A REVIEW of EFFICIENT MARKETS HYPOTHESIS: an ANALYSIS of EUGENE FAMA and KEN FRENCH's RESEARCH by Austin N. Hughey Submitted

A REVIEW OF EFFICIENT MARKETS HYPOTHESIS:

AN ANALYSIS OF EUGENE FAMA AND

KEN FRENCH’S RESEARCH

Austin N. Hughey

Submitted in partial fulfillment of the

requirements for Departmental Honors in

the Department of Finance

Texas Christian University

Fort Worth, Texas

May 4, 2015

A REVIEW OF EFFICIENT MARKETS HYPOTHESIS:

AN ANALYSIS OF EUGENE FAMA AND

KEN FRENCH’S RESEARCH

Project Approved:

Supervising Professor: Steven Mann, Ph.D.

Department of Finance

Larry Lockwood, Ph.D.

Department of Finance

Silda Nikaj, Ph.D.

Department of Economics

ABSTRACT

The field of Finance has moved from the single factor model first created by

Sharpe in 1964, into modern day with the Fama-French five-factor model. Each step in the chronology of empirically tested models of equilibrium adds more risky variables in an attempt to understand exactly how, we as humans, price risky assets. Each superseding model seems to offer more explanatory power, but how strong are the variables realistically and is it possible to achieve outperformance on the basis of these variables alone? This paper will test the research presented by Eugene Fama and Kenneth French in an attempt to understand if markets truly are efficient, or if it is possible to achieve statistically significant returns, implying consistent mispricing prevalent in the market. v

TABLE OF CONTENTS

INTRODUCTION ...... 1

REVIEW OF LITERATURE ...... 4

Fama-French Literature ...... 4

Non-Fama French Literature ...... 7

Rational Model: ...... 7

Behavioral Model: ...... 9

CURRENT APPLICATIONS OF FAMA-FRENCH RESEARCH ...... 15

Dimensional Fund Advisors ...... 15

DFA Fund Return Analysis: ...... 17

Factor Definitions...... 19

FACTOR PORTFOLIO PERFORMANCE ...... 20

Portfolios formed on Be/Me ...... 21

Value Weight Portfolios: ...... 21

Equal Weight Portfolios: ...... 22

Portfolios formed on Size and Be/Me ...... 23

Value Weight Portfolios: ...... 23

Equal Weight Portfolios: ...... 24

Portfolios formed on Dividend Yield...... 24

Value Weight Portfolios: ...... 25

Equal Weight Portfolios: ...... 25

CONCLUSION ...... 26

APPENDIX A: VALUE WEIGHT PORTFOLIOS FORMED ON BE / ME ...... 27

APPENDIX B: VALUE WEIGHT PORTFOLIOS FORMED ON BE / ME ...... 28

APPENDIX C: EQUAL WEIGHT PORTFOLIOS FORMED ON BE/ME ...... 29

APPENDIX D: EQUAL WEIGHT PORTFOLIOS FORMED ON BE/ME ...... 30

APPENDIX E: VALUE WEIGHT PORTFOLIOS FORMED ON SIZE AND BE/ME . 31

APPENDIX F: VALUE WEIGHT PORTFOLIOS FORMED ON SIZE AND BE/ME . 32

APPENDIX G: EQUAL WEIGHT PORTFOLIOS FORMED ON SIZE AND BE/ME 33

APPENDIX H: EQUAL WEIGHT PORTFOLIOS FORMED ON SIZE AND BE/ME 34

APPENDIX I: VALUE WEIGHT PORTFOLIOS FORMED ON DIVIDEND YIELD . 35

APPENDIX J: VALUE WEIGHT PORTFOLIOS FORMED ON DIVIDEND YIELD . 36

APPENDIX K: EQUAL WEIGHT PORTFOLIOS FORMED ON DIVIDEND YIELD 37

APPENDIX L: EQUAL WEIGHT PORTFOLIOS FORMED ON DIVIDEND YIELD 38

APPENDIX M: DFA FUND RETURNS COMPARED TO BENCHMARKS ...... 39

APPENDIX N: ALL PORTFOLIOS T-TEST VALUES ...... 40

REFERENCES ...... 41

INTRODUCTION

Arguably no two individuals have contributed more to the field of finance than

Eugene Fama and Kenneth French over the past 40 years. Eugene Fama is even referred to by many as the “father of modern finance,” largely because of his work establishing the efficient markets hypothesis and his development of models of market equilibrium.

After the advent of the Capital Asset Pricing Model in 1964 and the Efficient Markets

Hypothesis in 1970, the field of finance began researching and improving upon the established rational models of market equilibrium. The result was the introduction of an increasing amount of risk factors into the models. These factors claim to have solved a fundamental question in finance, how we as humans accurately assess risk, and therefore value, of risky assets.

