Qir 2012q4 us

Theoretical and empirical research in

finance in the past few decades has led to

an evolution in our understanding of how

financial markets work.

This paper demonstrates that it’s possible to

apply the main findings from the research to

structure and implement investment solutions

that target the dimensions of expected

returns in a cost-efficient way in a multifactor

world with frictional markets.

02 Research Update

12 What’s New at Dimensional

14 Appendix

Integrated Equity Solutions

FOURTH QUARTER 2012

The material in this publication is provided solely as background information for registered investment advisors and institutional investors and is not intended for public use. Unauthorized copying, reproducing, duplicating, or transmitting of this material is prohibited. Dimensional Fund Advisors is an investment advisor registered with the Securities and Exchange Commission.

Expressed opinions are subject to change without notice in reaction to shifting market conditions. All materials presented are compiled from sources believed to be reliable and current, but accuracy cannot be guaranteed. This article is distributed for educational purposes, and it is not to be construed as a recommendation of any particular security, strategy, or investment product.

Once it is admitted that risk reduction is stipulated to be an economic good, the relevant

question for society is what real institutional arrangements will be best suited to produce

risk reduction or risk shifting. We no longer delude ourselves into thinking that the world

would be a more efficient place if only people would not be risk averse; the taste for risk

reduction must be incorporated into the concept of efficiency.

Given the fact of scarcity, risk reduction is not achievable at zero cost, so that the risk

averse efficient economy does not produce “complete” shifting of risk but, instead, it

reduces or shifts risk only when the economic gain exceeds the cost. Once we seek to

compare different institutional arrangements for accomplishing this, it is difficult to keep

scarcity from entering into our calculations so that it becomes obviously misleading and

incorrect to assert that an economy, free enterprise or otherwise, is inefficient if it fails to

economize on risk as it would if it were costless to shift or reduce risk.

Two types of adjustments to risk seem possible: pooling independent activities so that the

variance in expected return is reduced and facilitating the assumption of risk by those who

are less risk averse. The market is an institutional arrangement that facilitates both types of

adjustment by rewarding those who successfully reduce or shift risk.

—Harold Demsetz “Information and Efficiency: Another Viewpoint,” Journal of Law and Economics 12, no. 1 (April 1969): 1-22.

Risk and Markets

See “Appendix: Standardized Performance Data and Disclosures” for how to obtain complete information on performance, investment objectives, risks, advisory fees, and expenses of Dimensional’s funds.

2

RESEARCH UPDATE

Joseph ChiVice President,Co-Head of Portfolio Management Dimensional Fund Advisors

Jed FogdallVice President,Co-Head of Portfolio Management Dimensional Fund Advisors

Integrated Equity Solutions

The application of financial theory to the practical world of investing began approximately 40 years ago. Theoretical and empirical work in finance in the past few decades has led to an evolution in our understanding of how financial markets work. For instance, 40 years ago, most financial economists and some market participants thought there was only one dimension of expected returns in equity markets—the market itself. That one-dimensional world was best explained by the capital asset pricing model (CAPM). Today, we recognize several dimensions of expected returns and believe multifactor asset pricing models do a better job of explaining the behavior of stock returns than single-factor models. Economists have also done much work related to financial intermediation and the institutions of exchange. This work is highly relevant to financial market participants because it has improved our understanding of the price formation and discovery process, and of how trading and transaction costs vary in different markets and under different market structures. For investors, the existence of several dimensions of expected returns presents additional challenges to their asset allocation decisions. In the past, those decisions were relatively simple. Investors had to decide (1) how to split their money between fixed income and equities and (2) whether to invest in index funds, traditional active funds, or individual securities to build their own portfolios. Today, investors still need to make those decisions. But they can make better decisions by taking into account, among other things, the additional dimensions of expected returns in the equity markets and how those dimensions interact with each other, as well as how much exposure to each of those dimensions they have or want. While a multifactor world presents better opportunities to tailor investment decisions that match investors’ risk preferences and hedging needs more accurately, this complex exercise requires a greater degree of expertise to evaluate and manage the tradeoffs between risks and costs, on one hand, and expected returns, on the other.

This paper shows how we can apply the main findings from the theoretical and empirical research in finance to structure and

implement investment solutions that target the dimensions of expected returns in a cost-efficient way in a multifactor world with frictional markets. ASSET PRICING MODELS: FROM A SINGLE FACTOR TO A MULTIFACTOR WORLDAbout 50 years ago, financial economists began to identify commonality in the behavior of stocks. Building on the work of Harry Markowitz on portfolio selection and the efficient diversification of investments, William Sharpe and others initially developed a single-period, single-factor model: the capital asset pricing model.1 The CAPM postulates that an asset’s expected return is a linear function of its tendency to covary with the market portfolio, which is measured by beta. Beta represents an asset’s amount of market risk—that is, the risk that cannot be eliminated through diversification. This is the risk for which investors expect to receive compensation. In a CAPM framework, beta is all that is needed to explain differences in expected returns. High-beta assets are expected to have high average returns, while low-beta assets are expected to have low average returns, and the average return spreads between high- and low-beta assets can be fully explained by the spreads in their betas.

