Dimensional Fund Advisors, further referred to as DFA, is an investment company that bases its strategy mainly on academic research and related theories. They work together with proponents of the efficient market hypothesis, indicating a relatively strong belief in this theory and thus in efficient markets. However DFA also feels that skilled traders have the ability to contribute to a fund’s profits even when the investment is inherently passive and DFA does adjusts its strategy to new findings in the field. In this report we will evaluate the relevance and accuracy of the theories used by DFA, especially the value premium and the size premium where almost all of their funds are based upon. This will lead to comments on the usefulness of these theories to increase the return of DFA’s funds and to recommendations about changes in strategy that will enhance the performance of DFA overall.

Performance and strategy so far
DFA has performed relatively well over the years, aside from some relatively rough patches in the late 1990s. Growth of the company had been stable and profits high. There was no need to sell shares for liquidity reasons and shares were only sold if they did not fit into a fund anymore. This didn’t happen very often though as DFA had several funds that were “connected”, when a stock in the Micro Cap portfolio grew too big it could be placed into a fund with bigger companies (Small Cap portfolio).

An important part of DFA’s strategy, that contributed to the performance of DFA so far, is aimed at achieving discounts in trades through buying in large blocks. Results from research by Donald Keim1 show that the average discount obtained by DFA on block trades was 3.33%. These discounts were largely responsible for the fact that DFA’s passively managed small-stock portfolio outperformed the typical small-stock indexes by about 200 basis points per year on average. Another factor contributing to the relative success of these small cap indexes is the thorough research that DFA performs when it trades with other companies, preventing adverse selection and the negative implications of this phenomenon.

Despite DFA’s historic performance, the investment company is “only” ranked 96th (in Pensions and Investments) among other investment companies, changes in certain elements of DFA’s strategy and an increased focus on its competitive advantages will lead to a higher position on this list.

The logic behind the funds – The use of the Size premium and the Value premium findings
DFA manages several funds, based on academic research and different empirical findings. One of these funds is the U.S. Micro Cap Portfolio, which invests in stocks whose market cap fall below a certain cutoff point. This fund had been launched in 1981 as a reaction to findings of, amongst others, Rolf Banz2 (1981). Banz had found that risk adjusted returns on smaller stocks had been higher, on average, than returns on stocks of larger firms. DFA saw an opportunity to acquire investors by using this new insight, because many mutual funds in that time focused only on investments in stocks of large companies. Following the launch DFA added the U.S. Small Cap Portfolio and the U.S. Small XM Portfolio, which had different cut-off points regarding the market cap.

In addition to funds that are related to the so-called size premium, DFA also used findings of other economists, Fama and French, to set-up new portfolios. Fama and French had found that “value stocks”, stocks of companies with a high book-to-market value, had provided a higher return than “growth stocks”, stocks of companies with a low book-to-market value. As a reaction DFA used the preliminary findings of the authors to set up a U.S. Small Value investment fund in 1992 and several other value funds were created in the following years.

DFA thus used findings related to the value premium and the size premium through creating several funds. DFA’s strategy is as a result of this to a great extent depended on the actual existence and persistence of both effects. Did DFA react too quickly to these still relatively controversial findings, do they fit in with the relatively strong beliefs in efficient markets by DFA and could a change in DFA’s strategy increase both the performance of its funds and the company overall? These questions will be answered by a thorough analysis of the value, and the size premium.

Value premium
A lot of criticism on the CAPM has arisen over the last decades. One finding by Basu in 1977 is often used by opponents of the model in order to take down the foundation of the CAPM. Basu3 found that stocks with a low price -earnings ratio, called value stocks, tend to outperform stocks with a high price-earnings ratio, named growth stocks. As the CAPM only allows for fundamental risk to explain excess returns on stocks, the finding that stocks from companies with high fundamentals (earnings, sales, dividends) relative to price outperformed growth stocks was in contradiction with the classical CAPM.

Proponents of the CAPM and the efficient market argued that the value premium could be explained by their “classical” risk-and-return rewards, value stocks they argued earned higher returns due to higher risk related to poor performance in the recent history of the firm. Fama and French4 however also concluded that the value premium did exist and even found in the same paper that the book-to-market ratio and size premium together were able to explain excess returns of a stock while fundamental risk, the only ingredient in the CAPM, had no explanatory power anymore.

