The Three-Factor Model

Transcription

1 Chapter 5 The Three-Factor Model The CAPM revolutionized not just portfolio management, but also how we look at finance. Now the relationship between risks and returns is finally defined in a scientifically acceptable way. That high stocks should have high expected returns has become the accepted norm in finance. But Eugene Fama and Ken French published the famous beta is dead paper 1 in 1992 and changed the landscape again. 5.1 Is Dead? It is more precise to use portfolios when we estimate we should plot portfolios expected returns vs. their Fama and French (1992). 0 s. Therefore, if we want to test the validity of the CAPM, 0 s. The following table capturing said relationship is from Plot returns vs.. Can you see why it is called the beta is dead paper? This rather flat Security Market Line is the reason why people said beta is dead, but it is very likely the result of not-so-perfect beta estimates. More importantly, too flat SML seems to work only on data during Fama and 1 Fama, Eugene F., and Kenneth R. French. The cross-section of expected stock returns. The Journal of Finance 47, no. 2 (1992):

2 32 CHAPTER 5. THE THREE-FACTOR MODEL French s test period (1963 to 1990). Newer data do not show a flat SML. Nevertheless, Pandora s box has been opened. A better model for asset pricing seems to be necessary. 5.2 The Three Factor Model If our goal is to explain asset returns, why don t we include as many factors as possible, i.e. do a kitchen-sink approach? Chen, Roll, and Ross (1986) 2 did just that by providing a rather inclusive, yet powerful model: R i t = i + i IP IP t + i EI EI t + i UI UI t + i CG CG t + i GB GB t + t, where IP: changes in industrial production EI : changes in expected inflation UI : changes in unanticipaed inflation CG: excess return of long-term corporate bonds over long-term Treasuries GB: excess return of long-term Treasuries over T-bills. On the surface, this model uses various macroeconomic indicators to replace the market portfolio. It makes some sense if we return to William Sharpe s original idea of holding bad investments. Investors should be rewarded with more returns if the stock is too much correlated with the macro economy. But this model is too arbitrary and ad hoc. The real breakthrough is from Fama and French s Three-Factor Model. The three factors are : market, small-stock e ect (SML) and value-stock e ect (HML). We already know the market risk factor. Let s look at the other two Small Stock E ect The small-stock e ect was first documented by a student of Fama s, Ralf Banz 3. Banz found that small stocks consistently outperformed large counterparts from 1920s to 1970s. Fama and French took the research a step deeper and constructed the table you see previously in the beta is dead paper. Fama and French looked at all NYSE, Amex, and NASDAQ stocks and grouped them according to their market valuations, or the market equity (ME). They systematically grouped stocks in June of every year in their sample data to form portfolios and calculated the next year s monthly returns for these portfolios. It turned out that low ME stocks (small stocks in their definition) outperformed large ME peer. The findings were consistent with Banz s. It should be noted that the small-stock e ect does not mean being small as a stock is a good thing. It is quite the opposite. Think about risks and returns. But as noted previously, the small-stock e ect disappeared in later periods. 2 Chen, Nai-Fu, Richard Roll, and Stephen A. Ross. Economic forces and the stock market. Journal of Business (1986): Banz, Rolf W. The relationship between return and market value of common stocks. Journal of Financial Economics 9, no. 1 (1981): 3-18.

3 5.2. THE THREE FACTOR MODEL Value Stock E ect In the same beta is dead paper, Fama and French also documented the value stock e ect, which is well known in the industry 4 before their work. They just created a systematic way to group stocks by their value. There are various ways to separate stocks into value or growth 5. Some preferred measures include P/E ratios (low P/E: value) and P/Cash flow ratios. But the most frequently cited measure is the book-to-market equity ratio (BE/ME ratio). A low BE/ME ratio is a good value indicator. Fama and French constructed portfolios according to stocks BE/ME ratios. They found that returns of these portfolios are more correlated with their BE/ME ratios than the market. See the following table. This value stock e ect does not disappear over time. It is also true across various countries. Cochrane (2011) 6 even goes as far as claiming the variations of these various portfolios are mostly driven by the value stock e ect. See the following table. 4 This e ect is the basis for value investing. Value investing was popularized by Ben Graham and his disciple Warren Bu ett. I think this quote from Graham explains the philosophy of value investing well: In the short run, the market is a voting machine but in the long run, it is a weighing machine. 5 The finance industry seems to prefer glamour to growth at some point of time in history, but now growth is probably more appropriate and popular term to use, given glamour s bubble-like perception. 6 Cochrane, John H. Presidential address: Discount rates. The Journal of Finance 66, no. 4 (2011):

