asness frazzini pedersen

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1 Quality Minus Junk * Clifford S. Asness, Andrea Frazzini, and Lasse H. Pedersen This draft: October 9, 2013 Abstract We define a quality security as one that has characteristics th at, all-else-equal, an investor should be willing to pay a higher price for: stocks that are safe, profitable, growing, and well managed. High- quality stocks do have higher prices on average, but not by a very large margin. Perhaps because of this puzzlingly modest impact of quality on price, high-quality stocks have high risk-adjusted returns. Indeed, a quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns in the U.S. and globally across 24 countries. The price of quality i.e., how much investors pay extra for higher quality stocks – varies over time, reaching a – quality predicts a high future return of QMJ. low during the internet bubble. Further, a low price of Finally, controlling for quality resurrects the otherwise moribund size effect. * Andrea Frazzini is at AQR Capital Management, Two Greenwich Plaza, Greenwich, CT 06830, e-mail: [email protected]; web: http://www.econ.yale.edu/~af227/. Cliff Asness is at AQR Capital Management, Two Greenwich Plaza, Greenwich, CT 06830. Lasse H. Pedersen is at New York University, Copenhagen Business School, AQR Capital Management, CEPR and NBER, 44 West Fourth Street, NY 10012-1126; e-mail: [email protected]; web: http://www.stern.nyu.edu/~lpederse/. We thank Antti Ilmanen, Ronen Israel, Johnny Kang, John Liew, Toby Moskowitz, Per Olsson, and Scott Richardson for helpful comments and disc ussions as well as participants in the SIFR Institute of Financial Research Conference on Re-Thinking Beta.

2 When did our field stop being “ass et pricing” and become “asset expected ... Market-to-book ratios should be our left-hand variable, the thing we returning?” are trying to explain, not a sorting characteristic for expected returns. Cochrane, Presidential Address, American Finance Association, 2011 – The asset pricing literature in financial econom ics studies the drivers of returns, but, uences of market efficiency ultimately depend on prices, while linked, the economic conseq and Cochrane (2011). Do the highest quality not returns, as emphasized by Summers (1986) firms command the highest price so that these firms can finance their operations and invest? To address this question, we define quality as characteristics that investors should be willing to pay a higher price for, everything el se equal. We show that quality is priced, that is, investors pay more for firms with higher qu ality characteristics. However, the explanatory power of quality for prices is limited, presen ting a puzzle for asset pricing. This puzzle for 2 presented by of asset returns R asset prices is analogous to the famous puzzle of the low Roll (1984, 1988). Consistent with the limited pric ing of quality, high-quality stocks have historically delivered high risk-adjusted returns while low-quality junk stocks delivered negative risk-adjusted returns. Hence, a quality-minus-junk (QMJ) portfolio that invests long quality stocks and shorts junk stocks produces hi gh risk-adjusted returns. Further, we find that the price of quality (the marginal amoun t extra investors pay for higher quality characteristics) has varied over time as the market has sometimes put a larger or smaller price premium on quality stocks vs. junk stocks. For in stance, the price of quality was particularly low during the internet bubble. Since prices and returns are linked, the price of quality predicts the future return to the QMJ factor. Lastly, we show that QMJ has broader asset pricing implications, including re surrecting the size effect. we must identify stock characteristics that To apply the general definition of quality, simple framework to get growth model presents a Gordon’s should command a higher price. - Page 2 Quality Minus Junk - Asness, Frazzini, and Pedersen

3 intuition for the natural quality characteristics. Indeed, rewriting Gordon’s growth model , we 1 price-to-book value ( ) as follows: can express a stock’s P/B ܲ ’”‘ˆ‹–ƒ„‹Ž‹–›ή’ƒ›‘—–Ǧ”ƒ–‹‘  ൌ ሺͳሻ ܤ ”‡“—‹”‡†Ǧ”‡–—”െ‰”‘™–Š We scale prices by book values to make them more stationary over time and in the cross section. The four right-hand side variables form the basis for our definition of quality. These variables are intuitive and extend beyond the Gordon model in terms of their relevance for 2 stock prices. For each quality characteristic, we cons ider several measures in order to have a robust analysis and ensure that the explanatory power of quality on price (or the lack thereof) is not driven by a specific measurement choice: i. Profitability. Profitability is the profits per unit of book value. All else equal, more profitable companies should command a high er stock price. We measure profits in several ways, including gross profits, margins , earnings, accruals and cash flows, and focus on each stock’s average rank across these metrics . ii. Growth. Investors should also pay a higher price for stocks with growing profits. We measure growth as the prior five-year growth in each of our profitability measures. iii. Safety. Investors should also pay, all-else-equal, a higher price for a stock with a lower required return, that is, a safer stock. What should enter into required return is . We do not attempt to resolve those issues still a very contentious part of the literature here, rather we take a simple common sense approach. We consider both return-based nd volatility) and fundamental-based measures measure of safety (e.g., market beta a ௉ †‹˜‹†‡† ଵ ’”‘ˆ‹–Ȁൈ†‹˜‹†‡†Ȁ’”‘ˆ‹– 1  ൌ We rewrite the Gordon model simply as ൌ . ”‡“—‹”‡†Ǧ”‡–—”ି‰”‘™–Š ஻ ”‡“—‹”‡†Ǧ”‡–—”ି‰”‘™–Š ஻ 2 Equation (1) is a special case of the general present-value relation. We use the Gordon model to simplify the general present-value relation. notation but the same intuition applies to - Page 3 Quality Minus Junk - Asness, Frazzini, and Pedersen