Fama (1970) sets the foundation for the efficient markets hypothesis (“EMH”), a theory stating information is continuously and instantaneously embedded into the price of securities at any given time. This theory implies that all humans are perfectly logical and rational decision makers. The primary implication of the EMH is outsized returns on the market are impossible, making activist investing obsolete. While Fama states markets are efficient in this work, he simultaneously claims efficient markets can never be disproven unless you can disprove the model for market equilibrium, which he himself designed.

This theory is known as the joint hypothesis theory.

The original model for market equilibrium actually came before Fama’s marquee work on EMH with Sharpe’s (1964) work on the Capital-Asset Pricing Model

(“CAPM”), a now industry and educational standard for assessing the discount rate on

equity. He did so by proposing an equation that is strictly a linear function of risk, based fundamentally on the risky variable, Beta. By obtaining a beta, one is able to measure the riskiness of an asset relative to the overall market. A riskier asset requires a higher required rate of return to compensate for the enhanced risk. The Capital Asset Pricing

Model was not perfect however. Individuals have been pricing on the basis of other variables beyond simply beta. This drove Fama and French to expand off their previous work.

Fama and French elaborated on CAPM in Fama and French (1993) with the well- known Fama-French 3-factor model. The two added factors are size and value. This three-factor approach is known as an empirical approach. In other words, Fama and

French worked backwards to reveal which variables explain the shortcomings in the traditional CAPM model. Interestingly, Fama essentially discounts his previous work with Fama (1993) claiming to generate outsized returns based on companies with good

Price/Book ratios, although under the strong and the semi-strong from of the efficient markets theory Fama proposed, that is impossible.

Carhart (1997) further expands on the 3-Factor model with the introduction of the

4-Factor model, which contains an additional monthly momentum factor. The monthly momentum factor (“MOM”) is calculated as the long prior-month winners and short prior-month losers. The basic definition of momentum in regards to equity pricing is a stock with positive momentum has been rising and is therefore expected to carry momentum and continue rising. While negative momentum is a stock that has been declining and is expected to continue to decline, based on market trading prices.

Fama and French reignited their efforts recently with their working paper Fama-

French (2013) by adding yet another risky variable to their new factor model. Believing the 4-factor model was incomplete, Fama and French introduced a differing fourth factor, profitability, and a new fifth factor, investment. By adding an ever increasing amount of risky variables into previous models of market equilibrium, Fama and French are working in risky variables strictly through backwards empirical testing, rather than offering any concrete theory as to why the variables themselves are risky.

Recently, even the father of modern finance has addressed competing schools of thought, such as the growing field of behavioral finance. One of the most famous authors combatting the traditional claims of Fama and French, Robert Shiller, actually shared the

2013 Nobel Prize in Economic Studies with Eugene Fama and Lars Hansen. In Shiller

(2013), Shiller suggests another approach focusing on departures from rational investor behavior, known as behavioral finance. Behavioral finance takes into account institutional restrictions, such as borrowing limits, which prevent smart investors from trading against any mispricing in the market. Suggesting our current perception of value is skewed by innate processes, which do not always correspond with rational, predictable behavior.

By comparing literature of famous authors in the field of finance and economics, this paper will examine the financial theory proposed by Eugene Fama and Kenneth

French, specifically their research concerning the pricing of risky assets. A quantitative review of various factor portfolios developed by Fama and French over the last 15 years will be analyzed and compared against actual performance of several real-world funds

and the overall market indices. The paper will conclude with an evaluation and analysis of the performance of the various Fama-French factor portfolios.

REVIEW OF LITERATURE

In the following section, a review of notable works in the field of finance, primarily the work of Eugene Fama will be surveyed. Fama has produced a number of extremely notable works in the field of finance and economics during his life, focusing much of his attention towards efficient markets and models of market equilibrium. An examination of opposing and supporting research from Fama and French’s peers in the field will also be surveyed.

Fama-French Literature

Often seen as the leader in developing the efficient markets hypothesis, Eugene

Fama is responsible for a large amount of the writing concerning the topic. The most influential paper, which set the stage for EMH, is Fama (1970). Fama (1970) introduces the three forms of the EMH that exist, weak form, semi-strong form, and strong form. It also Fama establishes what is known as the joint hypothesis theory by arguing that market efficiency cannot be disproven unless one is able to simultaneously disprove models calculating expected returns. In other words, there must be a ‘correct’ test to compare the expected price to actual prices. Any discrepancies in what a mathematical model suggests and the actual trading price of a security is attributable to an incomplete model not taking into account other relevant factors.

The paper establishes a few key definitions, which are necessary for our understanding of future EMH literature. An efficient market is a market in which

information is “fully reflected” in the price of a security. One of the foundations of Fama

(1970) is the implementation of the three different levels of EMH, weak form, semi- strong, and strong form. The differing levels reflect which information is actually utilized in an efficient market. Weak form EMH is based on information available from historical prices. The semi-strong form of EMH is based on all information publically available.