The CAPM is a single-period, single-factor model. In the early 1970s, Robert Merton built on the intuition of the CAPM to develop a more sophisticated model, the intertemporal capital asset pricing model (ICAPM).2 The ICAPM modifies the CAPM in two key aspects. First, it is a multiperiod model, which more accurately reflects the intertemporal nature of investing. Second, in addition to the market factor, the ICAPM recognizes that investors also care about how their investment/consumption opportunity set might change in the future. Because labor income or human capital is one of the factors investors should consider when evaluating their investment/consumption opportunity set, investors are likely to care about the covariance between asset returns and labor income. That gives rise to hedging demands against negative changes in their investment/consumption opportunity set, which in turn gives rise to additional factors, state variables, or sources of priced


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risk. Merton did not specify the additional factors beyond the market factor or how many there were. However, we know that these factors represent the commonality behind the variance in the performance of stocks with similar characteristics. Because it is often difficult to identify and measure those state variables directly, financial economists have used more indirect ways to link asset prices to changes in the investment/consumption opportunity set. One way of doing this is by creating so-called factor-mimicking portfolios—zero-investment portfolios that have long exposure to stocks with certain characteristics (e.g., stocks with a low relative price) and short exposure to stocks with the opposite characteristics (e.g., stocks with a high relative price)—that contain the same pricing information as the true factors and act as proxies for those factors. The empirical work that started in the 1970s confirmed the need for additional price factors to explain differences in average returns.3 This work showed that, contrary to the predictions of the CAPM, differences in beta could not explain differences in average returns. In particular, small cap stocks and stocks with a low relative price with respect to some measure of fundamental value—such as book value, earnings, or cash flow—tended to have higher average returns than indicated solely by market betas. Researchers found other patterns in the cross-section of average returns also unrelated to beta, such as the tendency of short-term winners (losers) to continue to do better (worse) than indicated by their market betas for a few months after portfolio formation.

In a highly influential paper published in 1992,4 Eugene Fama and Kenneth French synthesized much of the previous empirical work and showed that, controlling for market capitalization, there was no relation between beta and the cross-section of average stock returns. They also found that, controlling for market capitalization, variation in relative price—measured, for instance, by the ratio of book-to-market equity—captured substantial variation in the cross-section of average stock returns. Companies with a low relative price (i.e., a high relative book-to-market ratio) have historically had higher average returns than companies with a high relative price. Controlling for relative price, market capitalization also captured substantial variation in average returns. Small capitalization companies have historically had higher average returns than large capitalization companies.

Those results led Fama and French to conclude that there were at least two additional dimensions of expected returns in equity markets: one related to market capitalization or company size and the other related to relative price, as measured, for instance, by the ratio of book-to-market equity.

Thus, in the spirit of Merton’s ICAPM, Fama and French proposed a multifactor model to explain the average returns of stocks: the Fama/French three-factor model.5 According to that model, the expected return of an asset in excess of a risk-free rate is a function of that asset’s sensitivity to three common risk factors:

(1) A market factor, as measured by the excess returns of a broad equity market portfolio over a risk-free rate (in the case of the US, the 30-day US Treasury bill is usually considered the risk-free asset).

(2) A market capitalization (or size) factor, as measured by the return difference between a portfolio of small capitalization stocks and a portfolio of large capitalization stocks.

(3) A relative price (or value) factor, as measured by the return difference between a portfolio of value stocks or stocks with high financial ratios (high book-to-market stocks, in our case) and a portfolio of growth stocks or stocks with low financial ratios (low book-to-market stocks).

More recent research by Fama, French, and Robert Novy-Marx, among others, shows that expected profitability—as measured by the direct profitability of book equity, for instance—is another reliable and robust dimension of expected returns. Controlling for the previously mentioned dimensions of returns, more profitable firms have higher expected returns than less profitable firms.6 The research breakthrough in this case is not the discovery of expected profitability as a dimension of expected returns per se, something that financial economists have suggested for quite some time and a finding that is well established in different versions of theoretical stock valuation formulas; rather, it is the discovery of reasonable proxies for expected profitability, which allow us to use profitability as another dimension of expected returns in the creation of investment solutions.

In short, here are the main lessons of the theoretical and empirical research conducted over the past few decades:

(1) There are multiple dimensions of expected returns, and, therefore, multifactor asset pricing models are needed to explain differences in the cross-section of average returns.

(2) Four factors—the market, size, relative price, and expected profitability—capture much of the common variation in average stock returns in a way that is consistent with multifactor asset pricing models.


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RESEARCH UPDATE

For any given portfolio, the higher the exposure to those factors or dimensions, the higher the expected returns, all other things being equal. Thus, portfolios can be structured and managed to obtain the desired exposure to those dimensions (and capture the expected premiums associated with them), resulting in either of the following:

(1) A portfolio with a higher expected return than the market. (2) A portfolio that satisfies some specific hedging needs.

Before thinking about how to create optimal and cost-efficient investment solutions, however, we need to have a better understanding of the characteristics and behavior of those factors, how they interact with one another, and how best to gain or avoid exposure to them. First, we need to determine the conditions under which markets incorporate information about fundamental values and expectations into prices, and the implications for investors when that happens.

EXPECTED RETURNSThe expected performance of any stock is driven mainly by its exposure to the factors that determine expected returns. Each individual stock, however, has an idiosyncratic component of performance that is associated only with that stock. This component is commonly called abnormal return and is not shared by companies with similar characteristics. The expected return or premium associated with this idiosyncratic component is zero. This raises two important and related questions. First, why do market prices reflect available information about fundamental values in a manner such that factor exposure is the main driver of expected returns? And, second, is it possible to determine a priori when the premiums associated with those factors are expected to be high or low? In other words, are those factors predictable?

