“Don’t fight the Fed” has long been a profitable strategy for stock market speculators. Following this maxim on August 17, 2007, a week after the Federal Reserve injected a massive dose of liquidity to contain the subprime mortgage problem, would have produced a tidy profit. The Dow-Jones Industrial Average has risen by about 5% since then. But those who think this Wall Street aphorism also signals the end of the crisis that began last summer would do well to revisit the history of the Great Crash. The Federal Reserve will provide only a temporary reprieve if mortgage credits are fundamentally unsound.

The stock market collapse in October 1929 marked the end of prosperity and the beginning of a depression. Most people do not realize that the Federal Reserve succeeded in controlling the damage — for a while. On October 30, 1929, a day after the 16 million share debacle, the Federal Reserve Bank of New York pumped reserves into the banking system to provide much needed cash to Wall Street investors. Two days later the Federal Reserve Bank lowered its lending rate — the discount rate — by a full percentage point, making it easier for banks to borrow reserves.

The central bank’s activism prevented the crash from triggering a shortage of liquidity. And Wall Street cheered. Less than six months after the Great Crash stock prices had erased almost all of their losses. The Dow Jones Industrial average closed at 301 on Friday, October 25, 1929, immediately before the precipitous drop. It reached 294 on April 17, 1930, eliminating all but 2% of the big decline.

We all know what happened after that. America had sidestepped a liquidity crisis only to fall into the worst economic depression ever. The problem in the fall of 1929 was not just a shortage of liquidity. A more fundamental malaise stalked the economy: Industrial production had peaked in June 1929. When the underlying weakness intensified in spring 1930, the stock market began a sickening two-year slide to less than 15% of its pre-crash level.

The mortgage crisis that began this past summer precipitated a shortage of liquidity. Institutions that needed to raise funds for immediate payments were denied access to short-term credit markets. The Federal Reserve provided additional funds by injecting reserves into the banking system. The central bank then signaled its willingness to provide more help by cutting the discount rate by .5%. The stock market celebrated the end of the liquidity crisis, recovering all its losses and then some.

The Federal Reserve’s injection of liquidity will work its magic unless there is a more fundamental malaise because mortgages are flawed credits rather than just temporarily illiquid. And no one knows for sure, not the banks and not the Federal Reserve. The credit-worthiness of mortgages will become known over time, as homeowners make, or fail to make, their monthly payments.

Then why is the stock market celebrating? For the same reason it did after the Great Crash. In 1929 everyone worried about a replay of the then most recent panic — the Panic of 1907. Without a central bank in October 1907 there was no lender of last resort to provide liquidity. The demand for cash led to a run on the banks and a sharp contraction in the economy. In 1929 the Federal Reserve demonstrated it could do the job of injecting liquidity. The stock market rallied — at least temporarily — because there would be no replay of 1907.

Today the Federal Reserve has shown that it has the will to prevent a liquidity crisis. The stock market is celebrating because the Fed has succeeded before. On October 20, 1987, the day after the largest one-day percentage price decline in stock prices, the central bank prevented a meltdown in the nation’s payments system by flooding the country with liquidity. The Fed encouraged banks to borrow whatever they needed at the discount window to keep the system afloat.

But what if the current problem is a credit crisis, where investors have underestimated the true probabilities of default on mortgages, rather than a liquidity crisis, a temporary inability to sell the assets for what they are really worth? Central bankers are not in business to rescue institutions or individuals who have made poor credit decisions. That would just encourage irresponsible decision-making in the future, the so-called moral hazard problem.

The Federal Reserve can prevent the mortgage crisis from disrupting the economy only if the fundamental credits are sound, in other words, if bank balance sheets are creditworthy but just illiquid. That, however, remains to be seen. The stock market apparently thinks the central bank can make all the risks disappear. Investors would do well to remember that the Chairman of the Federal Reserve is named Ben Bernanke, not Harry Houdini.

Mr. Silber is the Marcus Nadler Professor of Finance and Economics at the Stern School of Business at New York University and author of “When Washington Shut Down Wall Street: The Great Financial Crisis of 1914 and the Origins of America’s Monetary Supremacy.”