Finally, the strong form of EMH states that all information, both public and private, is represented in the prices of securities. Consequently, weak form generates the most voluminous body of research. Another key definition introduced in the work pertains to fair game EMH models. Fair game is a basic model of market equilibrium, in which we state that market equilibrium can be stated in terms of expected returns. As this is one of the initial works in the field, the majority of the paper is involved in setting these definitions and fundamental theory related to the efficient markets hypothesis.

Ever since Sharpe (1964) introduced a rational model for market equilibrium, there has been question if one variable is enough to accurately predict the riskiness of a firm. Fama and French answered with a newer rational model with the addition of the

Fama-French Three-Factor Model in Fama (1993). In addition to Beta, Fama and French utilized empirical testing and found that historic excess returns have occurred in small capitalization companies vs. big capitalization companies and in value companies, as opposed to growth companies. The new variables are (“SMB”) for small market capitalization minus big capitalization and (“HML”) for High book-to-market ratio minus low. By utilizing the empirical method, they were able to describe approximately 90% of portfolio returns, as opposed to the traditional Sharpe model, which accounted for

roughly 70%. Despite seeing progress, Fama and French realized their work was far from complete.

Two years later, Fama and French (1995) found that the three variables are correlated. High B/M value stocks tend to have low profitability and investment, and low

B/M growth stocks, especially large low B/M stocks, tend to be profitable and invest aggressively. Fama (1997) elaborates further on his previous work in regards to costs of equity. Noting standard errors are still high for both his three-factor model, as well as

CAPM, Fama expands on the various causes for the discrepancy. Fama finds the cause of the large standard errors is primarily the result of the uncertainty around the true factor risk premiums and imprecise estimates of period-by-period risk loadings. These two papers helped understand the weaknesses still prevalent in the current models of market equilibrium and paved the way for the addition of even more risky variables.

Another important article written by Fama speaks to the current focus on behavioral finance and the existence of long-term anomalies. Fama (1998) argues the efficient markets hypothesis withstands the test of time, especially in defense of literature concerning long-term return anomalies. The reason long-term anomalies are more significant than short-term is due to the expected returns in short time frames. As Fama stated in 1970, market efficiency must be tested simultaneously with a model for expected returns. Expected daily returns are near zero, making it is hard to decipher any true market inefficiencies taking place in the short term. Fama argues in favor of EMH for two key reasons. First, Fama agrees that prices overreact at times, but over the long term, overreaction and under-reaction in the market will balance into market efficiency.

Secondly, Fama claims that long-term return anomalies are a byproduct of their modeling methodology, and therefore long-term return methodologies can be attributed to chance.

He challenges alternative models because they are not enough to effectively disprove efficient markets. Any new alternative model must be able to accurately and empirically specify biases in information processing that cause investors to underreact and overreact.

Understanding both the three and four factor model were still imperfect rational models, Fama and French went back to the drawing board with their most recent working paper to detail a new five-factor model in Fama (2013). While they include one more factor than Carhart’s model, they opt to not include MOM and instead add profitability and investment factors. Fama and French estimate this model describes between 71% and

94% of the cross-sectional variance of expected returns. This latest addition to the model of market equilibrium family seems to inch closer to a complete model.

Non-Fama French Literature

Rational Model:

Fama and French have developed numerous notable works in the field over the years, but they are not the only authors to create substantial works concerning rational models. Arguably one of the most integral and widely utilized studies in the financial world is Sharpe (1964) and Lintner (1965) for their work on the Capital Asset Pricing

Model. Despite having empirical flaws, it is still widely used based on its simplicity and utility across a diverse set of situations. The model takes into account the non- diversifiable risk through its use of the market risk variable, beta.

Fama’s addition of investment of a variable is interesting when referring to

Titman, Wei, and Xie (2004), where the authors found that as firms invest more, they tend to be capital destroyers. More specifically, controlling for variables such as the prevalence of hostile takeovers, firms that increase their capital investments experience subpar benchmark-adjusted returns.

Carhart (1997) proposes the four-factor model, effectively adding one additional momentum factor. The definition of the monthly momentum factor (“MOM”) is calculated by taking the weighted average returns of the lowest performing firms and subtracting the weighted average of the highest performing firms over the last 12-months.

If the number is positive, the stock is considered to have positive momentum and the stock has a strong likelihood of going higher, valuing the company at a slightly higher premium.

One of the closet works available to the Fama-French five-factor model is Hou

(2012). This model is predicated from the Carhart four-factor model as they compare their results of their own four factor model to Carhart’s. Hou’s four factors include a market factor, a size factor, an investment factor, and a return on equity factor.