Financial markets are characterized by their extremely competitive nature. There is competition among firms for investors’ capital, and between buyers and sellers of securities to execute at the most attractive prices. In competitive markets with many independent buyers and sellers, it is extremely difficult for one trader to significantly influence prices, especially if those markets are also very liquid. Given their preferences and needs, buyers think purchased securities will add to their portfolios by more than what they paid for them. Similarly, given their preferences and needs, sellers have the opposite view—the money received is worth more to them than the securities sold. Buyers and sellers meet their opposite expectations at the traded price, which they both see as fair, without anyone being forced to trade. This competition between opposite views in liquid markets is what

makes prices reflect the expectations of market participants and drives them toward equilibrium.

In liquid and competitive markets, the price system acts as a mechanism to aggregate and disseminate disperse bits of information. As F.A. Hayek first pointed out in the 1940s,7 there are two types of knowledge or information: (1) general knowledge widely available to all market participants and (2) specific knowledge of the particular circumstances of time and place, including the preferences and needs of each investor, which vary by investor. The price system aggregates both types of information, including the knowledge about the specific circumstances of all market participants, into one single statistic—the price—so that investors have the knowledge necessary to make decisions for themselves. Because both types of knowledge can move prices, market participants compete with one another to be the first to bring information not yet reflected in prices to the market and profit from it, but no participant has the full set of information because each participant has some specific knowledge not generally available to others. That competition and interaction among market participants makes market prices reflect information about fundamental values and expectations, with no single participant able to interact with the market in isolation, up to the point at which the marginal benefit of acting on information that is not reflected in prices (that is, the profits to be made) is at best equal to the marginal cost of gathering that information and acting on it.

Market frictions, such as trading and borrowing costs, and taxes may delay the convergence of market prices to their fundamental values or, in extreme cases, prevent prices from converging to a utopian fair price, particularly in less competitive markets. However, in most public equity markets, competition is vigorous enough to drive price movements very fast,8 and thus most investors should always act as if prices reflect information about fundamental values at all times and invest based on longer-term expectations. Crucially, because the market price of a security reflects its expected return, having a good investment experience does not depend on attempting to participate in the price discovery process.

The competitive nature of markets and the existence of widely dispersed information also make it unlikely, if not impossible, that any investor can consistently be the first to incorporate information and expectations not yet reflected in prices and thus obtain abnormal profits on a regular basis. If any investor had a persistent informational advantage, the existence of abnormal returns or economic profits associated with that advantage would drive additional investors into the information-gathering business. Because barriers to entry


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RESEARCH UPDATE

in financial markets are relatively low, market participants would continue to enter that business until those abnormal returns disappeared. Second, the existence of widely dispersed information makes persistence unlikely because it is impossible to know in advance which bits of information are going to be relevant for the formation of prices or for making prices converge to their fundamental value.

A third reason that a persistent informational advantage is unlikely, if not impossible, has to do with trading. To be useful, informational advantages have to be large enough to overcome trading costs and other market frictions. Thus, the greater the frictions, the greater the informational advantage required to generate abnormal returns. If the same investors could persistently identify deviations of market prices from their “true” value, eventually the true value forecasted by those investors would become the market value. By trading, those investors would reveal their informational advantages to other market participants, and market prices would start to incorporate that information. The more trading they do, the more information they reveal and the closer market prices get to their true fundamental value. What’s more, if market participants perceive that their counterparties have informational advantages, liquidity is likely to dry up, bid/ask spreads will probably widen, or the depth of the book will probably become thinner to hedge the possibility that some of those counterparties may have information, further increasing the costs of acting on information.

In regard to the second question, whether factor performance is predictable, the theoretical and empirical research indicates that state variables should forecast returns and that expected returns vary over time.9 Investors demand a higher expected return to hold risky assets; this expected return should be higher during times of greater uncertainty. But that variation in expected returns and the predictability associated with it occur over very long horizons, such as business cycles, whose turning points and lengths are unpredictable. Furthermore, the predictability derived from standard regression analysis is so weak and the noise-to-signal ratio is so high that, for all practical purposes, it is of no use. Over shorter horizons such as daily, monthly, yearly, and multi-year periods, stock and factor returns are essentially unpredictable. For that reason, the best approach is to assume that, a priori, premiums have the same expected return every day and that abnormal returns are close to zero (i.e., that factor performance is unforecastable). From a practical perspective, this approach implies that no day is better than any other day to target those market premiums, and therefore, market premiums should be targeted on a daily basis.

The next section looks at the sources and magnitudes of those premiums so that we can better understand why targeting those premiums on a daily basis is the optimal approach.

SOURCES OF INVESTABLE PREMIUMSBy no means do market participants demand the same rate of return for all securities when setting prices. Securities with different characteristics will have different expected returns, so it is important to identify those dimensions of higher expected returns that may offer investable portfolios excess returns relative to the market as a whole.

Theoretical and empirical research conducted over decades has identified four dimensions of expected returns in equity markets: the overall market, market capitalization or size (small/large), relative price (value/growth), and profitability (high/low).

The market dimension reflects the premium demanded by market participants for investing in a broadly diversified portfolio of equity securities without any style bias. A common way to assess the level of the expected premiums is to look at historical data and compute how those premiums have performed in the past. From 1927 to 2011—a period that includes up and down markets, economic expansions and recessions, wars, and extraordinary technological and medical breakthroughs, among other developments—the US equity premium had an annual average of 7.94% and was reliably different from zero, as indicated by a t-statistic of 3.51.10 Because the premium is reliably different from zero, we can say with a high level of confidence that the positive equity premium was not a random event.

