Commentary

Bears Shouldn’t Do Math

Since the stock market’s March 9 low, the S&P 500 rose from 676.53 to 929.93 and the Dow Jones industrials jumped from 6,547 to 8,574 by May 8 — gains of 37.5% and 31%, respectively. Such stunning gains encouraged bears to dust off the same argument they used two months ago to predict the S&P 500 could fall to 500 and the Dow to 5,000.

A May 11 Wall Street Journal headline claims, “By Most Measures, Stocks No Longer Look Cheap.” In this article, Tim Lauricella alludes to three measures of valuation: a trailing ratio of S&P 500 stock prices to operating earnings over the past 12 months; a forward ratio of stock prices relative to estimated earnings over the next 12 months; and a nostalgic ratio of stock prices to a 10-year history of inflation-adjusted earnings. The latter is thought to be “the most widely followed of these barometers … created by Yale Professor Robert Shiller.”

The trouble is that such valuation measures were also cited in a March 9 Wall Street Journal front page feature — “Dow 5,000? There’s a Case for It” by Annelena Lobb. “Looking solely at valuations,” she wrote, “the S&P at 500 isn’t necessarily a wild stretch.”

[S]tock valuations are not just a matter of opinion, gyrating unpredictably between waves of optimism and pessimism.”

Relying on Professor Shiller’s valuations, Barrons’ March 7 cover story claimed, “the Dow could fall a further 25%, to 5,000, and the S&P could drop to about 500.” In a March 12 commentary on Forbes.com, Nouriel Roubini used forward P/E ratios to predict that “even in the best scenario” the S&P was unlikely to exceed 500-600 this year. The following Sunday, The New York Times posted Shiller’s chart emphasizing that the ratio of stock prices to earnings “hasn’t fallen as far as the market bottoms of 1932 and 1982.”

By March 23, after the DOW had risen 14% from the bottom, Mark Gongloff’s “Ahead of the Tape” column in The Wall Street Journal suggested “such rallies are fairly typical of the worst markets.” He compared it to other “dead cat bounces” between 1929-32. Relying on Shiller’s figures, Gongloff said “the S&P is priced about 13 times earnings. … But that ratio has fallen below 10 in the grimmest bear markets. … A 30% plunge in the S&P to 530 would take its P/E ratio to 10 in a hurry.”

All of these gloomy projections of falling stock prices have been based on falling valuations, not falling earnings. We’re told the ratio of stock prices to earnings could supposedly fall below 10 simply because that happened before, in years like 1982.

But stock valuations are not just a matter of opinion, gyrating unpredictably between waves of optimism and pessimism. On the contrary, the graph shows that P/E ratios mainly depend on interest rates. It makes that point by simply turning the P/E ratio upside down, resulting in an earnings-price ratio or “earnings yield.”

The previously mentioned New York Times graph highlighted the fact that the P/E ratio briefly fell to seven in early 1982, which is equivalent to an E/P ratio of 14.3 (one divided by seven). My graph, however, reveals that such a low multiple (high E/P ratio) made sense in January 1982 only because the yield on 10-year Treasuries was 14.6%.

S&P 500 Ratio of Trailing Earnings to Price Tracks the 10-year Treasury Bond Yield

This graph bases the earnings-price ratios on trailing earnings over the past four quarters rather than relying on analysts’ estimates of the future or on Shiller’s decade of ancient history. I used annual figures from the Economic Report of the President for 1980-88 because quarterly data from the Standard and Poor’s Web site don’t go back that far. After 1988, bond yields in the graph are for the last month of each quarter because that captures changing rates better than a three-month average.

Since 1960, the yield on 10-year Treasury bonds averaged 6.68%, while the earnings yield averaged 6.43. The earnings yield on stocks rarely deviates much from the coupon on bonds partly because stocks and bonds compete with each other, and because stock prices gauge the discounted present value of expected earnings. Expectations of future earnings differ from recent reported earnings, of course, yet nonetheless involve estimating changes from that starting point.

Note that the E/P ratio was lower than bond yields toward the end of the recessions of 1991, 2001 and 2008. That is because trailing earnings are an increasingly bad indicator of future earnings as recessions near an end. Year-to-year comparisons of earnings become easy to beat during the early stages of recovery.

The relatively low E/P ratio in 1999, despite a rising bond yield, does suggest some unduly euphoric momentum, though scarcely a “bubble.” Conversely, the E/P ratio was higher than the bond yield in 2005-2006, suggesting prescient pessimism about future earnings but also accurate optimism about rising bond prices (falling yields).

It is not hard to envision future earnings disappointments as a result of higher tax rates on companies or shareholders, health care price controls or cap and trade schemes. But these are threats to earnings, not to multiples. They are to some extent reflected in the weakness in stock prices ever since the election.

Any big drop in P/E multiplies, by contrast, requires a big increase in bond yields. It is certainly possible to envision massive federal borrowing and aggressive Fed easing culminating in a sizable increase in long-term interest rates. Yet such a future of “reflation” and “crowding out” presupposes faster growth of overall demand, gross domestic final sales. In that case, earnings would be rising so the net effect on stock prices might well be positive. Bearish economists, by contrast, typically assume depressed demand and deflation — forecasts impossible to reconcile with the double-digit interest rates required to push the E/P ratio to 10 or more.

I first met Bob Shiller in the early 1980s, when I invited him to speak at Lew Lehrman’s Institute in Manhattan. He thought stocks were grossly overpriced then too. Indeed, Shiller always seems to see the current P/E ratio as too high relative to some historical average. But the stock multiple is not a mean-reverting series. On the contrary, the height of today’s P/E ratio relative to the past tells us nothing except that (1) interest rates are far below average and (2) future earnings are very likely to rise from today’s depressed base.

Unless those who have spent the past two months predicting P/E ratios of 8-10 are also predicting a tripling of long-term rates, their forecasts of stock prices are inconsistent and unworthy of the slightest attention.

Alan Reynolds is a senior fellow with the Cato Institute and the author of Income and Wealth.