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Stock market watchers are hoping U.S. Federal Reserve chairman Ben Bernanke, seen here Feb. 29, 2012, will announce a third round of quantitative easing.JONATHAN ERNST/REUTERS

For much of the past three years, the world's stock markets have relied on central bankers the way junkies rely on drug dealers. The question now is whether the next fix will come – and what will happen if the markets are forced to go cold turkey.

More than any other single factor, the recovery in equities has been fuelled by the largesse of the world's leading central banks, especially the U.S. Federal Reserve Board, as those key financial institutions have expanded their balance sheets to prime the struggling global financial system and keep money flowing.

From the Fed's initial ramp-up of quantitative easing (now known as QE1) that revived stocks from the depths of the bear market in March, 2009, to the launch of the European Central Bank's long-term refinancing operation (LTRO) last December, equities climbed higher each time central banks poured new cash into the financial system.

Last week, rumblings that the Fed is looking into another round of quantitative easing (which would be QE3, for those keeping score) underpinned another strong gain for stocks – despite the fact that the Fed is highly unlikely to announce any such moves at Tuesday's policy-setting meeting.

Balance sheet expansion takes place when a central bank increases the supply of money in the economy, typically by creating funds that it uses to purchase bonds or other credit instruments from private investors. The Fed is probably looking at further balance-sheet expansion only as a months-down-the-road contingency in case Europe's sovereign-debt crisis deteriorates. Still, the debate over the likelihood of QE3 is likely to dominate stock market chatter in the coming months.

"The key catalyst for the equity rally, in our view, was global central bank easing," said Barry Knapp, head of U.S. portfolio strategy at Barclays Capital in New York, in a recent research note. "It served to mitigate (for now) the two most significant external risks to U.S. equities: European bank deleveraging and slowing emerging markets growth. Any sign the spigot might be closing could prove disruptive."

Balance-sheet expansions by central banks affect stock prices by shifting the equity risk premium (ERP) – the difference between the earnings yield on stocks (annual earnings per share as a percentage of stock price) and the yield on government bonds. This reflects the higher returns that investors demand from equities to compensate them for the perceived risk in these investments relative to the near-zero risk of a stable government bond (the 10-year U.S. Treasury is a typical benchmark). When the ERP falls, that pushes stock valuations higher, and vice-versa.

Mr. Knapp found that since the financial crisis began, ERPs have consistently declined during each new Fed program of balance-sheet expansion (QE1, QE2 and the so-called "Operation Twist"). The resulting rise in price-to-earnings multiples fuelled stock-market rallies each time.

Similarly, research by Montreal-based BCA Research Inc. found that lower interest rates – the typical result of central-bank monetary easing, whether it be balance-sheet expansions or more traditional cuts in policy rates – have long been closely linked to lower ERPs. In the past decade, global equities have twice staged rallies that more than doubled their prices after global central banks reached extreme levels of easing; those same conditions are in place again this year.

"Expansive monetary policy almost always eases equity multiple compression, allowing stock prices to rise," BCA said in a report last week. "With virtually all central banks in easing mode, and in the absence of negative exogenous shocks, the tendency will be for stocks to rise."

In a recent report, Goldman Sachs strategist Kamakshya Trivedi and economic analyst Stacy Carlson also saw grounds for bullishness. "Easing is positive on net for the overall global growth picture, which should provide support for asset markets," they argued. "Indeed, stabilizing growth and easier policy should be a sweet spot for equity markets."

But Mr. Knapp cautioned that based on the market's experience during the current Fed easing cycle, "The end of [each QE]program poses a problem."

He said ERPs began to creep upward again toward the end of QE1 and QE2, and surged once the program was over. And after each program, ERPs ultimately rose higher than they had been before the program began. This suggests investors have become increasingly accustomed to having the central bank's liquidity support. With Operation Twist set to end in June, we could be on the cusp of another rise in ERPs.

Indeed, the stock market actually seemed disappointed in late February when Fed chairman Ben Bernanke, in his semi-annual report to Congress, sounded more positive about the economy – because, presumably, that implies no more QE is coming down the pipe.

"The fact that this reaction was mostly negative points to a surprising fragility in the prices of risk assets," said Capital Economics chief international economist Julian Jessop in a note to clients. "If equity investors are banking both on stronger economic growth and further monetary easing to support current valuations, they are almost certain to be disappointed."

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