The size dimension reflects the excess premium demanded by market participants for investing in small capitalization stocks relative to large capitalization stocks. From 1927 to 2011, the US small cap premium had an annual average of 3.66% and was reliably different from zero, as indicated by a t-statistic of 2.37.

The relative price dimension is generally used to differentiate so-called value from so-called growth securities. The premium associated with this dimension reflects the excess expected performance investors demand from securities with a low relative price (value stocks) in excess of the return demanded from securities with a high relative price (growth stocks). From 1927 to 2011, the US relative price premium had an annual average of 4.73% and was reliably different from zero, as indicated by a t-statistic of 3.13.


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RESEARCH UPDATE

All the aforementioned dimensions use price, but the market forms the price to achieve a desired expected return. To transform price to expected return, it is necessary to take into account the expected cash flows to investors. The profitability dimension provides a way to discern expected returns of companies with similar price-driven characteristics; if two companies trade at the same relative price, the one with higher profitability will have a higher expected return, all other things being equal. From 1975 to 2011, the annualized US profitability premium was 4.68% on average and was reliably different from zero, as indicated by a t-statistic of 2.74. (Data availability precludes extending the analysis beyond 1975.)

Research has shown that the premiums associated with each dimension are more or less driven by stock migration—that is, stocks moving across size, relative price, and profitability portfolios from one period to the next. In the case of the size premium, for instance, it is primarily driven by the extreme positive performance of a random subset of small cap stocks that unpredictably moves to the mid or large cap space from one period to the next. The relative price premium, on the other hand, is mainly driven by three factors: (1) the extreme positive returns of a random subset of stocks with low relative prices that migrate to neutral or growth portfolios; (2) the poor performance of a random subset of stocks with high relative prices that migrate to neutral or value portfolios; and (3) stocks with low relative prices that remain in the same category that historically have had higher average returns than stocks with high relative prices that remain in the same category from one period to the next.11

Table 1Historical US Premiums, 1927-2011

Annual Daily

Equity Premium (1927-2011) 7.94 0.032

Size Premium (1927-2011) 3.66 0.015

Value Premium (1927-2011) 4.73 0.019

Profitability Premium (1975-2011) 4.68 0.018

Daily premiums are calculated by dividing the annual premiums by 250, the approximate number of trading days in one year. Past performance is no guarantee of future results.

Asset class and profitability filters were applied to data retroactively and with the benefit of hindsight. Returns are not representative of indices or actual portfolios and do not reflect costs and fees associated with an actual investment.

Source: Profitability premium data provided by Dimensional. All other premium data provided by Fama and French, available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

The analysis of the drivers of the premiums performed by Fama and French (2007) has important implications for investors because it highlights the importance of diversification in the creation of reliable investment solutions. Let’s assume, for instance, that we have two portfolios with the same factor exposure and, therefore, the same expected return. One portfolio is broadly diversified across the universe of eligible stocks, while the other is heavily concentrated on a few of those stocks. As Fama and French, among others, have shown, not all securities contribute equally to the premiums. Some securities do extremely well, while others have average returns or perform poorly. Research has also shown that it is not possible to reliably predict which of these securities that share common factor exposure are going to do well, because in many cases news about why they will do well has not arrived yet (e.g., a new discovery or a new need by some other company), so it is not yet in the price. For that reason, the most reliable way to capture the premiums is to have a diversified strategy with full exposure to the segments of the market expected to provide those premiums. Concentrated portfolios may inadvertently exclude from their holdings the companies that ultimately generate most of those premiums, whereas broadly diversified portfolios have a better opportunity to include those securities and capture those expected premiums.

Just as it is almost impossible to reliably predict which securities will make the largest contributions to the factor returns, it is also very difficult to reliably determine when the premiums will be realized. Under these conditions, it is useful to expect the premiums to be earned every day. Thus, to increase the reliability of outcomes and the likelihood of capturing different market premiums on a daily basis, strategies should be continuously exposed to those premiums, instead of being rebalanced at arbitrarily defined frequencies or dates.

What is the best way, then, to design and implement investment strategies that aim to capture those premiums over any period?

CONTINUOUSLY CAPTURING MARKET PREMIUMSSuccessful investing requires expertise in identifying and managing tradeoffs between risk and costs, on the one hand, and sources of expected returns, on the other. It also requires expertise in managing competing premiums because stocks are often exposed to more than one dimension of expected returns. Pursuing one premium without taking into account how that pursuit will impact a stock’s exposure to the other factors can result in a stock having a net negative impact on a portfolio, even if that stock has captured a premium along one dimension of expected return. It is difficult, yet essential, to properly account for the interaction among the different


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RESEARCH UPDATE

dimensions and the costs associated with implementing investment solutions along several dimensions. Managers who can perform this exercise well and consistently will likely add value to their portfolios.

To maximize the chance of earning those premiums, portfolio managers need to constantly monitor strategies to ensure they have the right exposure on a daily basis and that trading costs, which are function of turnover and cost per trade, are low. The expected contribution of any stock to a strategy’s return will be equal to its daily return, which will be a function of its exposure to the different premiums multiplied by the number of days that stock remains in the strategy, minus the costs of buying and selling the stock.

Expected Contributed Performance = Sum of Daily Premiums x Number of Days in Portfolio – Cost of Buying & Selling

Before deciding whether a premium is worth pursuing, the following three questions should be answered for every stock we consider: What is the expected return on a daily basis? How long do we expect the stock to remain in the portfolio? What is the expected cost we will need to incur to get that return?