After these findings by Fama and French a lot of other papers have been written about the value premium, while some of these are highly critical on the value premium5 most of them conclude that there has indeed been a premium on returns of stocks with a high book-to-market ratio at least for some periods in time. This premium has been quite extensive in certain times, Fama and French6 for example found that small value stocks had made 8% per year on average in excess of market returns from 1934 till 2006 and that the premium for big value stocks had been 2.8%. When you look at the graph below however you can also see that the value premium has been far from constant over time. In most of the 90’s for instance growth stocks outperformed value stocks, while after the internet bubble a reversal set-in and value stocks did a lot better than growth stocks. Some argue that cyclical circumstances can clarify these changes in the value premium7, but if you take another look at the graph it is hard to defend this explanation since the value premium was negative and didn’t go up during the most recent “financial crisis”.

Despite the changing value premium most researchers conclude that the value premium does exist. Several “causes” of the value premium have been given. As said before, Fama and French argue that value stocks earn a higher return just because they are riskier. This higher risk stems from the fact that value stocks are often stocks with a poor recent performance and profitability, resulting in an increased chance that these companies will collapse. Others, mainly behavioral economist, think that investor sentiment causes the high premium for value stocks. They feel that investors just like growth stock better, leading to overpriced growth stocks and poor performance relative to value stocks. There is also a third group of researchers who feel that the value premium results from statistical biases and thus does not exist in reality.

The fact that the value premium does change a lot and has often been negative makes it compelling to believe this last explanation, especially since any relationship of the value premium with the business cycle doesn’t seem to hold anymore in the most recent recession. There are however so many researchers that found substantial evidence for the value premium, therefore it would be too easy to explain the value premium just as a statistical illusion.

Fama and French’s explanation does not suffer from the same drawback. It sounds indeed compelling that some value stocks have a higher return due to more risk, related to poor recent performance, a lower stock price and a higher chance of collapse. Investors that hold value stocks would then “just” be compensated for being exposed to more risk; this would also fit in with the efficient market hypothesis. Nevertheless more research should be performed to provide at least some evidence that the value premium is indeed nothing more than a compensation for higher risk.

In this light DFA’s choice for setting-up value funds does not seem to be fully consistent with their beliefs in the efficient market. DFA’s value funds may indeed offer a higher return, due to the value premium, but this would be nothing more than compensation for more risk (the efficient market explanation). As the value premium has also been negative for sustained periods casting doubt on the existence of the value premium, like in the late 90’s and in more recent years, the choice of DFA to create value funds becomes even more questionable. Despite the fact that DFA’s decision to create various value funds did lead to more customers and profit, a strategy more coherent with their beliefs in the efficient market in combination with their superior skills in arranging discounts would most likely have led to an even better performance.

Size premium
Supporters of the size premium theory believe that stocks of firms with small market capitalizations outperform stocks of companies with large market capitalizations on a structural basis. The first evidence for this theory arose from a research covering the U.S. stock market, in which it was concluded that in the period prior to 1980 small-caps indeed provided significantly higher returns than large-caps.8 After these findings, Fama and French’s paper about the three factor model and the conclusion that all three factors (market returns, value and size) had explanatory power created an ever brighter spotlight for the size premium.The size premium itself had been 5.4% on average per year for the period 1926-2001, while the beta adjusted size premium was 2.62% for the same period9.

Several “causes” for the existence of the small size effect have been proposed. Behavioral economists tend to blame overreaction for the small size effect. They argue that small size firms are often firms with a poor recent performance and that people overreact causing the stock price to go down too much compared to bigger firms. To fix this “mistake”, stock prices of smaller firms will need to increase in value leading to a higher return than on big stocks. A competing explanation of the size effect comes from Fama and French, who argue (ones again) that the small size premium is nothing more than a compensation for extra (non-fundamental) risk that small stocks are exposed to.

Whatever the cause of the size premium, the relevant question is whether this premium still exists. Recent research does not sketch a univocal picture of the size premium. Although Fama and French hold on to their prior beliefs, a number of critical scholars allege that the size premium has never existed, while some academics even state that the size premium has disappeared and has changed into a size discount.10 The most devastating findings for the existence of the size premium arise from the research of Horowitz (2000), who finds no proof of the size effect in the period 1980 – 1996 and therefore concludes that the earlier findings for the size premium are ‘strong in-sample evidence, weak out-of-sample results.’ The graph below shows a similar picture, as the difference between returns on small stocks and large stock seem to get smaller over time. It looks like that in recent times the small size premium has disappeared completely.
Another explanation for the decline of the size premium can be found in the efficient market hypothesis: when it is public knowledge that small-caps outperform large-caps on a structural basis, all rational investors will be eager to invest in small-caps. This buying pressure will push up the price of small-caps until the arbitrage opportunity relative to large-caps is dissolved. As the size premium has indeed seem to have disappeared in more recent times and differences between returns on small stocks and large stocks have converged to some extent, this EMH effect might have had its impact.

