Will rising interest rates cause a collapse in stock valuations this year?

It's a question investors have been struggling to answer, as evidenced by the selling that greeted testimony from Alan Greenspan Tuesday, which appeared to move the economy one step closer to a rate hike. Greenspan -- who is scheduled to address Congress again Wednesday -- told the Senate Banking Committee that signs of deflation have dissipated and the financial system looks properly braced for a monetary tightening.

Tuesday's stock market action illustrated the specific concern about valuations. While the pain of higher interest rates is conventionally thought to land most squarely on economically sensitive companies, it has been the high-priced Nasdaq -- which fell 2.1% Tuesday to the Dow's 1.2% dip -- that has borne the brunt of selling since rate jitters first started spreading in late January.

Bulls argue that if the Federal Reserve raises rates over the summer, it will be a sign that the economy is getting better. This, in turn, suggests that earnings will accelerate and that investors will pay a higher price for stronger growth.

Bears, on the other hand, say price-to-earnings multiples and interest rates always move inversely. They argue that P/Es will contract as rates rise, because investors won't be willing to pay the same price for the same amount of earnings when other investments, such as bonds, are suddenly yielding more.

For example, let's say XYZ stock is trading for $10 and produces 50 cents in annual earnings. If the 10-year Treasury is yielding 3.75%, XYZ's earnings yield of 5% might seem reasonable. But if the 10-year note shot up to 4.5% because of expectations for a Fed rate hike, XYZ suddenly becomes less desirable.

Several analysts also point out that the price of a stock is the discounted present value of the future dividends to investors. In other words, when interest rates go up, the present value of future cash flows goes down, and the P/E should fall.

Of course, higher interest rates can have a direct impact on the bottom line, as corporate borrowing costs creep higher. And Tom McManus, equity analyst at Banc of America, notes that low interest rates have stimulated demand for such items as homes and cars. As rates move up, he said, this demand could well fall off.

"I think if rates do rise, even in a strengthening economy, over the medium term it would probably lead to some P/E compression," said Cliff Asness, principal at AQR Capital Management.

The Fed model, which compares the 10-year Treasury yield with the earnings yield on the S&P 500, has already pointed to some deterioration in the stock market's relative valuation over the past month.

Back on March 16, the S&P 500 was considered to be about 33% undervalued relative to bonds, meaning the price of the S&P would need to increase by 49%, or the 10-year note yield would need to rise by 49%, before the earnings yield and the Treasury yield were equal. (A 33% decline requires a 49% rise to retrace.)

Today, thanks to a surge in interest rates, the S&P 500 index is considered to be about 20% undervalued, meaning that the 10-year yield or the price of the S&P would need to rise by 25% before the yields are even.

Jordan Kahn, a portfolio manager at Berger & Associates and contributor to Street Insight, said the model "could move toward equilibrium simply by rates moving higher, without much of a rise in stocks."

Kahn said he would expect P/Es to contract going forward if future rate hikes are the result of higher inflation. "Higher inflation leads to lower P/Es, as investors begin to place less value on any future earnings stream," he said.

The consumer price index rose to a larger-than-expected 0.5% in March, or 0.4%, excluding food and energy. The S&P 500 currently trades at 18.5 times this year's operating earnings.

Jeff Bagley, portfolio manager for McCabe Capital Managers and contributor to Street Insight, said inflation can be a good or bad thing for stocks. "Inflation, depending on the extent to which companies have pricing power for their final products, can either enhance or crimp corporate earnings," he said.

Still, Bagley believes that P/Es are likely to decline going forward. "Rising interest rates are not good for stock valuations," he said. In this environment, "sector selection becomes critical," and investors must steer clear of industries that are particularly sensitive to changes in rates, he said.

Bullish analysts generally dismiss concerns about P/E contraction, noting that earnings growth is likely to be very strong this year. But Tobias Levkovich, an equity strategist at Smith Barney, said earnings rose more than 20% in 1994, and yet stocks still slumped, as the Fed embarked on a series of rate hikes.

"We would point out that ... robust economic growth ... may lead to higher 10-year bond yields and P/E multiple compression, as was the case in 1984 and 1994," he wrote in a recent note. "We would be very wary in just assuming that stock prices go up when GDP and earnings growth are in place -- interest rates expectations could interfere with that conclusion."

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