Berk (1995) evaluates size-related anomalies and finds that, all else equal, the riskier firm is smaller. Berk asserts that size regularities in asset prices are not anomalies at all, and are in fact the opposite. Berk posits size-related regularities are common and should be witnessed in the economy and that size will generally explain deviations in expected return models.

Barberis (1998) present a quantitative model of how investors form expectations of future earnings. The paper is largely based off the work of Amos Tversky, stating people pay too much attention to the strength of the evidence they are presented with and too little attention to its statistical weight.

Behavioral Model:

When analyzing the rational works of Fama and French, it is important to understand the competing school of thought known as behavioral finance. Although a strict definition of behavioral finance does not exist, loosely defined, behavioral finance is the study that seeks to understand and predict systematic financial market implications of psychological decision processes. The subject focuses on a number of specific human psychological processes and then applies the outcomes of these processes to the financial realm. Perhaps the most prominent and widely studied of these processes is known as loss aversion, the idea that humans frame losses in a more negative light than gains, even if the two involve equally positive or negative outcomes. Other common behavioral processes include herd behavior, mental accounting, and overconfidence, among others.

These processes have wide ranging implications in the world of finance, ranging from excess stock-price volatility, to the belief that risk diminishes with time, known as the value of time diversification. Understanding the fundamental attributes of behavioral finance is important when understanding EMH because due to its ability to explain the inconstancies that are often overlooked in similar rational model research.

Behavioral finance has produced studies as early as 1951; however, interest in the subject struggled to gain any significant momentum until the late 1980s. This is primarily

a result of two factors, recent evidence suggests modern financial theories fail to describe market outcomes with significant accuracy, and the work on behavioral finance by

Tversky and Kahneman (1979) revitalized the subject by offering a new, more legitimate model of decision making called prospect theory, also known as loss-aversion.

Tversky and Kahneman (1979) won the Nobel Prize in economic sciences for integrating how humans actually make decisions in uncertain situations. They found individuals tend to use irrational guidelines such as perceived fairness and loss aversion, which are based on emotions, not logic. The paper also shows people tend to use general rules such as representativeness to make judgements that contradict the laws of probability.

Tversky and Kahneman (1991) describe several behavioral processes present in the human psyche in their paper. The paper specifically focuses on three factors regarding human evaluation of risky prospects, reference dependence, loss aversion, and diminishing sensitivity.

Reference dependence is also known as anchoring. Effectively, the way humans frame a gain or a loss depends on where we establish our reference point relative to the gain or loss. A simple example is how we frame buying a $100 shirt at Neiman Marcus around much more expensive items and buying a $20 shirt at Wal-Mart. The Wal-Mart shirt may seem very expensive relative to the other options, but the Neiman Marcus shirt may seem like a steal around other $500 shirts, despite costing five times as much as the

Wal-Mart shirt.

Essentially, loss aversion states that we hate losses much more than we enjoy gains. For example, if an investor is given the opportunity to gain $50 or gain $100 and lose $50, thus giving $50, the same as the gain, the investor will almost always take the gain without the loss. This is also known as instant endowment. This example proves a sort of strange math, wherein 1+1=2 and 3-1=1. This is the essence of behavioral finance.

Rational behavior and logic does not always prevail.

Diminishing sensitivity is akin to economies of scale. Tversky and Kahneman

(1991) found that, marginally, people view gains as losses less as their scale increases.

Adding diminishing sensitivity allows for the elongated “S” curve Tversky and

Kahneman are famous for, which shows the effects of a gains and losses on the x-axis and value on the y-axis.

Shiller (2003) describes the growing importance of behavioral finance relative to the currently held beliefs in efficient markets theory and discusses how excess volatility prevalent in the market supports his claims. Lastly, Shiller overviews growing behavioral theories and a reaffirmation of the importance of the growing field of behavioral finance.

Shiller uses data compared to the S&P 500 in order to try and explain how these differences occur. His results are varied when he looks at trend lines in comparison, such as the present values discounted by constant discount rates, interest rates, and consumption. His findings showcase that the S&P swings violently during 1860-present day for no apparent reason. Shiller goes on to discuss current behavioral theories for valuation in the market place. Shiller elaborates on the idea of price-to-price feedback theory, wherein the price of assets can be represented by the degree of public attention

towards a specific stock. This then causes general support and increased investor feedback resulting in speculative pricing. This can also work with negative behavior and excess price drops. Essentially, price-to-price feedback theory showcases the behavioral process known as herding behavior. Lastly, Shiller expands on the differences between what he calls ‘smart money’ investors and ‘ordinary investors.’ The ordinary investors are normal people who tend to invest without little true information concerning the market. Smart money investors are the institutional investors who supposedly make the correct decisions in regards to investing.

Kahneman (2003) attempts to satisfy the rational model desired by economists while simultaneously describing psychological processes in the most accurate and realistic way. Kahneman, being a psychologist by trade, established the paper as a conceptual paper, seeing it more fitting for the type of analysis realistic in psychology.

