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Dr. Alex Castaldo



Article Review: "What stock market returns to expect for the future?"

by Peter A. Diamond
Social Security Bulletin, Vol 63 #2, 2000
Updated July 1, 2001

Make no mistake: the purpose of this article was to shoot down the Bush proposals for investing Social Security funds in the stock market, and to preserve the traditional FDR type Social[ist] Security. Nevertheless, leaving aside the partisan aspect, the article is sufficiently well done as to be worth summarizing and discussing. Keep in mind that when this article was written the S&P was approximately 1331.

The Chief Actuary of Social Security has assumed a 7% real return on stocks and a 3% real return on Treasury bonds over the next 75 years. The author argues that the 7% figure is unrealistically high; the main objective of the article is to shoot down the 7%.

The Historical Record

Compound annual real returns, by type of investment, 1802-1998 (in percent)
Period    Stocks  Bonds   Bills   Gold   Inflation
1802-1998   7.0    3.5     2.9    -0.1     1.3
1802-1870   7.0    4.8     5.1     0.2     0.1
1871-1925   6.6    3.7     3.2    -0.8     0.6
1926-1998   7.4    2.2     0.7     0.2     3.1
1946-1998   7.8    1.3     0.6    -0.7     4.2

The stock returns seem fairly stable, so as a starting point a 7% forecast for stocks (based on the full historical record) seems plausible. For Bonds, on the other hand, there seems to have been a steady decline in returns as the US changed from an emerging market to a superpower, so a figure from a more recent period (say 2.2% for the last 75 years) may be more appropriate as a forecast of future returns.

Why the Future May Differ from the Past

1. Stock ownership is easier and more widespread

This would argue for a declining risk premium from investing in stocks, but the author is skeptical. Although mutual fund accounts have increased rapidly, mutual funds own less than 20% of U.S. equity outstanding; most stock is held by institutional investors and the super wealthy. Similarly, the share of households investing in stocks in any form has increased from 32% in 1989 to 41% in 1995. Theoretically a larger number of investors sharing in stock market risk should lower the equilibrium risk premium. But the importance of these trends is reduced by the low size of investments by such new investors. The author feels that the decline in future returns from these factors is likely to be minimal.

2. Current market valuations

Current dividend yields are very low, between 1% and 2%. However, these yields cannot be taken at face value and must be adjusted upwards before they are used in a valuation model. For one thing dividends are currently very low relative to corporate earnings, implying that corporations will be able to increase dividends in the future (recall that dividends respond to earnings increases with a lag, the famous Lintner model). For another, corporations have been buying back their shares at a high rate; these buybacks are in a sense equivalent to a dividend.

The author feels that the 'adjusted dividend yield' is probably 2.5% or at most 3%. For analysis purposes he will investigate four possibilities for adjusted dividends: 2%, 2.5%, 3% and 3.5%.

The author then applies the Gordon Model of equity valuation: k = D1/P0 + g In the steady state, the rate of growth of stock prices, g, must be equal to the rate of growth of real GDP, for which the author will use the Chief Actuary's estimate of 1.5%. Even assuming a 3.5% adjusted dividend rate, the rate of return on stocks k=3.5+1.5 = 5% would fall considerably short of the Chief Actuary's assumed 7%. Thus the Chief Actuary is being inconsistent.

In conclusion: "Either the stock market is overvalued and requires a correction to justify a 7% return thereafter, or it is correctly valued and the long-run return is substantially lower than 7%. (Some combination of the two is also possible)".

Assuming the former case, the author computes the decline in real stock prices that would have to occur over the next 10 years to bring about correct valuation and a 7% expected return forever after:

Table 3.

Required percentage decline in real stock prices over the next 10 years to
justify a return of 7, 6.5 and 6 percent thereafter

             Percentage decline to justify a
                   long run return of
Adjusted dividend    7%      6.5%     6%
     yield      --------------------------
     2.0            55       51      45
     2.5            44       38      31
     3.0            33       26      18
     3.5            21       13       4

Source: Author's calculations. Derived from Gordon formula.

3. Demographics

The retirement of the baby boomers has the potential to bring stock prices crashing down, according to some. The author cites two papers that are skeptical of this view. Poterba "does not find a robust relationship between demographic structure and asset returns". "The connection between demography and returns is not simple and direct". [An article googled by Vic attributed to Poterba a forecast of a market crash: two very different readings of Poterba's views!!]. Another paper by Goyal also reaches the same conclusion: "demography is not likely to effect large changes in the long run rate of return".


Of the three main bases for criticizing the Chief Actuary's assumption, by far the most important one is the argument that a constant 7% stock return is not consistent with the valuation of today's market and the projected slow economic growth. The best remedy would be to assume a lower rate for the next 10 years and a return to a 7% rate for the following 65 years.


Today (Nov. 11, 2005) the market is valued about 15% lower in real terms than when this article was written six years ago. This figure is more benign than most of the entries in the author's Table 3 but is still within the limits of that table. Keeping in mind that these are just back of the envelope calculations, the author can pat himself on the back for being not too far from right.

Alessandro Castaldo, CFA, is a researcher and trader for Manchester Trading. Dr. Castaldo wrote his PhD dissertation on stock market volatility at the City University of New York, and taught courses in finance and options to undergraduates at Baruch College (CUNY) from 1998-2001. He has been associated with Circle T Partners, LP, a $400 million equity hedge fund; and Willowbridge Associates, a $1 billion-plus commodities trading adviser, where his responsibilities included the ongoing refinement of a market-neutral statistically based ("stat-arb") stock selection model. Dr. Castaldo holds a B.S. in electrical engineering/computer science and an M.S. in management from the Massachusetts Institute of Technology, and worked as a software engineer at SEI Corporation/TMI Systems, Software Research Corp. and Systems Constructs Inc. before entering the finance profession.

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