4 of safety (e.g., stocks with low leverage, low volatility of profitability, and low credit risk). Payout. The payout ratio is the fraction of profits paid out to shareholders. This iv. nt and can be seen as a measure of characteristic is determined by manageme Management’s agency problems are diminished if free cash shareholder friendliness. flows are reduced through higher dividends (Jensen (1986)). We also consider both net payout as well as issuance (dilution). Payout is an example of how each of these measures is about their marginal effect, all else being equal. Indeed, if a higher payout is associated with a lower future profitability or growth, then this should not command a higher price, but a higher pay out should be positive when we hold all other factors constant. ese quality characteris For the market to rationally put a price on th tics, they need to be measured in advance and pred ict future quality characteristics, that is, they need to be persistent. We show that this is indeed the cas e; profitable, growing, safe, and high-payout stocks continue on average to display these characteristics over the following five or ten years. sample of U.S. stocks from 1956 to 2012 We test the pricing of quality over a long and a broad sample of stocks from 24 developed markets fr om 1986 to 2012. To evaluate the book on each stock’s pricing of quality, we first run cross- sectional regressions of price-to- overall quality score. Both in the long and broad sample, we find that higher quality is significantly associated with higher prices. However, the explanatory power of quality on 2 is only 12% in the long sample and 6% in the broad sample. price is limited as the average R When we also control for the firm’s size and past 12 -month stock returns, the cross-sectional 2 R increases to, respectively, 31% and 26%, still leaving unexplained a large amount of the cross sectional distribution of prices. Inter estingly, larger firms are more expensive controlling for quality, the analogue of the size effect on returns (Banz (1981)). We also regress the price-to-book on the four quality measures separately and in a 2 R sures separately modestly increases the joint regression. Having all four quality mea . Further, while profitability and growth are unambiguously associated with higher prices, - Page 4 Quality Minus Junk - Asness, Frazzini, and Pedersen

5 ve controlling for size and past returns, and stocks with high safety is mixed and even negati payout appear to command a lower, not a higher, price. There could be several potential reasons for the limited explanatory power of quality on prices: (a) market prices fail to fully reflec t these characteristics for reasons linked to behavioral finance or constraints (e.g., an inabili ty to lever), (b) market prices are based on superior quality characteristics than the ones we consider, and (c) the quality characteristics are correlated to risk factors not captured in our risk adjustments (so while the quality measure alone might command a higher P/B, the risk increase we fail to capture could imply an offsetting lower one). To examine these potential explanations, we first consider the returns of high- vs. eciles based on their quality score and consider low-quality stocks. We sort stocks into ten d We find that high-quality stocks have the value-weighted return in each portfolio. significantly higher raw returns than junk stocks. The difference in their risk-adjusted returns -quality stocks have relatively lower market, (i.e., 4-factor alphas) is even larger since high size, value and momentum exposures than junk stocks. We then construct a QMJ factor with a methodology that follows that of Fama and French (1993) and Asness and Frazzini (2013). Th e factor is long the top 30% high-quality stocks and short the bottom 30% junk stocks within the universe of large stocks and similarly 3 its large-cap only and small- This QMJ factor (as well as within the universe of small stocks. cap only components) delivers positive returns in 23 out of 24 countries that we study and . QMJ portfolios have our long and broad sample highly significant risk-adjusted returns in negative market, value, and size exposures, pos itive alpha, relatively small residual risk and QMJ returns are high during market downturns, presenting a challenge to risk-based explanations relying on covariance with market cr ises. Rather than exhibiting crash risk, if anything QMJ exhibits a mild positive convexity, that is, it benefits from flight to quality during crises. 3 As noted by Fama and French (2013) we can chose to orthogonalize each factor (size, value, momentum, nd dimensionality, or to to construct our factors more quality) to each other in a potential nightmare of choices a simply allowing some correlation among them. We choose the latter. - Page 5 Quality Minus Junk - Asness, Frazzini, and Pedersen