4 34 CHAPTER 5. THE THREE-FACTOR MODEL The Model Fama and French (1996) 7 formally include both value stock and small stock e ect, together with market risk premium, in a factor model: R i t = + i mr m t + i smb SMB t + i hml HML t + t, where R i t is stock i s excess return at time t; i are risk factor loadings for the three risk factors (market, small stock and value stock); SMB t and HML t are small stock and value stock risk premiums, respectively, which are discussed below. If stocks are highly correlated with market risk factor, small stock risk factor, and value stock risk factor, they should demand higher expected returns. To accommodate the new small stock and value stock factors, Fama and French construct time-varying SML and HML risk premiums. Every year in June, they looked at all tradable stocks on NYSE, Nasdaq, and Amex and separate them into six portfolios according to their ME and BE/ME ratios. Then they calculate the next year s monthly returns for these portfolios. Specifically, these six portfolios are HML 30% 40% 30% SMB S/L S/M S/H B/L B/M B/H Risk premium HML (high minus low) = S/H + B/H 2 S/L + B/L ; 2 7 Fama, Eugene F., and Kenneth R. French. Multifactor explanations of asset pricing anomalies. The Journal of Finance 51, no. 1(1996):55-84.

5 5.2. THE THREE FACTOR MODEL 35 Risk premium SML (small minus large) = S/L + S/M + S/H 3 B/L + B/M + B/H. 3 It is at times confusing for students who are first exposed to the factor models, especially when both the premiums and betas are presented. But if you can recall the CAPM, which has only one premium and one beta, you will grasp the other two factors and the premiums much more easily. Now in industry and academic practice, when we want to evaluate a manager or a strategy s performance, we use the Three-Factor Model, instead of the CAPM, to calculate Q & A about FF s Three-Factor Model 1. Are small stocks the ones with small numbers of employees, smaller plants, less revenue, and smaller scope of business? 2. Do growth stocks have fast-growing earnings, sales, or assets? 3. How are SMB and HML factors are construed? 4. Can we summarize the model by saying We can explain the average returns of a company by looking at the company s size and book-to-market ratio? 5. Which gets better returns going forward: stocks that had great past growth in sales over the last 5 years, or stocks that had poor past growth in sales? 6. Value stock e ect is so strong, but we can t all buy value stocks. Someone has to hold the growth stocks. Also if we all buy value, the e ect will disappear. How do Fama and French explain this conundrum? 7. If the small-stock e ect no longer works, why did Fama and French still include SML in their factor model? Are There More Factors? The literature on factor models gradually accepts momentum as a plausible addition to the FF model. In finance, we often contrast momentum with contrarian. One bets on stocks following a continuous trend, while the other on the trend reversal. But in factor models, the momentum e ect is not saying that rising stocks will keep rising or that falling stocks will keep falling. It means when a stock is in a top-performing group this year, it is likely to be in the same group next year. Once the momentum factor is established, we don t actually look at whether a stock is in the top or bottom group. We see how it co-moves with the momentum portfolio. Beyond the momentum factor, a new factor called QMJ, Quality-Minus-Junk, is proposed by a student of Fama. Cli Asness, a founder of AQR Capital Management, believes that if we include the quality measure QMJ, we can revive the small stock e ect. He defines quality stocks as the ones that are well managed with good earnings and healthy growth rates. QMJ seems promising, but is not yet part of the mainstream factor models.