The theories in behavioral finance have historically retained the basic architecture of the rational model, but go one step further and add assumptions about cognitive limitations designed to account for specific anomalies. Kahneman (2003) covers a broad range of psychological topics including the architecture of cognition, the accessibility dimension, prospect theory, framing effects, attribute substitution, and prototype heuristics. Most notably, Kahneman insists on the structure of the two part cognitive system. The guiding principles behind this theory are most judgments made by individuals are made intuitively and that the rules that govern intuition are very similar to the rules of perception. This focus on intuition is quite possibly responsible for much of the overreaction and under-reaction found within the marketplace.

The research by Tversky and Kahneman, as well as Shiller, helped shape the academic trend towards behavioral finance. Their work opened the door for many subsequent works in the field. Olsen (1998). Olsen opens by briefly discussing the origins of behavioral finance and how exactly it is defined and ends with the implications various human behavioral process have on creating excess stock-market volatility. Lakonishok

(1994) provides evidence that value strategies, such as buying based on low prices relative to earnings, dividends, book assets, etc. yield higher returns, not because these strategies are riskier, but because these strategies exploit the suboptimal behavior of the typical investor. Lee (2002) empirically tested the effect of investor sentiment as a systematic risk that is priced. They find that excess returns are positively correlated with shifts in sentiment. Furthermore, the magnitude of bullish/bearish changes in sentiment correspond to downward/upward revision in volatility and higher/lower future excess returns. Wermers (1999) looks at the effect large block trading mutual fund herding has on the price of securities. Their research finds little impact on stock prices as a whole, but much higher impact when it comes to small company stocks and trading by growth- oriented funds. Jegadeesh (2001) documents the profitability of momentum strategies over time. The authors find the abnormal performance of the momentum portfolio one to five years following the formation of the portfolio is negative, suggesting momentum profits are generated by delayed overreaction.

Lo (2005) offers a new perspective on EMH called the Adaptive Markets

Hypothesis (“AMH”). The AMH implies the degree of market efficiency is related to environmental factors characterizing the market, such as the number of competitors in the

market, the magnitude of profit opportunities available, and the adaptability of the market participants. As such, the paper posits humans are not rational beings as the EMH suggests, but rather make decisions based of behavioral biases that arise from changing environments via simple heuristics.

While we have had great success in many respects describing a rational model for expected returns, there is still work to accomplish in the field of finance and economics, particularly as it pertains to irrational behavior in the marketplace. Our current empirically tested models have the power to describe the returns historically witnessed in the market, only because they are backed into, essentially guaranteeing a seemingly correct answer. All the while, lofty assumptions of rational behavior are put into play, making the theories hold true in a utopian world. Of course, the rational models will fail when investors start to behave irrationally. Nonetheless, Fama posits his articles are descriptive of the real world, despite proving his own assumptions with the joint hypothesis theory. By attributing all discrepancies to chance or bad modeling, the theory has carried his work a long way making Fama’s work nearly impossible to disprove.

Fama himself is hypocritical of his marquee work on EMH stating no investor can achieve excess returns in the market, all the while publishing papers to the contrary and even serving on the board of a mutual fund manager utilizing his research. While the nature of Fama’s work is bounded in a rational world, his assumptions themselves are almost irrational.

CURRENT APPLICATIONS OF FAMA-FRENCH RESEARCH

The key element underlying the three EMH theories is the inability to generate excess returns, at least in the long-run, because the market is actively and accurately pricing newly available information into the value of the company; with the only true way to achieve higher returns through increasing the overall portfolio risk. However, there are always fund managers who are able to outperform the market on a risk adjusted basis. Fama’s defense to this statement is the prevalence of chance, asserting that the only reason stock pickers are able to achieve their returns is simply a byproduct of luck.

Despite this assertion, Fama and French are actively involved with a money manager who tries to achieve just this.

Dimensional Fund Advisors

Perhaps the key takeaway from Fama and French’s research is that activist investing is obsolete. Despite this, there are still money managers across the world implementing their own distinctive strategies in an attempt to game the market, including

Fama and French themselves. Their work inspired the founding of Dimensional Fund

Advisors (“DFA”), an investment firm based of Austin, Texas, where both Fama and

French are currently on the board of directors and active consultants to the firm. DFA was formed under the EMH assumptions of Fama and French, that stock picking is a too inconsistent and unpredictable method for beating the market. DFA is not focused on activist investing, but instead focuses on exploiting factor tilts, sophisticated trading techniques, and a focus on tax efficiency. DFA is significantly equity focused with approximately 80% of its assets in stocks, and the primary focus on small and micro-cap

stocks. DFA typically augments the higher expected returns from smaller companies in order to achieve superior returns.