6 It is interesting to consider how the pricing of quality varies over time: Each month, we cross-sectionally regress er the time series of these price-to-book on quality and consid efficients that reflect the pricin g of quality at each time. cross-sectional regression co of quality reached its lowest level in Consistent with conventional wisdom, the price February 2000 during the height of the intern et bubble. The price of quality was also relatively low leading into the 1987 crash and leading into the Global Financial Crisis of 2007-2009. Following each of these three eye-open ing events, the price of quality increased, reaching highs in late 1990 (first gulf war), in late 2002 (after the Enron and WorldCom scandals), and in early 2009 (during the height of the banking crisis). Prices and returns are naturally connected, and we show that the pric e of quality negatively predicts the future return on QMJ; that is, a higher price of quality is naturally associated with a lower return on buying high-quality stocks. We note that the QMJ strategy of buying profitable, safe, growing, high payout stocks while shorting unprofitable, risky, shrinking, low-yielding stocks is very different from the e negatively correlated). QMJ is buying and standard value strategy HML (in fact the two ar of stock prices, while HML is buying selling based on quality characteristics irrespective based on stock prices irrespective of quality. Naturally, the two concepts can be combined, which we call quality at a reasonable price (Q ARP). This concept goes back at least to Graham and Dodd (1934) who stated that “ investment must always the price as well as the Naturally, value investing is impr oved by QARP, consistent with the quality of the security .” finding in the accounting literature that accountin g information can improve value investing (e.g., Frankel and Lee (1998) and Piotroski (2000)). Last, we show what happens when we switch things around and put QMJ on the right-hand-side to help explain other factors. We find that controlling for quality makes the value effect stronger, just like QARP is st ronger than HML alone. This makes sense as quality is positively associated with future ret urns, and negatively correlated with value. Further, controlling for quality has a surprisingly significant effect on the size factor. We show that including quality on the right-hand-side resurrects the formerly moribund size is highly negatively correlated to the strong effect. Indeed, the small-minus-big (SMB) factor ge firms are high quality, on average. While quality factor since small firms are junky and lar SMB has an insignificant alpha of 13 basis points per month controlling for the other - Page 6 Quality Minus Junk - Asness, Frazzini, and Pedersen

7 t -statistic of standard factors, this increases to a highly significant alpha of 64 basis points ( 6.39). In other words, when comparing stocks of similar quality, smaller stocks significantly outperform larger ones on average, which corr esponds to our finding in price space that larger firms are more expensive. Our paper is related to a lar ge literature. A number of papers study return-based anomalies. It has been documented that stocks with high profitability outperform (Novy- Marx (2013)), stocks that repurchase tend to do well (Baker and Wurgler (2002), Pontiff and Woodgate (2008), McLean, Pontiff, and Watanabe (2009 )), low beta is associated with high alpha for stocks, bonds, credit, and futures (Black, Jensen, and Scholes (1972), Frazzini and Pedersen (2013)), firms with low leverage have high alpha (George and Hwang (2010), Penman, Richardson, and Tuna (2007)), firms with high credit risk tend to under-perform (Altman (1968), Ohlson (1980), Campbell, Hilsch er, and Szilagyi (2008)), growing firms outperform firms with poor growth (Mohanram (2005)), and firms with high accruals are more likely to suffer subsequent earning s disappointments and their stocks tend to underperform peers with low accruals (Sloan (1996), and Richardson, Sloan, Soliman, and fferent and appear disconnected, our framework Tuna (2005)). While these papers are very di illustrates a unifying theme, namely that all th ese effects are about the outperformance of high-quality stocks, and we link returns and prices. Our paper is also related to the literature that considers how the price-to-book predicts future returns and future fundamentals based on the present-value relationship. Campbell and Shiller (1988) consider the ove rall market, and their divide nd growth variable can be interpreted an as aggregate quality vari able. Vuolteenaho (2002) and Fama and French (2006) consider individual stocks. Cohen, Po lk, and Vuolteenaho (2009) consider how cash- flow betas affect price levels and long-run retu rns, but they do not consider the pricing of other quality measures. See also the overview by Cochrane (2011) and references therein. characteristics that we study are well-known accounting In summary, most of the variables, but we complement the literature by studying (i) how quality affect price multiples and how much of the cross-sectional variation of price multiples can be explained by quality; (iii) how the current price of quality predicts (ii) how the price of quality varies over time; the future return on quality factors; (iv) how our quality framework unifies a number of - Page 7 Quality Minus Junk - Asness, Frazzini, and Pedersen