6 36 CHAPTER 5. THE THREE-FACTOR MODEL 5.3 What is behind the Risk-Return Relationship? Researchers in academia are still debating whether the abnormal returns observed in various model are compensation to risk or anomalies in the market. If they are market anomalies, we will have to deal with human irrationality. It is a plausible explanation and we will cover it in the next chapter. But if they are compensation to risk, how do we understand this risk-return relationship? What is driving it? William Sharpe s idea that investors demand more returns for assets that are bad and that badness is defined as how correlated with the market portfolio leads us to the concept of Intertermporal CAPM or simply ICAPM 8. Human beings are rational. We are always analyzing and optimizing the consumption and saving plan to maximize our satisfaction in life. In a simple scenario where we have a steady, well-paying job, we still constantly worry that we might starve if the job is lost in the future. So we save some of our current earnings to smooth out our potential lack of income. When we save, we are also dealing with the problem of picking the right asset. If our current steady job relies on the overall economy to a great extent, which is true to most people, we will want to put our savings in assets that are less correlated with the overall economy. This is the intertemporal view of the world and how we define badness of investments. A di erent perspective is called the Arbitrage Pricing Theory. The APT demands less accurate understanding of any pricing model. After all, not every human being is capable of doing tough math like an investment guru. The APT only assumes that investors somehow hold the stocks in equilibrium (maybe on the SML or something else). If they are out of whack, arbitrageurs will take advantage of the mispricing and bring the stocks back to equilibrium. As for why we need more compensation for value stocks, we don t know and don t have to know. In either the ICAPM or APT view, risks must be compensated with returns. I personally believe this concept better explains the long-lasting anomalies (persistent ). But who knows? 5.4 Eugene Fama and Dimensional Fund Advisors As of 2016, DFA has over $400 billion under management. If you recall Michael Lewis s The Evolution of an Investor, you will remember DFA as the odd-ball mutual fund company, which bars advisors from watching CNBC at work. It has its root in the Three-Factor Model. Both founders of DFA, David Booth and Rex Rex Sinquefield, were Eugene Fama s student at the business school of the University of Chicago. Booth and Sinquefield were among the first people to hear Ralf Banz s small stock e ect. They believed there was a business opportunity and started DFA. Later on, Fama introduced them to the value stock e ect and DFA quickly expanded into various value trading strategies. They don t do fundamental analysis and pick stocks the way Fama and French separate the stock universe. It is one of the most successful stories in the money manager history. It always puzzles me that DFA can charge fees for a strategy that any investor can employ without anyone else s help. But with DFA s size and clout, their trading does add value to investors. For example, DFA is willing to 8 This concept was first discussed by another Nobel Prize winner, Bob Merton.

7 5.5. EMPIRICAL DATA IN KEN FRENCH S DATA LIBRARY 37 absorb a big lot of stocks in exchange for a price discount. As they mostly deal in small and value stocks, their willingness to provide liquidity wins them unquestionable advantages. DFA, AQR, and passive index funds are testaments to the success of academic research in finance. After this chapter, you should have great confidence in yourself that achieving the performance level of DFA should not be too di cult. David Booth not only treats his teacher at University of Chicago well by having him as a well-paid consultant, but also donated $300 million to Chicago s business school. That is why you hear the name Chicago Booth School of Business all the time! 5.5 Empirical Data in Ken French s Data Library Ken French, the long-term co-author with Eugene Fama, a professor at Dartmouth and also a DFA consultant, maintains a data library that collects up-to-date risk-premiums. It has become a public utility and is used frequently and extensively by both academics and practitioners. Google Ken French to see what is included in this rich data library. You will need to use it some time in your career if you want a serious money manager career.

8 38 CHAPTER 5. THE THREE-FACTOR MODEL 5.6 Case: Vanguard Small-Cap Index Fund Performance Go to Yahoo! Finance to download VB s monthly prices. Periods are from March 2009 to December Convert the price series into returns. Note that 2/2/2009 3/1/2009 is considered as March 2009 s monthly return. It looks like the series starts from 2/2/2009, but the monthly series actually uses end of 2/2009 s price. 1. Contrast VB s mean monthly return and standard deviation with SPY s. 2. Contrast VB s Sharpe ratio with SPY s, assuming 0% risk-free rate The Three-Factor Model Download Fama and French s factor premiums (just the basic Three-Factor) from Ken French s data library. Pay attention to the time period alignment and the decimal points. 1. Use VB s data and Fama and French s factor premiums to run the CAPM regression. Report the estimated model. You need to include both the coe cient values and their significance. Does VB have a statistically significant? Economically significant? 2. Run the regression again, but with all the three factors this time. Does VB have a statistically significant? Economically significant? Exploit Alpha Replace VB with SPY. Rerun the CAPM and the Three-Factor Model regressions. Use SPY and VB to build a market-neutral portfolio. 1. Use 0 s you obtain from the CAPM regressions to determine the zero-beta portfolio s allocation. 2. Use the Three-Factor Model s coe cient estimates to forecast your portfolio s return.