As indicated above, a priori market premiums should have the same expected magnitude every day, so the expected annual premium for each of the factors can be assumed to be the composite of equal daily premiums. Using the historical annual data shown in Table 1 and assuming 250 trading days per year, the historical daily premiums for the US are 3.2 basis points for the equity premium, 1.4 basis points for the size premium, 1.9 basis points for the value premium, and 2.1 basis points for the profitability premium. Because the magnitude of the daily premiums is small, it is important to understand how the premiums associated with each factor are achieved. A low-turnover factor whose premium is produced by a large and stable set of stocks is going to be much more attractive than a high-turnover factor whose premium is produced by stocks constantly coming in and out of the factor for short periods of time, even if the high turnover factor has a higher expected premium.

To illustrate that point, let’s compare, for instance, the relative price and momentum factors. Historically, the expected relative price premium is about 5% per year and has comparatively low turnover. The expected momentum premium, on the other hand, is about 10% per year, but it has very high turnover. Although on paper the momentum factor may appear to be the more attractive of the two because it has the higher expected return, that is not the case once we

understand how the premiums associated with each factor are achieved and take trading costs into account. Our typical relative price strategy has an annual turnover of around 25%. So, on average, a value stock will remain in the strategy for about four years. If the relative price premium is 5% per year, that stock’s expected gross return will be approximately 20%, assuming the stock is fully exposed to the relative price premium for the whole period. Because the security is expected to be in the strategy for a long period, implementation can be done with enough patience and flexibility to avoid paying for liquidity in the market, something that, as we will see below, can be very expensive. The break-even trading cost when buying and selling that will make the strategy unprofitable is very high, around 10%, taking into account a round-trip trade. In contrast, a long-only momentum strategy may have an annual turnover of around 300%. So, on average, a stock will remain in upward momentum for about four months. If the momentum premium is 10% per year, that stock’s expected return will be approximately 3.3%, assuming that the stock is fully exposed to the momentum premium for the whole period.12 For the momentum strategy, the break-even trading cost for each stock is much lower, around 1.7%, because of the high turnover. If the high turnover increases the need to demand liquidity when trading, that break-even number will be even lower.

The preceding hypothetical example shows the difference between investable premiums and non-investable premiums that are fragile or not robust after taking into account trading costs. A good portfolio design will recognize that difference and invest in those factors whose securities have a high daily expected premium and are expected to make a large contribution to performance after taking costs into account. Targeting investable premiums makes implementation more efficient because it allows us to treat securities with similar characteristics as close substitutes for one another, at least over short time frames, which in turn increases our ability to capture the premiums in a cost-effective manner. Good portfolio design will also recognize that non-investable premiums must be taken into account when managing and implementing strategies to screen out stocks that may have detrimental effects on the performance of the portfolio.

IMPLEMENTATION AND TRADINGOnce we decide which premiums are worth pursuing, we can focus on implementation and trading. In the absence of market frictions, the best way to capture those premiums over time is to ensure that portfolios constantly hold only those stocks that have the desired exposure to the factors associated with those premiums. Because stock prices continuously move, stocks’ exposures to the factors also move (stocks


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RESEARCH UPDATE

migrate). So to continuously maintain the desired exposure to the targeted factors, we need to sell stocks that no longer have the desired exposure and expected return and purchase stocks that currently have the desired exposure and expected return. That turnover increases our ability to capture the expected return differential between those stocks.

But, because markets are not frictionless, it is important to balance the benefits of achieving the desired exposure to the factors that determine expected returns against the expected costs of achieving that exposure; otherwise, trading costs could more than offset the expected return differential. So, for instance, small differences in expected returns due to stocks moving along the dimensions of expected return should not drive a trade if the expected return pickup is small compared to the costs of implementing the trade. It is important to be confident that, when selling a security, it has moved well outside the dimension of expected returns targeted and that, when buying a security, it has moved well inside that dimension. By having a hold range that has high enough expected returns for us not to sell a security, but not

so high that we continue to buy securities in that region, we balance the need for consistent factor exposure against the concern that high turnover generates costs that detract from actual returns. The economics of transaction costs—in particular, the relationship between trading costs and immediacy of execution13—and over thirty years of experience trading stocks that are difficult to trade have informed our approach to implementation and trading. As stated above, trading costs are equal to turnover times the cost per trade. We have discussed some ways to minimize turnover and make all turnover meaningful. In regard to the cost per trade, that will be a function of the desire to complete an order and the need for immediacy in trading. Seeking liquidity moves prices and increases trading costs. The higher the immediacy and quantity needed to execute, the higher the price paid. At the very least, a liquidity seeker will pay the bid-ask spread (see Table 2 for bid-ask spreads in different markets and different market capitalization segments for notional amounts of shares). More often, however, demanding liquidity will impose higher

Table 2Seizing Opportunities to Add Value

Market Cap Range (USD millions) Names

Market Cap (%)

Average Bid/Ask Spread (%)

Average Daily Trading Volume per Issue (USD)

UNITED STATES

> 5,000 541 82.3 0.06 177,881,444

1,500–5,000 678 11.6 0.10 23,641,764

500–1,500 781 4.3 0.20 6,672,029

200–500 615 1.2 0.46 1,752,674

50–200 681 0.5 1.39 499,204

INTERNATIONAL (23 markets)

> 5,000 657 79.5 0.12 68,708,009

1,500–5,000 821 12.1 0.22 9,129,241

500–1,500 1,160 5.5 0.43 2,282,158

200–500 1,169 2.0 0.80 793,233

50–200 1,485 0.9 1.46 237,391

EMERGING MARKETS (20 markets)

> 5,000 401 79.1 0.27 38,745,973

1,500–5,000 475 12.5 0.32 8,081,738

500–1,500 711 5.3 0.48 2,935,589

200–500 641 2.2 0.62 1,422,550

50–200 880 1.0 0.84 517,457

US data from January 26, 2011. Data provided by Instinet. © 2013, Instinet Incorporated and its subsidiaries. All rights reserved. International and emerging markets data from January 1, 2011, to January 15, 2011. Data provided by Bloomberg. Developed international markets are Dimensional’s eligible universe (Canada, Europe, Japan, Asia Pacific, UK). The bid/ask spread is generally regarded as an indication of the cost of liquidity.


