Dimensional Fund Advisors

The Dimensions of Stock Returns: 2002 Update

Dimensional Fund Advisors

Based on the limited amount of data available, size and value effects also appear in emerging markets. The IFC Investables Total Return Index represents a portfolio of tradable stocks in emerging markets countries that non-resident investors are permitted to own. During 1989-2001, emerging markets small cap stocks and value stocks had higher average returns than the IFC index (Figure 9).8

The international findings are consistent with Fama and French's interpretation of the size and value effects as rewards for bearing non-diversifiable risk. If size and value effects were related to risk factors unique to the US, forming globally diversified portfolios could eliminate them. Instead, the existence of similar size and value effects in both domestic and international stock returns demonstrates that these effects are global phenomena reflecting exposures to ubiquitous sources of risk.

Implications for Global Equity Allocation9

EAFE is the international equivalent of the S&P 500. EAFE returns, expressed in US dollars, are determined jointly by stock returns computed in local currencies and foreign-exchange gains or losses against the dollar. Because the two indexes contain stocks with similar size and value characteristics, it is reasonable to assume that the costs of capital of EAFE and the S&P 500 are approximately equal. If it is also assumed that currencies have zero expected returns, EAFE should have about the same expected gross rate of return as the S&P 500.

While their expected gross returns are similar, the expected net return of an S&P 500 portfolio will be greater than that of an EAFE portfolio due to differences in trading costs and taxes. International stocks are more costly to trade, and the dividends of international stocks are subject to foreign taxation-even when the recipients are tax-exempt in the US For example, American pension funds pay no taxes on dividends received from US firms, but they are taxed at rates of 15 to 20 percent on dividends received from many foreign companies.10

Many American investors rely on EAFE-like portfolios for international diversification. But given the likelihood that the S&P 500 offers a higher expected net rate of return and similar risk exposures, EAFE is nothing more than an expensive substitute for the S&P 500. The diversification benefits afforded by EAFE are minimal and not worth their cost.

Instead of EAFE, Dimensional recommends that American investors use international and emerging markets small cap and value stocks for global diversification. These asset classes have higher expected gross returns than the S&P 500 that can compensate for the higher costs and taxes of international investing.

Concluding Comments

The identification of size and value factors by Fama and French has important implications for equity portfolio design. Relative to traditional market-like portfolios, portfolios with greater exposures to the size and value factors offer higher expected long-term rates of return.

Structured portfolios can be designed that provide targeted sensitivities to the size and value factors. Dimensional's asset class portfolios can serve as building blocks for these structured portfolios.

International and emerging markets equity returns also exhibit size and value effects. For global diversification, Dimensional recommends the use of its international and emerging markets small cap and value stock funds.

Structured portfolios only make sense for investors with long time horizons and sufficient tolerance for increased risk. For the right investors, structured portfolios are promising alternatives to old-fashioned market-like portfolios.


My thanks to Jim Davis and Weston Wellington for their helpful comments.


1 Fama and French (1992) examined data beginning in 1963. Davis, Fama and French (2000) investigated data from 1929 through 1963. Davis, Fama and French found evidence of similar size and value effects in this earlier period. This demonstrates that the original Fama and French findings are not unique to a particular sample period. Size and value effects are pervasive determinants of US stock returns.

2 The higher average return of the CRSP 6-10 relative to the S&P 500 also illustrates the size effect.

3 Size and BtM are firm characteristics that tend to be associated with fundamental risk factors, but they are not risk measures or factors themselves. Small stocks are not riskier than large stocks just because they are smaller. Value stocks are not riskier than growth stocks just because they have higher BtMs. Instead, size and BtM on average appear to be linked to fundamental risk factors that have yet to be identified. Identification of these fundamental risk factors is a challenge for future research.

4 Although the estimated market sensitivities of the three small cap portfolios suggest similarity to stock/bond mixes, these portfolios were invested fully in equities. The model's estimated slope coefficients depend on the sample period, and they change when the sample period changes. For the sample period 1991-2000, the estimated market sensitivities were .97 for Small Cap, .87 for Micro Cap and .94 for Small Value. For the sample period 1992-2001, the estimated market sensitivities for these three portfolios were lower, as reported in Table 1.

5 The factor sensitivities of portfolios P1-P4 are weighted averages of the sensitivities of component portfolios. For example, P2's value sensitivity (h=.22) equals .7 times the S&P 500's value sensitivity (.05) plus .3 times the Large Cap Value fund's value sensitivity (.61).

6 Taxes also influence the suitability of structured portfolios for investors. Dimensional's "pure" asset-class funds often have large capital-gains distributions. This makes the pure strategies more appropriate for tax-exempt and tax-deferred accounts than for taxable accounts. Dimensional offers tax-managed versions of some of its asset-class strategies, and these funds can be used to build structured portfolios for taxable accounts. For select wealthy investors, Dimensional offers separate accounts that employ a comprehensive tax-management system to increase long-term after-tax returns.

7 Fama and French (1998) documented the existence of a value factor in international stock returns.

8 Different time periods were used to compute the returns statistics for domestic (Figure 1), international (Figure 8) and emerging markets (Figure 9) equities. The sample periods were determined by data availability.

9 This section is based on the arguments and findings of Sinquefield (1996).

10 Taxable investors receive credits for foreign taxes paid. Tax-exempt investors do not. US tax-exempt investors may petition foreign governments for return of taxes withheld, but the process of reclaiming foreign withholding taxes on dividends often is time-consuming, frustrating and expensive.


Davis, James L., Eugene F. Fama and Kenneth R. French. "Characteristics, Covariances and Average Returns: 1929-1997." Journal of Finance 55 (2000), 359-406.

Fama, Eugene F. and Kenneth R. French. "The Cross-Section of Expected Stock Returns." Journal of Finance 47 (1992), 427-65.

Fama, Eugene F. and Kenneth R. French. "Size and Book-to-Market Factors in Earnings and Returns." Journal of Finance 50 (1995), 131-55.

Fama, Eugene F. and Kenneth R. French. "Value versus Growth: The International Evidence." Journal of Finance 53 (1998), 1975-99.

Sinquefield, Rex A. "Where are the Gains from International Diversification?" Financial Analysts Journal 52 (1996), 8-14.

This article contains the opinions of the author and those interviewed by the author but not necessarily Dimensional Fund Advisors Inc. or DFA Securities Inc., and does not represent a recommendation of any particular security, strategy or investment product. The author's opinions are subject to change without notice. Information contained herein has been obtained from sources believed to be reliable, but is not guaranteed. This article is distributed for educational purposes and should not be considered investment advice or an offer of any security for sale. Past performance is not indicative of future results and no representation is made that the stated results will be replicated.



April 2002