8 anomalies; and (v) how a unified quality factor can be used in asset pricing more broadly and, importantly, how it resurrects the size effect. Our evidence presents a puzzle: why is the price of quality (the amount investors are willing to pay for higher quality characteris tics) positive but still quite low and why, presumably a related or even the same question, is the return to QMJ so high? Our results are consistent with a too low market price of quality and inconsistent with an alternative view that the market prices simply reflect better me asures of quality due to the high returns of QMJ. Furthermore, our QMJ factor has a negati ve market beta and factor loadings and performs well in recessions and crises, presen ting a challenge to risk-based explanations, although that possibility, as always, remains open. The rest of the paper is organized as follo ws. Section 1 presents our data and quality recasts future quality (i.e., quality is sticky measures. Section 2 shows that ex ante quality fo e of quality. Section 4 as would be necessary for it to be priced). S ection 3 analyzes the pric considers the return of quality stocks and Sect ion 5 the return of QMJ. Section 6 connects the current price and future return of quality. Se ction 7 considers QARP. Section 8 shows how QMJ affects the standard factors. Section 9 concludes. The appendix contains a number of additional results and robustness checks. 1. Data, Methodology, an d Quality Measures In this section we describe our data sour ces and the methodology for constructing our quality measures. Data Sources Our sample consists of 39,308 stocks cove ring 24 countries between June 1951 and rrespond to the countries belonging to the December 2012. The 24 markets in our sample co MSCI World Developed Index as of December 31, 2012. We report summary statistics in Table I. Stock returns and accounting data ar e from the union of the CRSP tape and the - Page 8 Quality Minus Junk - Asness, Frazzini, and Pedersen

9 XpressFeed Global database. All returns are in USD, do not include any currency hedging, 4 We follow the standard and are measured as excess returns a bove the U.S. Treasury bill rate. convention and align accounting variables at the end of the firm’s fiscal year ending anywhere in calendar year t -1 to June of calendar year t . of U.S. stocks and a We focus on a long sample broad sample of global stocks. Our available common stocks on the merged long sample of U.S. data includes all 5 CRSP/XpressFeed data. The CRSP/XpressFeed database’s first available date for U.S. securities is June 1951 since accounting data star ts in fiscal year 1950. However, since some of our variables are five-year growth measures, the first available date for our regressions and return test is June 1956. of global data includes all available common stocks on the union Our broad sample 6 of the CRSP tape and the XpressFeed Globa l database for 24 developed markets. We assign sed on the location of the primary exchange. individual issues to the corresponding market ba For companies traded in multiple markets we use the primary trading vehicle identified by ption of Canada (whose coverage starts in XpressFeed. As shown in Table I, with the exce 1982) for most countries XpressFeed’s Global coverage starts in 19 86. Our sample runs from January 1986 to December 2012. Quality Score We use a variety of quality measures. We are interested in identifying stocks of profitable, stable, safe and high payout compan ies. To avoid data mining, we use a broad set average them to compute four composite proxies: of measures for each aspect of quality and Profitability . We then average the four proxies to compute a Payout and , Growth , Safety single quality score. Our results are qualitatively robust to the specific choices of factors. 4 Delisting returns are not available for our international We include delisting returns when available in CRSP. missing, we investigate the reason for disappearance. If sample. If a firm is delisted but the delisting return is the delisting is performance-related, we follow Shumway (1997) and assume a -30% delisting return. 5 Common stocks are identified by a CRSP share code (SHRCD) of 10 or 11. 6 Common stocks are identified by an XpressFeed issue code (TPCI) of 0. - Page 9 Quality Minus Junk - Asness, Frazzini, and Pedersen