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RESEARCH UPDATE

trading costs because traders will move prices in addition to incurring the costs of that spread.

If immediacy is expensive, why do people trade with immediacy? First, some investors may have personal views about future prices and will seek immediacy in their trades. As long as the price paid is lower than their assessment of the future price, those investors will not mind demanding liquidity and paying a premium for it, even if those trading costs are greater than many days’ worth of expected returns.

Second, other investors, such as index investors, will demand immediacy in their trades to satisfy low tracking error constraints. Indices usually control turnover by rebalancing infrequently, sometimes only once per year, but that turnover all happens in one day or over a handful of days, instead of being spread out over the whole year. And that makes their trading very expensive because it unnecessarily imposes huge liquidity demands over a limited number of rebalancing days. Index investors control turnover but not the cost of each trade, which can make their trading costs very high. Another problem for index investors is that low or zero tracking error does not guarantee they will have the desired or correct exposure at all times (see Figure 1). Indices that, in theory, represent the same asset class have meaningful tracking error with respect to one another. So none of those indices has the “perfect” exposure, partly because of infrequent rebalancing and the migration of stocks. Indices may hold securities that used to have the desired exposure instead of securities that currently have that exposure, which introduces unnecessary uncertainty into an investor’s asset allocation as the investor tries to capture the premiums.

To avoid immediacy in trades and keep trading costs low, good portfolio design creates flexibility and patience in the portfolio implementation process through broad portfolio diversification, a desire and ability to spread turnover over time, and a focus on aggregate portfolio characteristics. We can design portfolios with built-in flexibility if we are willing to accept some tracking error with respect to a target portfolio, which does not imply a negative effect on expected returns, and focus on the overall characteristics of a portfolio, not on having a specific number of securities from a precise set of issuers. The immediate consequences of that flexibility are twofold: First, over short periods, we can look at securities with similar characteristics and exposures as close substitutes for one another. Therefore, we can be somewhat indifferent over the short term with respect to the individual stocks that we trade on any day, as long as those stocks fit the overall strategy and are expected to contribute to the investment goals of a portfolio, and the portfolio maintains the diversification requirements. Second, by giving traders some measure of real-time flexibility—the degree is ultimately determined by portfolio managers—they can be patient and opportunistic in executing candidate orders from portfolio managers. Crucially, that flexibility also includes the option to walk away from trades if market conditions are not favorable. Traders can therefore avoid paying high prices for liquidity and attempt to capture the liquidity premiums that people who want immediacy in their trades are willing to pay.

INVESTMENT SOLUTIONSSome investors may decide to satisfy their investment needs by allocating assets to different asset classes using a building-block approach. The process of identifying reliable and investable dimensions of expected returns and finding the most efficient

Figure

1

Tracking Error and Correlations among Indices

January 1999–June 2012

Russell 2000 Value

Dow Jones US Small Cap

Value

S&P SmallCap

Value

S&P/Citigroup Small Cap 600

Value

MSCI US Small Cap

Value

MSCI USA Small Value

Russell 2000 Value 0.98 0.97 0.98 0.97 0.98

Dow Jones US Small Cap Value 3.50 0.99 0.97 0.99 0.99

S&P Small Cap Value 4.91 3.24 0.96 0.98 0.98

S&P/Citigroup Small Cap 600 Value 4.20 4.90 5.65 0.95 0.97

MSCI US Small Cap Value 4.33 2.72 3.65 6.30 0.98

MSCI USA Small Value 4.00 2.56 3.83 4.80 3.92

Russell 2000 Value Index, Dow Jones US Small Cap Value Index, S&P United States Small Cap Value Index (gross dividends), S&P/Citigroup 600 Value Index, MSCI US Small Cap Value Index (gross dividends), and MSCI USA Small Value Index (gross dividends). Russell data copyright © Russell Investment Group 1995-2013, all rights reserved. Dow Jones data provided by Dow Jones Indexes. The S&P data are provided by Standard & Poor’s Index Services Group. MSCI data copyright MSCI 2013, all rights reserved. It is not possible to invest directly in an index.


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RESEARCH UPDATE

way of capturing those premiums can be applied at the asset class level. Because the expected return of a portfolio before costs is the weighted average of the expected returns of the securities in the portfolio— expected returns that are driven by the factor exposures of each security—many different sets of holdings can achieve similar levels of expected returns. A concentrated portfolio can have a pre-cost expected return like that of a diversified portfolio in the same asset class, but the reliability of the outcomes can be very different. Moreover, if the diversified portfolio is managed for consistent exposure to the desired premiums, instead of being artificially rebalanced at predefined frequencies to arbitrary security weights, expected transaction costs and turnover should be lower, which implies that post-costs expected returns should be higher.