DFA actively utilizes Fama and French research in every aspect of their business model. In 1992, Fama and French published their three-factor model which built on the

CAPM with the addition of value and size variables. Recently, DFA has incorporated the profitability factor as suggested by Fama and French, focusing on companies with higher than average profitability relative price, cash flow, and other metrics. Dimensional's value strategies based on the Fama-French research and are designed to capture the return premiums associated with high Be/Me ratios. The value portfolios are constructed by first ranking the total market by total capitalization and identifying those companies that fall within the defined size range. This universe is then ranked by Be/Me ratio.

DFA’s competitive advantage, as they see it, is sophisticated trading techniques and access to block trading. This allows them to acquire and liquidate positions for lower costs. It serves as a market-maker for the 14,000 stocks it owns. By serving the market and offering liquidity, DFA has more control over the small and micro-cap space and retains the ability to sell when buying has sent bids higher and take stock off traders’ hands when prices are low.

DFA also employs factor tilts into their portfolios to improve efficiency. DFA seeks to buy the total US market in proportions that provide higher exposure to the risk premiums associated with size and value identified by Fama and French. The total market is defined as the aggregate capitalization of the NYSE, AMEX, and NASDAQ. The total market is weighted by market capitalization, causing large cap growth companies to

dominate. Their strategies alter the weighting of stocks by considering both a company's market cap and its price-to-book ratio. As a result, exposure to the small and value shares that research shows offer higher expected return is increased. To balance out the greater small and value exposure and still include every stock in the market, the weight of large cap and growth stocks is reduced.

DFA Fund Return Analysis:

The following sections includes an analysis three Dimensional Fund Advisors

Funds. The three funds represent three of the four corners as it pertains to value-to- growth and small-to-large capitalization (see Appendix M). The small capitalization growth fund is represented by DFA’s US Small Cap fund (DFSTX), small capitalization value is represented by DFA’s US Small Cap Value Fund (DFSVX), and the large capitalization value corner is represented by DFA’s Large Cap Value Fund (DFLVX).

All return analysis is calculated over a 15 year span, starting January 1st 2000.

The US Small Cap Fund aims to invest in companies with the bottom 8% smallest market capitalizations. The objective is to realize the higher expected returns that accompany small stocks as purported by Fama and French. Over the last 15 years, the US

Small Cap Fund returned a CAGR of 9.46% with an annualized Sharpe ratio of .46 (see

Appendix M). This performance is marginally superior relative to the comparable index, the Russell 2000, which returned a CAGR of 7.35% with an annualized Sharpe ratio of

.37 over the same time period (see Appendix M).

DFA defines small companies as those whose market capitalization comprises the smallest 10% of the total market. The US Small Cap Value Portfolio generally buys

companies whose market cap falls within the smallest 8% of the total market, with a hold or buffer range up to the bottom 10% of the universe or below the 1,000th largest company in the universe, whichever results in a higher market capitalization break. A

"buffer" range allows small cap strategies to hold securities that grow out of the buy range, in order to minimize transaction costs and keep portfolio turnover low. After analyzing the returns of DFA’s US Small Cap Value fund (DFSVX), the findings show the fund witnessed a CAGR of 11.62% and an annualized Sharpe ratio of .55 (see

Appendix M). This performance is in line with the relevant benchmark, the Russell 2000 value index. The value index returned a CAGR of 10.25% with annualized Sharpe Ratio of .55 (see Appendix M). The only real difference in the performance of the funds is the increased risk on the US Small Value fund, whose standard deviation was .68 higher and beta was also .15 higher.

The US Large Cap Value portfolio invests in the largest 90% of companies which simultaneously are considered value plays on the basis of their book-to-market equity ratios. As expected, the US Large Cap Value portfolio was less risky than the two small capitalization portfolios, but also returned less. Over the last 15 years, the Large Cap

Value fund realized a CAGR of 8.44% with a corresponding annualized Sharpe ratio of

.44 (see Appendix M). Again, this fund outperformed the relevant index, the Russell

1000 value, but only on the basis of increased risk. The Russell 1000 returned a CAGR of

6.61% with an annualized Sharpe Ratio of .4 (see Appendix M).

When analyzing the three portfolios compared to their respective indices, as well as the S&P500 value and equal weight indices, it is clear the only true difference is the

increased risk in the DFA fund portfolios. Just as advertised, the DFA funds have shown to successfully tilt the market portfolios, adding a marginal amount of risk to achieve a marginal outperformance. After accounting for fees, the returns of the portfolios are extremely negligible compared to investing in a benchmark.

Factor Definitions

The whole notion of adding an ever increasing amount of risky variables into the latest models of equilibrium has become the norm over the past few years. Since the single factor model was introduced in 1964, the rational model of expected returns has evolved into its newest form, the Fama-French five-factor model. Each new model imposes a new risky variable into the equation, now including the five factors, the market, size, value, profitability, and investment. The following section offers a more in- depth look into the various risky variables utilized by Fama and French in their latest five-factor model.