10 Having multiple measures of quality makes our finding of a low explanatory power of quality on prices all the more surprising. Our quality measures are constructed as follows (details are in the appendix). We ets (GPOA), return on equity (ROE), return on measure profitability by gross profits over ass assets (ROA), cash flow over assets (CFOA), gross margin (GMAR), and the fraction of , ACC). In order to put each measure on equal earnings composed of cash (i.e. low accruals footing and combine them, each month we convert each variable into ranks and standardize z -score. More formally, let ݔ be the variable of interest and ݎ be the vector of to obtain a ሺ ሻ , where ݔሺ݇݊ܽݎൌ ߪሻȀ ሻ . Then the z -score of x is given by ݖ ݔ ߤ ݖൌ ߤെݎൌሺ ݎ ranks, ௫ ௥ ௜ ௥ ௜ ௥ ߪ score is are the cross sectional mean and standard deviation of r . Our ݕ݈ܾ݅݅ܽݐ݂݅݋ݎܲ and ௥ the average of the individual z -scores: ݖ൫ݖൌݕݐ݈ܾ݅݅ܽݐ݂݅݋ݎܲ ݖ൅ ݖ൅ (2) ݖ൅ ൯ ݖ൅ ݖ൅ ௖௙௢௔ ௥௢௔ ௔௖௖ ௥௢௘ ௚௣௢௔ ௚௠௔௥ Similarly, we measure growth as the five-year pr ior growth in profitability, averaged across over measures of profitability: ݖ൅ ݖ൅ ൯ ݖ൅ (3) ݖ൅ ݖ൅ ݖ൫ݖൌ݄ݐݓ݋ݎܩ ୼௚௠௔௥ ୼௔௖௖ ୼௥௢௔ ୼௥௢௘ ୼௚௣௢௔ ୼௖௙௢௔ Here, ȟ denotes five-year growth. Specifically, fo r each profitability measure, we definite five-year growth as the change in the numerator (e.g. profits) divided by the lagged rities as companies with low beta (BAB), low denominator (e.g. assets). We define safe secu idiosyncratic volatility (IVOL), low leverage (LEV) , low bankruptcy risk (O-Score and Z- Score) and low ROE volatility (EVOL): ሺ ሻ ݖൌݕݐ݂݁ܽܵ ݖ (4) ݖ൅ ݖ൅ ݖ൅ ݖ൅ ݖ൅ ௕௔௕ ௭ ௟௘௩ ௘௩௢௟ ௜௩௢௟ ୭ We define our payout score using equity and debt net issuance (EISS, DISS) and total net payout over profits (NPOP): ݖ൫ݖൌ ݐݑ݋ݕܽܲ ݖ൅ ݖ൅ ൯ (5) ௘௜௦௦ ௡௣௢௣ ௗ௜௦௦ Finally, we combine the four measures into a single quality score: - Page 10 Quality Minus Junk - Asness, Frazzini, and Pedersen

11 ሻ ሺ ݖൌݕݐ݈݅ܽݑܳ ݐݑ݋ݕܽܲ൅ݕݐ݂݁ܽܵ൅݄ݐݓ݋ݎܩ൅ݕ݈ܾ݅݅ܽݐ݂݅݋ݎܲ (6) Portfolios Our portfolio analysis relies on two sets of test factors: quality-sorted portfolios and quality-minus-junk factors (hereaf ter, QMJ factors). For both appro aches, we form one set of portfolios in each country and compute global portfolios by weighting each country’s portfolio by the country’s total (lagged) market capitalization. To form quality-sorted portfolios, at the end of each calendar month, we assign stocks in each country to ten quality-sorted portfoli os. U.S. sorts are based on NYSE breakpoints. every calendar month, and rebalanced every Portfolios are value-weighted, refreshed calendar month to maintain value weights. The QMJ portfolio construction follows Fama and French (1992, 1993 and 1996) and Asness and Frazzini (2013). QMJ factors are co nstructed as the intersection of six value- weighted portfolios formed on size and quality. At the end of each calendar month, we assign stocks to two size-sorted portfolios based on th eir market capitalization. For U.S. securities, the size breakpoint is the media n NYSE market equity. For Inter national securities the size breakpoint is the 80th percentile by country (whi ch in the U.S. corresponds approximately to NYSE breakpoints). We use conditional sorts, fi rst sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high-quality portfolios minus the average return on the two low-quality (junk) portfolios: ଵ ଵ ሺ ሻ ሻ ሺ ൌܬܯܳ ‹‰ — ƒŽŽ—ƒŽ‹–› ൅ െ ‹‰—ƒŽ‹–› ƒŽŽ — ൅ ଶ ଶ ଵ ଵ ሻ ሺ ሻ ሺ െ Big Junk Small Quality െ (7) ൅ ൌ ‹‰—ƒŽ‹–› ƒŽŽ — ଶ ଶ ܬܯܳ in small stocks ܬܯܳ in big stocks of quality (profitability, growth, safety Separate sub-portfolios based on the four components and payout score) are constructed in a simila r manner. We consider alphas with respect to a - Page 11 Quality Minus Junk - Asness, Frazzini, and Pedersen