Other investors may prefer to integrate all the different asset class exposures in one portfolio and eliminate the artificial barriers among the different components of a portfolio to create a more fluid structure, which can increase net expected returns in markets with frictions. This portfolio can overweight securities with higher expected returns, such as value, small cap, and/or high direct profitability securities, while underweighting lower expected returns securities to achieve an expected excess return relative to the market. This integrated solution should reduce turnover because there is no need to fully sell securities that migrate from asset class to asset class. Turnover is also reduced by the ability to use dividends or other cash flows from one asset class to rebalance the overall portfolio or fill needs in other asset classes, even ones that did not produce the cash flows. This integrated solution also facilitates better risk controls at the overall asset allocation level, because it controls the overall asset allocation, and considers and oversees all the over- and underweights using an integrated methodology. For example, in a globally integrated solution, overweights of a sector in a given region can be taken into account when deciding sector allocations in other regions, something more relevant in recent years given the higher integration of some sectors across markets.

Figure 2An Integrated Solution

CONCLUSIONResearch has shown that several dimensions of expected returns are related to the market, size, relative price, and expected profitability. Research has also shown that actual returns related to these expected premiums are largely unpredictable, both in terms of when any dimension might outperform and which individual stocks will drive the performance.

For those reasons, the best way to invest is to structure portfolios along the different dimensions of expected returns and target those dimensions continuously. This approach maximizes the likelihood of capturing the expected premiums associated with each dimension.

That requires expertise in managing competing premiums, because stocks are often exposed to more than one dimension of expected returns. It also requires expertise in managing trading costs and other market frictions.

Integrated equity solutions that combine continuous exposure to the dimensions of expected returns with a portfolio design that facilitates patient trading and low turnover maximize an investor’s chance of capturing the higher expected returns predicted by financial theory. n

Component Approach

Provides sharp exposure to limited segments of the market

Dimensional’s Integrated Approach

Provides marketwide exposure with greater emphasis on risk premiums

Growth Value Growth Value

Larg

e

Larg

e

Smal

l

Smal

l


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RESEARCH UPDATE

REFERENCESThe helpful comments of Stephen Clark, Gerard O’Reilly, Eduardo A. Repetto, and L. Jacobo Rodríguez are gratefully acknowledged.

1. William F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance 19, no. 3 (September 1964): 425-42. Financial economists John Lintner, Jan Mossin, and Jack Treynor developed different versions of the CAPM at around the same time.

2. Robert C. Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica 41 (1973): 867-87.

3. For more information on this empirical work, see, for instance, James L. Davis, “Explaining Stock Returns: A Survey of the Literature,” (Dimensional Fund Advisors paper, December 2001); and John H. Cochrane, “Financial Markets and the Real Economy,” (NBER working paper no. 11193, March 2005).

4. Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance 47, no. 2 (June 1992): 427-65.

5. Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics 33, no. 1 (1993): 3-56.

6. See, for instance, Eugene F. Fama and Kenneth R. French, “Profitability, Investment, and Average Returns,” Journal of Financial Economics 82 (2006): 491-518; Eugene F. Fama and Kenneth R. French, “Dissecting Anomalies,” Journal of Finance 63, no. 4 (August 2008): 1,653-78; Robert Novy-Marx, “The Other Side of Value: The Gross Profitability Premium,” Journal of Financial Economics, (2012); and Gerard O’Reilly, Eduardo A. Repetto, and Savina Rizova, “Profitability: A New Dimension of Expected Returns,” (forthcoming Dimensional Fund Advisors paper, 2013).

7. See F.A. Hayek, “The Use of Knowledge in Society,” American Economic Review 35, no. 4 (September 1945): 519-30.

8. For additional evidence on this issue, see, for instance, Tarun Chordia, Richard Roll, and Avanidhar Subrahmanyam, “Evidence on the Speed of Convergence to Market Efficiency,” Journal of Financial Economics 76 (2005): 271-92.

9. See, for instance, John H. Cochrane, Asset Pricing, Revised Edition, (Princeton, N.J.: Princeton University Press, 2005); and John H. Cochrane, “Presidential Address: Discount Rates,” Journal of Finance 66, no. 4 (August 2011): 1,047-1,108.

10. The sample mean of a random variable is more likely to be close to the true mean of that variable the larger the sample size used to estimate that average. For that reason, to assess premiums and their reliability, it is important to use as large a sample as possible. To determine the reliability of an estimated value, we use statistical analysis. A t-statistic tests whether the estimated value of a random variable with unknown variance is reliably different from zero in a statistical sense. It is calculated by dividing the estimated mean by its standard error, which is computed by dividing the standard deviation of a random variable by the square root of the sample size.

11. Eugene F. Fama and Kenneth R. French, “Migration,” Financial Analysts Journal 63, no. 3 (2007): 48-58.

12. With a 10% annual momentum premium, the expected momentum premium over four months is equal to 3.3%.

13. See, for instance, Harold Demsetz, “The Cost of Transacting,” Quarterly Journal of Economics 82, no. 1 (February 1968): 33-53; and Sunil Wahal, “Trading Advantages of Flexible Portfolios.” (Dimensional Fund Advisors paper, April 2010).

Past performance is no guarantee of future results. Diversification neither assures a profit nor protects against loss in declining markets.