The market variable is denoted as beta and is the original and most well-known risky variable. Beta is a measure of volatility, or systematic risk, of a security or portfolio in comparison to the market as a whole. Beta is the risky variable associated with CAPM and is calculated using regression analysis. CAPM is an attractive solution for many due to its simplicity. However, the failure of CAPM in empirical tests implies that beta as a standalone risky variable is not sufficient.

Size is denominated as the market capitalization of the company. It is calculated as share price multiplied by the number of shares outstanding. The size factor, SMBBM, is

the average of the three small stock portfolio returns minus the average of the three big stock portfolio returns.

The value factor is represented by the ratio of the book value of equity of firm to its actual market value of equity (“B/M” or “Be/Me”). The value factor HML is the average of the two high B/M portfolio returns minus the average of the two low B/M portfolio returns. Equivalently, it is the average of small and big value factors constructed with portfolios of only small stocks and portfolios of only big stocks.

Profitability is denoted as the variable RMWt. RMWt is the difference between the returns on diversified portfolios of stocks with robust and weak profitability. Just as it is with HML, RMW can be interpreted as averages of profitability factors for small and big stocks.

The variable for investment is CMA. CMA is the difference between the returns on diversified portfolios of the stocks of low and high investment firms, which Fama and

French refer to as either conservative or aggressive. Same as HML and RMW, CMA is interpreted as the average of investment factors for small and large stocks.

FACTOR PORTFOLIO PERFORMANCE

Fama and Shiller both won the Nobel Prize for Economic Sciences in 2013 for their empirical analysis of asset prices. Both the rationalists and behaviorists agree on the facts regarding asset prices, but disagree on their interpretation. The following section takes a deeper look into the empirical data utilized by Fama and French while developing their research on models of equilibrium. Fama and French construct the portfolios based on various groupings of the different variables. This creates portfolios of small size with

high B/M, large size with low B/M, etc. The other differentiator in the portfolios lies in their weighting structure. Both equal-weight and value-weight portfolios are considered.

Equal weight indices are expected to outperform relative to value weight on the basis each stock in the portfolio is given the same weight. By giving the smaller, riskier stocks an equal weight, portfolio performance should mimic higher expected returns as a result.

Portfolios formed on Be/Me

The basis of the following Book-to-Market equity portfolios contains an analysis of the returns of 19 different value weighted and equal weighted portfolios, each compared to either the SPX or SPXEW, resulting in 40 portfolios total. The portfolios were created by Kenneth French and formed on Be/Me as the end of each June using

NYSE breakpoints. The different portfolios are constructed on the bottom 30%, middle

40%, top 30%, quintiles, and deciles of Be/Me. Firms with negative Be/Me are included in the “<=0” portfolio.

Value Weight Portfolios:

The value weight portfolios as a whole consistently outperform the market on nearly every measure. 16/19 of the test portfolios Sharpe Ratios, 15 year holding period returns, and betas were superior to the benchmark SPX (see Appendix B). However, only

7/19 we able to achieve a lower standard deviation of returns. The only portfolios not able to outperform on the basis of 15 year return and Sharpe Ratio were the lowest 10%,

20%, and 30% value portfolios. The results indicate, at least theoretically, forming portfolios on the basis of value will easily outperform the market.

In order to test for any statistically significant portfolio returns compared to the

S&P500, a T-test of the various portfolios was performed (see Appendix N). Only one portfolio (9-Dec) was able to achieve a T-test value over one, indicating, at least for value weighted portfolios, book-to-market equity does not offer any statistically significant returns.

Equal Weight Portfolios:

The primary difference between the value and equal weight portfolios is the much more volatile returns, and subsequently higher returns. Only 8/19 portfolios outperformed on the basis of standard deviation, but those portfolios also outperformed on every other metric compared to the SPXEW. The portfolios that outperformed were, as expected, the top 50% value portfolios. The top 50%, 40%, 30%, 20%, and 10% deciles outperformed on every metric along with the top two quartiles (see Appendix D). Again, it seems Fama and French’s theoretical portfolios are able to easily beat the market, not only on a pure return standpoint, but on a risk adjusted basis as well.

After analyzing the results of the T-test calculation, it seems once again there are no statistically significant returns on equal weight portfolios formed on book-to-market equity. The most significant value achieved was 1.13 on the highest 10% (Hi 10) portfolio, but even that falls short of any statistical significance (See Appendix N).

Although the returns are high for the equal weight portfolio, the increased returns are not significant.

