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October 9, 2002

Analysis of Grossís Prediction of Stock Price

by Paul DeRosa, Simpson & Co., LLC


Bill Gross, the guiding genius of Pacific Investment Management Companyís long and enviable success, recently has proposed an analysis of the equity market in which he concludes the proper level for the Dow Jones averages is about 5,000 and the NASDAQ is 650. As both of these levels were some 30% below prevailing markets on his publication day, Gross thus joined a company that includes names as illustrious as Robert Shiller and Andrew Smithers, who argue that equity prices still have a long way to fall. Gross arrives at his 5,000 level by a process of reverse engineering: since inflation- protected Treasuries offer a 3% yield, equities have to be priced to offer a prospective return of 5.4% -- the 3% Treasury yield, plus the 100-year average equity premium of 2.4%. With the Dow Jones at 8,000, the current dividend yield is barely 2%, and even if dividends were to grow as rapidly as an inflation adjusted 2% per year, they cannot provide a return of more than 4%. Investors, according to Gross, cannot expect further gains through a rise in the price to earnings ratio, as that ratio already has tripled during the past century.If dividends, then, are all an investor can hope for, prices have to fall to the level at which the current 4% becomes 5.4%, and that level is 5,000.

My first reaction to Grossí analysis is that valuing equities over a 100 year horizon as he does is rather a desperate act.† In a world where 90 days is a long time and a year is eternity, the willingness to apply a 100-year risk premium requires a particular prospective.† The reported earnings of the S&P 500 companies are now 50% of what they were just 18 months ago.† In a normal recovery, they easily could rise 30 or 40 percent over the next few quarters, and if they do, stock sales at current levels probably will be regretted.† As economist Bob Barbera has noted, the secular bears were absolutely right in December of 1974, but that didnít stop the market from rising 40 percent over the ensuing 15 months.

Nonetheless, efforts to take the long view are not entirely nugatory.† Two years ago, Grossí approach would have brought some much needed context to a market that had lost all its benchmarks. The force of his logic would then have been irresistible, as there was no growth rate of either earnings or dividends that could have reconciled prevailing prices with historically required returns.† He might well have been ignored, as were others who performed similar exercises, but given his standing in the profession, he might have saved some people money.

Aside from doubts about utility of 100-year analyses, there is another objection of a general nature that one can raise to Grossí conclusion. This derives from the observations that the 10-year inflation protected Treasury bond yields 2.2% and the 5-year yields 1.98%. † An investor has to be resolutely gloomy about the future to voluntarily forsake all other opportunities and accept 1.98% as the best return on his savings.† The yields on short-term issues are tied to the cost of funding, but issues as long as 5 or 10 years reflect a projection of future capital returns.† Simple transitivity suggests the sobriety that prevails in the bond market also governs equities and that stocks at current prices already are getting a hardheaded evaluation.

General considerations aside, some of the internal parts of Grossí argument look a little weak.† First, he needlessly complicates the analysis by acting as if the initial dividend yield is important.† Companies can reinvest their earnings and thereby cause them to grow, or they can pay them in dividends and surrender growth, or they can use earnings to buy back stock, which is equivalent to paying a dividend but gets better tax treatment. † In any case, it is preferable to assume that, one way or another, investors receive all of the earnings of the companies they own.† This simplifies the analysis and shifts the focus to earnings growth, where it belongs. † The firms in the S&P 500 currently paying out about 30% of their earnings in dividends, which provide a yield of about 2%.† This is approximately the figure Gross uses.† The sole source of Grossí pessimism is his assertion that inflation adjusted earnings per share of listed corporations grow at a rate of 0.6% per year. style="mso-spacerun: yes">† He gets this figure from research done by Peter Bernstein, who finds that 50% of reported earnings growth over the past 50 years has been fictitious, a figment of pro-forma accounting. (Odd how these things always surface in the late stages of bear markets.)† Gross also quotes Peter Lynch to the effect that earnings growth has been 8 to 9% per year.† So here we have it, the bid to offer spread, 0.6% versus 9%.† The resolution of this discrepancy goes to the heart of Grossí calculations.† If earnings grow appreciably faster than 0.6%, whether firms pay them down or keep them internally, Grossí argument disappears.

With stock splits, spin-offs, mergers and the like, the actual growth of per share earnings is a devilishly difficult number to compute.† There are very few people who can claim real expertise in this area, and Peter Bernstein may or may not be among them.† Work of this type quickly gets under the fingernails, but even without delving too deeply, one finds indications that Bernsteinís 0.6% is too low. † For example, the reported earnings of the S&P 500 companies have increased 2.75% per year since 1952. † These are reported earnings and not pro-forma.† They are overstated however because companies didnít properly account for options they wrote to executives during the 1990ís.† But even over the period ending in 1989, which excludes the option problem, but also excludes some of the economyís best years, real earnings grew at more than 2.1%. † If Bernsteinís 0.6% for all listed companies is correct, the yearly profit growth of S&P companies would have exceeded the total by between 1.5 and 2 percentage points, causing them over the 37 years to increase by some 85% more than the total, an unlikely event for the supposedly less dynamic segment of American firms.

The earnings of all corporations, listed and unlisted, have fluctuated between 8% and 12% of GDP for the past 50 years.  These earnings are calculated by the Department of Commerce for the National Income and Product Accounts, which tend to be, if anything, on the conservative side. In 2001, these earnings were toward the lower end of their range.† One can expect that over the next several years, earnings will grow at least as rapidly as real GDP. † The 50-year trend of real GDP is 3.4% per year.† Just a few years ago, a putatively informed consensus held that the next 50 years would be much faster than the last, and though such views are presently out of fashion, most people would agree the 3.4% figure is still a good guess for both GDP and profit growth.

If the 2.75% actually reported by the S&P 500 or the 3.4% GDP based figure turn out to be better than Bernsteinís 0.6%, Grossís calculations change considerably. † Even if real dividends grow at only 1% per year, which would mean the payout rate would be falling steadily, and the P/E ratio remained constant, the long-term returns to holding common stock would be between 5.25% and 5.9%.† With the yield of the inflation-indexed 30 year bond at 2.60% these figures would provide an equity premium of between 2.65% and 3.30%, both at least a match for the 2.4% Gross asserts is required.