The most vivid image amid last week’s financial turmoil came from Calabasas, Calif., home to the nation’s biggest mortgage lender, Countrywide Financial Corporation. At a retail branch down the street from Countrywide’s headquarters, depositors reportedly “besieged” a representative on Thursday, demanding to get their money out.

The next day similar scenes played out at other Countrywide branches, conjuring those grainy black-and-white images of Depression-era bank runs. “I know a little about what happened in the 1930s,” one customer told Reuters. “It smells like it could be the same.”

These vignettes may have been swollen out of proportion by the journalistic magnifying glass, but they capture the essence of the moment. For the chaos in the markets has become as scary and as arbitrary as an old-fashioned bank run. Fear has taken over, and sound institutions are suffering along with poorly managed ones. It is a reminder that the markets are an exquisite instrument for pricing risk and allocating capital — except during those brief periods when they go stark raving nuts.

Consider the case of Countrywide, which finances nearly one in every five home mortgages, almost all of them to “prime” borrowers, rather than the riskier “subprime” sort.

Despite that commanding position, Countrywide’s stock price has been halved since the start of this year. In fact, it’s fallen so much that you could buy the entire firm for less than it would cost to buy its assets: It’s as though the market were valuing a piggy bank at less than the value of the coins it held.

If Countrywide is getting short shrift from the stock market, its fate in the debt market is altogether worse. The company has access to enough cash to pay everything it owes everyone for more than a year, analysts say.

But investors who used to lend to Countrywide by buying its short-term bonds — known as “commercial paper” — now refuse to do so. Whether or not those nervous depositors at Countrywide branches are the advance guard of a general panic, the company has already suffered the bond-market equivalent of a bank run.

So markets are punishing Countrywide irrationally — and dozens of other basically sound companies are caught up in the maelstrom.

Despite some tut-tutting from inflation hawks, the Fed had no choice but to throw a lifeline to the financial system on Friday, softening the terms on which it stands ready to lend to banks and signaling that it will cut interest rates if need be. At times like these, the Fed’s responsibility to stand tough against inflation is trumped by its responsibility to stand tough against financial panic. When nobody is willing to put money in banks and thereby keep them solvent, it is the Fed’s duty to serve as the lender of last resort. But the mystery is why the panic took hold. After all, markets are supposed to be efficient: If irrational money is fleeing institutions such as Countrywide, smart money is supposed to smell an opportunity and come to the rescue. In the stock market, reassuringly, some of this is happening.

Countrywide shares bounced up a bit on Friday, and it’s striking that financial companies — which have more to lose from a credit squeeze than industrial or service firms —have nonetheless been the stock market’s top performers this August.

But the bond market is a different story. Bargain-seeking contrarians have yet to rescue borrowers from sky-high interest rates. After the Fed’s intervention Friday, interest rates on some commercial paper actually rose.

What is going on here? Financial theory says that if interest rates spike to an irrationally high level, new capital will flow into the lending market and rates will come back down.

It shouldn’t matter that most investors are scared or dumb or inattentive. So long as there are a few smart guys with an eye for opportunity, any mispricing in financial markets will be traded away.

But this theory has a limit, and as Berkeley’s Brad DeLong has argued recently, we are up against that limit now.

Efficient-market theory assumes away important real-world frictions; it supposes, for example, that the smart guys can borrow all they need to trade on market inefficiencies until they go away. But when market inefficiency is created by a credit squeeze, the theory may become self-canceling.

The hedge funds and other smart investors that would normally leverage themselves up to take advantage of distressed bond markets now have difficulty doing so — because the credit squeeze that creates the investment opportunity also affects their own access to credit.

And so, for the moment, a panicky majority outguns the smart commandos. The normal rule in markets, that the sophisticated money sets prices, is turned upside down.

Given time, normality will reassert itself. The smart guys will persuade enough investors to back them with enough capital, they will profit mightily by acting as contrarians, and the bond market will stabilize. Given time — but how much time? Institutions faced with the prospect of a bank run don’t have time on their side.

Mr. Mallaby is a fellow for International Economics with the Council on Foreign Relations.