Portfolios formed on Size and Be/Me

The data provided by Kenneth French used by Fama and French is broken into five book-to-market groups called 5x5 B/M sorts, with the smallest and largest quintiles representing microcaps and megacaps, respectively. The first digit in the portfolio naming convention is size, 1 representing the smallest firms and 5 representing the largest. The second digit in the naming convention represents the B/M ratio, with 1 representing the lowest ratio values and 5 representing the highest ratio values. The intersections of the 5 portfolios built on size and 5 portfolios built on Be/Me results in 25 portfolios total. After accounting for two sets of equal and value weighted 5x5 sorts and the corresponding market indices, SPX and SPXEW, 52 portfolios are analyzed.

Value Weight Portfolios:

Now that the portfolios are not only controlled for value, but size as well we expect based on Fama and French’s research that the returns on a risk adjusted basis should be superior to portfolios formed on value alone. The average Sharpe Ratio for the value weight returns formed on Size and B/M is .46 which slightly has the edge over the average Sharpe Ratio of portfolios formed only on B/M at .39 (see Appendix F and B).

The most noticeable difference after including a size variable is the greatly increased risk.

Only 2/25 portfolios had lower stand deviations compared to the industry benchmark, and only 1/25 portfolios outperformed on every measure (see Appendix F).

The average T-test value was much higher after controlling for size and one portfolio (portfolio 3-5) even appears to attain a statistically significant T-value over 2

(see Appendix N). Portfolio 3-5 is comprised of average size companies with the highest

value ratios. This seems to indicate there is a point where the risk of the smallest stocks is offset by the security of a larger company.

Equal Weight Portfolios:

The equal weight portfolios formed on size and B/M performed much more irregularly. Outperformance is spotty with no clear sign if, when equal weighted, the factors are much riskier or not. Primarily, only the largest firms outperformed on standard deviation, with the smallest firms outperforming consistently on holding period return

(see Appendix H). The T-test values are also much lower than the value weight portfolios. The average T-test value for value weight is .96 compared to just .1 for equal weight (see Appendix N).

Portfolios formed on Dividend Yield

The following portfolios are formed on the basis of dividend yield-to-price. While dividend yield is not utilized currently in any Fama-French models, an analysis of the factor is included to contrast their other risk factors. Essentially, these portfolios are formed on how much you pay for the expected dividend cash flows. The various portfolios are broken out into 19 separate portfolios of 10 deciles, 5 quartiles, 3 percentiles, and no dividends (<=0). Although not currently incorporated, analyzing this additional variable allows us to compare the performance of another conservative, value metric, based on the receipt of actual cash flows compares to Fama and French’s current risky variables.

Value Weight Portfolios:

When analyzing the value weighted portfolios formed on dividend yield, perhaps the most prominent initial observation is the ability of theoretical Fama-French portfolios to outperform on nearly every metric, again. Nine out of the nineteen portfolios analyzed outperformed their relative index, the SPX which mirrors the S&P500, in every category analyzed (see Appendix J). At first it seems a little too unrealistic that by simply manufacturing portfolios on the basis of dividend yield you can outperform the market over 15 years based on Sharpe ratio, year holding period return, beta, and standard deviation.

Equal Weight Portfolios:

Despite 9/19 value weight portfolios outperforming on every metric, equal weighted portfolios performed even more substantially, with 17/19 portfolios out performing on every single metric (see Appendix L). This analysis suggests that from a pure face value standpoint, portfolios formed on the basis of dividends will outperform the market in nearly every way. You can achieve higher return at lower risk than the market, just as long as you do not form companies based on 0% dividend yield or form the portfolio on the bottom decile of dividend yield-to-price. This data is peculiar considering dividend yield is not utilized currently in any Fama-French factor portfolios, despite being the clear winner on risk adjusted returns. It is also peculiar that the theoretical portfolios developed by French are not achieved under real world circumstances.

CONCLUSION

Eugene Fama and Kenneth French have done a tremendous amount of work concerning models of market equilibrium over the course of their lives. Their work has inspired many individuals who continue to elaborate off of their research. However, their work has shown disconnects at times, especially when considering theoretical performance compared to real performance. After analyzing the returns of both value and equal weighted theoretical portfolios, alongside the actual returns witnessed by DFA funds and their respective benchmarks, it becomes clear generating excess returns is impossible without taking on excess risk. Despite Fama and French achieving outperformance on nearly every theoretical portfolio, the performance witnessed by DFA in reality is lackluster. Subsequently, there is little evidence of statistically significant outperformance by either theoretical or real portfolios. The data analysis suggests increased exposure to risk through the addition of risky factors is the key element in achieving superior returns. Going forward, it seems significant outperformance on the basis of risky factors alone is impossible, implying markets are not significantly mispricing in the long run. However, value tilting does seem to show promise in achieving marginally superior returns.

APPENDIX A: VALUE WEIGHT PORTFOLIOS FORMED ON BE / ME

Top Performer Bottom Performer Mean Performer Index Performance