The Dimensions of Stock Returns: 2007 http://www.dfaus.com/library/articles/dimensions stock_returns_2007/ 1 of 12 4/23/08 11:01 AM The Dimensions of Stock Returns: 2007 By Truman A. Clark September 2007 Print this E-mail this Average stock returns are related to firm size and relative price. Firm size is measured by the market capitalization of equity (price times shares outstanding). When stocks are ranked by size, small stocks tend to have higher average returns than large stocks. This is known as the size effect. Relative price is often measured by a firm's book-to-mark et ratio (BtM). When stocks are ranked by relative price, high BtM (or "value") stocks tend to have higher average returns than low BtM (or "growth") stocks. This is known as the relative-price or value effect. Many studies document the existence of size and relative-price effects in equity markets in the US and many other countries. These findings have important implications for equity allocation. Investors may be able to increase the expected returns of their portfolios by holding small capitalization stocks and value stocks in greater than market-capitalization proportions. Such portfolios are said to be "tilted" toward small cap and value stocks. Portfolio design can matter. A common way to build a tilted portfolio is to combine separate asset class funds. This building-block approach may generate trading costs that lower net returns. To help reduce the costs of maintaining tilted portfolios, Dimensional introduced Core Equity funds. The Core Equity funds are integrated, marketw ide portfolios designed to have lower trading costs than conventional tilted portfolios. Dimensional offers Core Equity portfolios for the US, international, and emerging markets. The Size and Relative-Price Effects Figure 1 displays the annualized averages and standard deviations of the monthly returns of five Fama/French indexes: market, value, growth, small, and large. The market portfolio holds all NYSE, Nasdaq, and Amex stocks except for ADRs, closed-end funds, and tracking stocks. 1 Th e value portfolio is composed of NYSE, Nasdaq, and Amex stocks with positive BtMs in the top 30% of the NYSE BtM distribution. The growth portfolio is composed of stocks with positive BtMs in the bottom 30% NYSE BtM. The small portfolio is composed of NYSE, Nasdaq, and Amex stocks with market capitalizations in the bottom 30% of NYSE market cap. The large portfolio is composed ofstocks with market caps in the top 30% of NYSE market cap. The sample period is July 1926 through December 2006. Figure 1 Fama/French US Equity Indexes Annualized Averages of Monthly Rates of Ret urn July 1926-December 2006 Dimensional Philosophy Application Strategies Service Library Articles Reprints Videos Glossary FAQs Bios Search Go Secure Site Login Username: Password: Go Remember me New user? Register here. Find an Advisor Use our online form to find an advisor near you with access to Dimensional funds.
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The size dimension has six rows. The largest 250 stocks (mega-cap) are in the first row. Other
large stocks (251-600) are in the second row. Mid cap stocks (601-1000) are in the third row. The
next three rows are groups of small cap stocks with stocks smaller than the 2,500th firm in the
last row.
The relative-price dimension has six columns. The BtM quintile breakpoints for the 1,000 largest
stocks determine the boundaries of the first five columns. Stocks with the lowest BtM (extreme
growth) are in the first column, and stocks with the highest BtM (extreme value) are in the fifth
column. The sixth column ("other") contains utilities as well as firms with missing or negative
book equity.
The height of each bar in Figure 2 indicates the proportion of market value held in a grid cell. By
definition, the market portfolio is neutral with respect to size and relative-price. Thus, the size and
book-to-market allocations of the market portfolio, such as those in Figure 2, may serve as
relative benchmarks for assessing a portfolio's size and value tilts and are not exact. Other
portfolios can be compared to the market portfolio to identify their relative overweighting or
underweighting of small cap and value stocks.
Figure 3 shows the composition of the S&P 500 Index. Dark cells indicate overweighting relative to
the market. Light cells indicate underweighting. Relative to the market, the S&P 500 tilts stronglyto very large cap stocks. Almost all S&P 500 stocks are in the two largest size categories, and
none is in the two smallest groups.
Figure 3
Allocation of Aggregate Market Capin Size and Book-to-Market GroupsS&P 500 IndexDecember 29, 2006
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Conventional Tilted Portfolios
The traditional way to build tilted portfolios is by combining an S&P 500 or other large cap index
fund with one or more asset class funds. Figure 10 shows the style composition of a blendedportfolio holding 40% in the S&P 500 Index, 30% in the US Large Cap Value fund, 20% in the US
Small Cap Value fund, and 10% in the US Micro Cap fund. This portfolio provides value and small
cap tilts, but it is perhaps operationally inefficient.
Figure 10
Allocation of Aggregate Market Capin Size and Book-to-Market GroupsBlended PortfolioDecember 29, 2006
Each asset class fund has defined investment guidelines. As stock prices change, an asset class
fund will sell stocks that no longer meet its guidelines. (For example, the Micro Cap fund will sell a
stock that has appreciated sufficiently to exceed its maximum capitalization limit.) An asset class
fund also will buy other stocks as they become eligible. For funds specializing in relatively illiquid
small cap stocks, this adjustment trading can be quite costly.
Core Equity Funds: Improving Tilted Portfolios
The Core Equity funds are designed to reduce the costs of maintaining tilted portfolios. Unlike asset
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directing turnover toward larger-cap stocks (which are cheaper to trade) and away from
smaller-cap stocks (which are costly to trade). With reduced trading costs, the Core Equity funds
strive to provide higher net returns than standard tilted portfolios of comparable risk.
Dimensional continues to expand its offerings of core equity portfolios. Core equity funds designed
for investors in Australia, Canada, and the UK are operational. Other core equity strategies are
under development.
1 The annualized average return equals 12 times the average monthly return. The annualizedstandard deviation of returns equals the square root of 12 times the standard deviation of monthly
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