Whatever the cause of the size effect, the extent, its existence and the cause of its decline, DFA’s decision in the early 80’s to create a U.S. Micro Cap and several other small cap funds can again be described as contradictory to their beliefs in efficient markets. Even if the small size effect is real, which is questionable according to more recent studies, a fund with small stocks will according to the EMH only lead to a size premium over a fund with bigger stocks due to a higher overall risk level.Despite the fact that DFA’s small cap funds did outperform other small cap funds, they experienced some very rough periods in the 80’s when the size premium didn’t seem to hold. Taken this together with increasing evidence that the size effect has disappeared (or has never existed) the same question as with the value funds comes to mind: would DFA not have done even better when it would have focused even more on arranging discounts through block trading and creating even more passive market funds with lower fees?

The main reason funds managed by DFA outperform markets and indexes is the discounts in trades DFA achieves. Another factor that contributes to the relative success of DFA funds is the thorough research performed by DFA to prevent adverse selection in block trading.

DFA takes pride in the academic foundation of its funds. As stated in previous sections, these foundations are questionable. DFA states that is has a solid belief in the efficient market hypothesis, according to this theory DFA’s value funds offer higher returns as compensation for more risk. So setting-up value funds to outperform the market contradicts with DFA’s strong belief in the efficient market. Furthermore the negative value premiums showed for sustained time casts doubt whether the value premium actually exists.

That DFA small stocks funds were set-up to outperform the market is also contradictory to their beliefs in the efficient markets. According to the efficient market hypothesis funds with small stocks will only perform better than funds with bigger stocks due to a higher overall risk level. So the creation of small stock funds is also contradictory to DFA’s confidence in the efficient market. In addition there is the increasing evidence that the size effect has disappeared, this could lead to less and less interest in the small stock funds of DFA.

The main question that can be raised from our findings is: Would DFA not have done better when it would have focused even more on arranging discounts through block trading and creating even more passive market funds with lower fees?

We believe that DFA, by focusing on arranging discounts, can increase the returns on its funds and through this increase their number of clients. Stepping away from small size and value funds will allow DFA to keep stocks even when they move-out of certain categories, leading to lower costs as stocks do not have to be sold as often. Furthermore fees can be lowered because funds do not have to be managed as actively, potentially increasing the number of clients even more. DFA, through aiming at achieving discounts, will not only get more clients via this new strategy, but will also be able to align its strategy with their belief in the efficient market.
1 Donald Keim, Exhibit 10 from Harvard Business Case (2003).
2 Banz, R.W., ‘The relationship between return and market value of common stocks’, Journal of Financial Economics, 9 (1981), pp. 3-18.
3 Basu, S., ‘Investment performance of common stocks in relation to their price-earnings ratios: a test of the efficient market hypothesis, Journal of Finance, 32 (1977), pp. 663-682.
4 Fama, E.F. & French K.R., ‘The Cross Section of Expected Stock Returns”, Journal of Finance, 47 (1992), pp. 427-465.
5 For instance: Kothari, S., Shanken, J., Sloan, R., ‘Another Look at the Cross-Section of Expected Returns, Journal of Finance’, Journal of Finance, 50 (1995), pp. 185-224.
6 Fama, E.F. & French K.R., ‘Migration’ (2007).
7 Chen, L., Petkova, R., Zhang, L., ‘The expected value premium’, Journal of Financial Economics, 87 (2008), pp. 269-280.
8 Banz, R.W., ‘The Relationship between Return and Market Value of Common Stocks.’, Journal of Financial Economics, 9 (1981), pp. 3-18.
9 Barad, M.W., ‘Technical analysis of the size premium’, Ibbotson Associates (2001).
10 For instance: Dimson, E., and P. Marsh. ‘Event Study Methodologies and the Size Effect.’ Journal of Financial Economics, 17 (1986), pp. 113-142.