12 domestic and global factors for the market (MKT), size (small-minus-big, SMB), book-to- 7 market (high-minus-low, HML), and momentum (up-minus-down, UMD). 2. Ex Ante Quality Forecasts Fundamentals We start by showing that a stock’s quality is a persistent characteristic. That is, by picking stocks that were profitable, growing, safe, and well managed in the recent past, we succeed in picking stocks that display these characteristics in the future. This step is important when we turn to the central analysis of whether the high quality firms command higher prices since, in a forward-looking rational market, prices should be related to future quality characteristics. Of course, predictability of quality is perfectly consistent with an efficient market – market efficiency says only that, since prices should reflect quality, stock should be unpredictable (or only predictable due to risk premia) not that quality itself returns should be unpredictable. Table II analyzes the predictability of quality as follows. Each month, we sort stocks defined in Section 1). The table then reports the into ten portfolios by their quality scores (as across stocks in the portfolio at the time of value-weighted average of our quality measures t the portfolio formation (time t + 120 months). We report ) and in the subsequent ten years ( the time series average of the value-weighted cross sectional means. The standard errors are adjusted for heteroskedasticity and autocorre lation with a lag length of five years (Newey and West (1987)). Table II shows that, on averag e, quality firms today remain high quality firms five and ten years into the future (condi tional on survival) and we can reject the null hypothesis of no difference in each of quality ch aracteristics up to ten years. Table A1 in the appendix reports additional results: we sort fi rms separately using each component of our quality score (profitability, growth, safety and payout) and report the spread in each variable up to 10 years, yielding similarly consistent results. 7 1996) and Asness and Frazzini (2013). We report a The risk factors follow Fama and French (1992, 1993, e Appendix. The data can be downloaded at detailed description of their construction in th http://www.econ.yale.edu/~af227/data_library.htm . - Page 12 Quality Minus Junk - Asness, Frazzini, and Pedersen

13 To summarize, quality is a persistent characteristic such that high quality today predicts future high quality. For both the U.S. long and global sample, profitability is the most persistent and, while still surprisingly stable, growth and payout are the least persistent. 3. The Price of Quality Given that quality can be measured in advan ce, we now turn to the central question of how quality is priced: Do high-quality stocks trade at higher prices than low-quality ones? cross-sectional regression of the z -score of each To address this question, we run a ௜ (defined in Section i MB ) ratio on its overall quality score, Quality 's market-to-book ( stock ௧ ௜ ௜ 1). Specifically, we let ܲ ሻܤܯሺݖؠ and run the regression: ௧ ௧  ௜ ௜ ௜ ܲ ܾ൅ܽൌ —ƒŽ‹–› (8) ߝ൅ ௧ ௧ ௧ This regression tests whether high quality is a ssociated with high prices in the cross section. Using z -scores limits the effect of outliers and it implies that the regression coefficient b has a simple interpretation: if quality improves by on e standard deviation, then the price-to-book 8 increases by b standard deviations. Panel A of Table III reports results of Fama and MacBeth (1973) regressions of prices on quality. Every month, we regress scal ed prices on quality measures and we report ope estimates. Standard errors are adjusted for time series averages of the cross sectional sl heteroskedasticity and autocorrelation (Newey and West (1987)) with a lag length of 12 months. We run the regression with and without country-industry fixed effects. These fixed z effects are implemented by varying the standardization universe of our -scores. That is, to implement country-industry fixed effects, we co nvert each variable into ranks by country- industry and standardize to obtain a z -score by country-industry pair, each month. In this rd deviation above its case, b has the interpretation that, if quality improves by one standa 8 Using (log) market-to-book on the left hand side as opposed to z-scores does not impact any of the results qualitatively. For brevity we only report results based on -scores. z - Page 13 Quality Minus Junk - Asness, Frazzini, and Pedersen

