting of the credit bubble has conjured fresh concerns: not about banks’ treatment of customers, but of their own money.

We now know that the models banks have used to measure their investment risks are flawed, to put it charitably. They base assessments of future risk on how markets have performed in the most recent few years, so the inflation of a bubble causes the models to proclaim that the world is growing more stable.

Even more bizarrely, the models factor in market behavior only during normal times — explicitly excluding the most extreme 1% of past experience. As the hedge fund manager, David Einhorn, says, “This is like an air bag that works all the time, except when you have a car accident.”

This might not matter if bankers were simply blowing their own money. But when Bear Stearns collapsed in March, the Federal Reserve had to pump in taxpayer-backed loans to get another bank to buy the wreckage. Moreover, the bankers are playing with the money of outside shareholders, too. Even though investment bankers frequently own stock in their own firms, this creates an incentive to take risks incautiously.

Which brings us to last week’s events at Lehman Brothers. On Thursday, Lehman removed its president and finance chief after announcing that it had lost $2.8 billion — about $30 million a day — in the three months to June. This was confirmation that one of the few supposedly smart risk managers on Wall Street had not been so smart after all.

But the real shock lay not just in Lehman’s willingness to gamble with investors’ capital but in the suspicion that the firm had been misleading those investors.

At the end of the previous quarter, Lehman reported a profit. The S&P 500-stock index had fallen by a tenth, but Lehman announced that it had a large basket of corporate investments that had somehow gained value. Lehman admitted that it held a huge portfolio of risky debt but claimed that the associated losses would be minimal. “The worst is behind us,” Lehman’s boss declared in April.

Well, now we know it wasn’t. And whether or not Lehman’s earlier results were intended to mislead, there is a broader point: Banks have enough wiggle room in how they value their assets that they can fudge their profits, at least in the short term. How, on this basis, can outsiders muster the confidence to invest in them — especially since opaque reporting is packaged along with cavalier risk taking?

For most of their history, investment banks have made enough money to paper over the cracks in their business model. America went on a debt binge, and the bankers who designed the debt were at the center of the party. But over the past half-decade, Goldman Sachs is the only major investment bank whose share price has beaten the S&P 500. Perhaps the titans’ structural flaws are catching up to them.

Mr. Mallaby is a fellow for International Economics with the Council on Foreign Relations. © 2008 The Washington Post.