12

WHAT’S NEW AT DIMENSIONAL

DAVID BOOTH RECEIVES OUTSTANDING FINANCIAL EXECUTIVE AWARD FROM FINANCIAL MANAGEMENT ASSOCIATION

US TREASURY DEPARTMENT APPOINTS ROBERT MERTON TO FINANCIAL RESEARCH ADVISORY COMMITTEE

Dimensional News

David G. Booth, Dimensional’s co-founder, chairman, and co-chief executive officer, was awarded the Outstanding Financial Executive Award at the Financial Management Association’s 2012 annual meeting in Atlanta on October 19, 2012.

The FMA established the award in 1984 to honor individuals who have made significant innovative contributions to the field of finance with the goal of bridging the gap between academic theory and practicing financial professionals. David was selected for his background and accomplishments in applying financial theory and research to the asset management industry, particularly his pioneering work in indexing and small capitalization investing.

Prior to accepting the award, David provided the keynote speech in which he addressed more than 1,000 finance professors from all over the world.

David joins an elite group of 28 other FMA award recipients, including John J. Phelan, former chairman of the New York Stock Exchange; Alger B. Chapman, former chairman and CEO of the Chicago Board Options Exchange; John Biggs, former chairman and CEO of TIAA-CREF; John Bogle, former chairman of the Vanguard Group; and Janet Yellen, vice chair of the Federal Reserve Bank.

The US Department of the Treasury appointed Nobel laureate and Dimensional Fund Advisors consultant Robert C. Merton to serve as a member of the Financial Research Advisory Committee of the Office of Financial Research (OFR).

The OFR was created by the Dodd-Frank Wall Street Reform and Consumer Protection Act in 2010 to assist the Financial Stability Oversight Council. According to Treasury, the committee provides an opportunity for academics, researchers, industry leaders, and other qualified individuals to offer their expert advice and recommendations to the OFR, which, among other things, is responsible for collecting and standardizing data on financial institutions and their activities, and supporting the work of federal financial regulators and researchers. Treasury issued a press release announcing the appointment on November 14, 2012.

The 30 members were chosen from a group of more than 150 applicants, among them notable professionals in economics, finance, financial services, data management, risk management, and information technology. Other members include Donald Kohn, former Federal Reserve vice chairman; Nobel laureate Robert Engle; and Anil Kashyap, professor of economics and finance at the University of Chicago Booth School of Business.

The committee held its inaugural meeting on December 5, 2012, in Washington, DC.

13

WHAT’S NEW AT DIMENSIONAL

JOHN ALKIRE TO HEAD DIMENSIONAL JAPAN

Dimensional Fund Advisors announced in December the appointment of John Alkire as chief executive officer of Dimensional Japan Ltd. He will serve as the head of Dimensional’s Japan operations. Prior to joining Dimensional, Alkire served as president and chief investment officer of

Morgan Stanley Asset & Investment Trust Management Co., Ltd. (now Morgan Stanley Investment Management (Japan)) in Tokyo, where he oversaw approximately US $45 billion of institutional assets.

Alkire first worked with David Booth in 1985 while at Morgan Stanley and helped launch a Japanese small company strategy for Dimensional in 1986. Alkire joined Morgan Stanley in 1981 as head of institutional equity for Asia in New York and established MSAITM in Japan in 1995. Clients included Japanese government pensions, sovereign wealth funds, family offices, and open-ended mutual funds in Japan, Europe, and the US. In 1996, MSAITM was selected by Nempuku (now GPIF) as one of the first three investment managers to manage its assets.

Alkire was the first non-Japanese vice chairman of the Japanese Securities Investment Advisors Association from 1998 to 2000. He was born and raised in Japan, speaks fluent Japanese, and graduated from the University of Victoria, British Columbia.

www.dimensional.com

A M S T E R D A M

A U S T I N

B E R L I N

L O N D O N

S A N TA M O N I C A

S I N G A P O R E

S Y D N E Y

VA N C O U V E R

APPENDIX

BRO-QIR

Performance data shown represents past performance. Past performance is no guarantee of future results, and current performance may be higher or lower than the performance shown. The investment return and principal value of an investment will fluctuate so that an investor’s shares, when redeemed, may be worth more or less than their original cost. To obtain performance data current to the most recent month end, access our website at www.dimensional.com.

Consider the investment objectives, risks, and charges and expenses of the Dimensional funds carefully before investing. For this and other information about the Dimensional funds, please read the prospectus carefully before investing. Prospectuses are available by calling Dimensional Fund Advisors collect at (512) 306–7400 or at www.dimensional.com. Dimensional funds are distributed by DFA Securities LLC.

Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission.

DISCLOSURES

Risks include loss of principal and fluctuating value. Investment value will fluctuate, and shares, when redeemed, may be worth more or less than original cost.

Small and micro cap securities are subject to greater volatility than those in other asset categories.

International investing involves special risks such as currency fluctuation and political instability. Investing in emerging markets may accentuate these risks.

Sector-specific investments can also increase investment risks.

Fixed income securities are subject to increased loss of principal during periods of rising interest rates. Fixed-income investments are subject to various other risks, including changes in credit quality, liquidity, prepayments, and other factors. Municipal securities are subject to the risks of adverse economic and regulatory changes in their issuing states.

Real estate investment risks include changes in real estate values and property taxes, interest rates, cash flow of underlying real estate assets, supply and demand, and the management skill and creditworthiness of the issuer.

Sustainability funds use environmental and social screens that may limit investment opportunities for the fund.

Commodities include increased risks, such as political, economic, and currency instability, and may not be suitable for all investors. The Portfolio may be more volatile than a diversified fund because the Portfolio invests in a smaller number of issuers and commodity sectors.

Economy & Finance

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