14 country-industry mean, then the price-to-book increases by standard deviations above its b country-industry mean. Columns (1)-(8) in Table III panel A show that the price of quality b is generally caled) prices. Indeed, the price of quality is positive: high quality firms command higher (s nd across specifications with controls and fixed positive both in the U.S. and global samples a effects. The highest estimated price of quality is 0.32, in the univariate specification, and it is highly statistically significant. This coefficien ts means that a one standard deviation change in a stock’s quality score is associated (in the cross section) with a 0.32 standard deviation change in its price-to-book score. 2 “should” be, t he R While theory does not provide specific guidance on what the explanatory power of quality on price appears limited. Quality explains only 12% of the cross sectional variation in prices in our U.S. sample and only 6% in our global sample. We also include controls for firm size and stock return over the prior year. We z measure each of these controls as the -score of their cross-sectional rank for consistency and ease of interpretation of the coefficients. We see that larger firms are more expensive controlling for quality. This result is the anal ogue of the size effect on returns (Banz (1981), see also Berk (1995)) expressed in terms of pric es. That is, big firms, even for the same quality, are more expensive, possibly leading to the return effect observed by Banz. The size effect could arise as large firms have less li quidity risk than small firms (Acharya and Pedersen (2005)) and thus we cannot dismiss that these higher prices are rational. Past returns have a positive effect on current prices. We include past returns to account for the fact that prices and book values are not measured at the same time. Hence, the positive coefficients on the past returns simply reflect that high recent returns will raise 2 9 prices while the book value has not had time to adjust. increases We see that the R markedly with these controls, but both the magn itude and the significance of the coefficient 2 on quality actually drops with the inclusion of controls. The maximum R is below 31% in all 9 See Asness and Frazzini (2013). - Page 14 Quality Minus Junk - Asness, Frazzini, and Pedersen

15 of these specifications, leaving the vast major ity of cross sectional variation on prices unexplained. . Panel B of Table III considers cross-se ctional regressions on each separate quality score, univariately and multivariately: ଷ ସ ଵ ଶ ௜ ௜ ௜ ௜ ௜ ௜ ƒˆ‡–› (9) ”‘™–Š ܾ ܾ൅ ܾ൅ܽൌ ”‘ˆ‹–ƒ„‹Ž‹–› ܾ൅ ܾ൅  ƒ›‘—– ߝ൅ ௧ ௧ ௧ ௧ ௧ ௧ e unambiguously positive, the price of safety We see that prices of profitability and growth ar is positive in a univariate regression but negati ve in the presence of other quality measures 10 consistently estimated to be negative. and controls, and the price of payout is It is natural that the market pays a price for profitability a nd growth. The surprisingly low price of safety is a price-based analogue to the flat security market line (Black, Jensen, and Scholes (1972) and Frazzini and Pedersen (2013)) and it is consistent with Black (1972) and Frazzini and Pedersen (2013) theory of leverage constraints. If investors are constrained from leveraging, risky assets command higher prices (and lower returns) while safe ass ets have lower prices (and higher returns). The negative price of payout could be driven by reverse causality: firms that have high (low) prices may opportunistically issue (repurchase) shares. 2 R The average increases when we include all four quality components, reaching 40% l leaving a large part of the cross section of in the U.S. and 31% in the global sample but stil prices unexplained. 4. The Return of Quality Stocks We turn from the pricing of quality to the cl osely related issue of the return of quality stocks. The return of quality stocks is important as it can help us further interpret our findings on the price of quality. We would like to shed light on our finding that quality explains prices t efficiency; (b) the se of (a) limited marke only to a limited extent: is this finding becau 10 Regressing prices on safety alone and controlling for si ze and past returns also yi elds an (insignificant) negative price of safety. - Page 15 Quality Minus Junk - Asness, Frazzini, and Pedersen

16 market uses superior quality measures (and, if we observed these measures, they would be e causality; or (c) quality is linked to risk in strongly related to prices) or in some cases revers a way not captured by our safety measure. Exp lanation (a) implies that high-quality stocks have higher risk-adjusted returns than low-qua lity stocks as investors are underpricing high on between our measured quality and ex post quality characteristics; (b) implies no relati returns or at least a greatly attenuated one; while (c) implies a univariate relation between quality and future returns which is reduced or eliminated by an effective risk model. Table IV reports the returns of stocks sort ed into ten deciles based on their quality score. The table reports both excess returns over T-bills and alphas with respect to, respectively, the CAPM 1-factor model, the Fama and French (1993) 3-factor model (which includes the size factor SMB and the value factor HML in addition to the market factor MKT), and the 4-factor model that also include s the momentum factor UMD (Jegadeesh and Titman (1993), Asness (1994), and Carhart (1997) ). Specifically, these alphas are the intercepts from the following regression with the first 1, 3, or 4 right-hand-side variables included: ௎ெ஽ ெ௄் ௌெ஻ ுெ௅ (10) ܶܭܯ ߚ൅ ܤܯܵ ߝ൅ ߚ൅ ߚ൅ߙൌ ܮܯܪ ߚ൅ ܦܯܷ ݎ ௧ ௧ ௧ ௧ ௧ ௧ We see that excess returns increase almost monotonically in quality such that high- quality stocks outperform low-quality stocks. The right-most column reports the return difference between the highest and lowest deciles and the associated t -statistic, showing that high quality stocks earn higher average returns than low quality stocks (between 47 and 68 basis points per month depending on the sample ) and we can reject the null hypothesis of no difference in average returns ( t -statistics ranging between 2.80 and 3.22). When we control for market risk and other factor exposures, the outperformance in the alpha of high-quality stocks is in fact even larger. This higher outperformance arises because high-quality stocks actually have lower market and factor exposures than low- quality stocks. Adjusting by the CAPM alone materially strengthens our results as higher quality stocks are, partly by construction, lower beta stocks. Across our three risk models in gh quality stocks and short low quality stocks our long U.S. sample, a portfolio that is long hi earns average abnormal returns ranging from 71 to 97 basis points per month with associated - Page 16 Quality Minus Junk - Asness, Frazzini, and Pedersen

17 t r broad global sample, we obtain similar -statistics ranging between 4.92 and 9.02. In ou results with abnormal returns between 89 to 112 basis points and t -statistics between 5.00 and 6.06. Our results are thus inconsistent with explanation (b) discussed above. Further, a simple risk explanation (c) is inconsistent with our finding that high-quality stocks have lower market exposures than junk stocks, but we study risk in more detail by considering the performance of the QMJ factor. 5. Quality Minus Junk In this section we examine the returns of our QMJ factors. As described in Section 1 ƒŽŽ—ƒŽ‹–› and ‹‰—ƒŽ‹–› portfolios and (Equation 7), QMJ is long the average of the portfolios. We also construct long/short short the average of the ƒŽŽ — and ‹‰ — factors based on each separate quality component using the same method. Hence, in addition to QMJ, we have quality factors based on pr ofitability, safety, growth, and payout. Table V reports the correlations between th e different quality components. The table reports the correlation both for the excess returns and for the abnormal returns relative to a 4- factor model (i.e., the correlations of the regressi on residuals). We see that all of the pairwise correlations among the quality components are positive, except the correlation between growth and payout. The negative correlation reflects that higher payout is naturally e pairwise correlation among the quality associated with lower growth. The averag components is 0.40 in the US and 0.45 in the global sample, and 0.38 for abnormal returns in ts measure different firm characteristics both samples. Hence, while the quality componen that investors should be willing to pay for, firms that are high quality in one respect tend to also be high quality in other respects. This did not have to be. Each of these variables, we argue, are quality measures investors should pay for at the margin, but they did not have to be related to one another. While theory is no guide here, we think these significant positive correlations lend support to our practical decision to combine these four thematic sets of measures as one quality variable. our quality factors in the US (panel A) Table VI reports the performance of each of and globally (panel B). Specifically, the table reports the average excess returns and the ctor models. We see that each quality factor alphas with respect to the 1-, 3-, and 4- fa - Page 17 Quality Minus Junk - Asness, Frazzini, and Pedersen

18 delivers a statistically significant positive excess return and alpha with respect to the 1-, 3-, and 4-factor models in the U.S. sample and significant 4-factor alphas in the global sample as well (the 3- and 4-factor results are quite similar as momentum, or UMD, does not change much). Naturally, the overall QMJ factor is th e strongest or the four, with highly significant alphas in the U.S. and global samples. The abnormal returns are large in magnitude and highly statistically significant. In our U.S. long sample a QMJ portfolio that is long high quality stocks and short junk stocks delivers 1-, 3-, and 4-factor abnormal returns of 55, 68, and 66 basis points per month (with corresponding t -statistics of 7.27, 11.10, and 11.20). Similarly, in our Global broad sample, the QMJ factor earns abnormal returns of 52, 61 and 45 basis points per month (with corresponding t -statistics of 5.75, 7.68, 5.50). Panels A and B of Table VI also report the risk-factor loadings for the 4-factor model. We see that the QMJ factor has a significantly ne gative market and size exposures. That is, QMJ is long low-beta and large stocks, while be ing short high-beta small ones. As would be expected, the safety factor has the most negative market exposure, though only growth attains a zero or small positive mposites also show negative market beta, the other quality co beta. The value exposure of QMJ is negative in the U.S. Since we expect that high-quality stocks have high prices while the value factor HML is long cheap stocks, we would expect a negative HML loading. We see that the profit ability, safety, and growth factors do have significantly negative HML loadings in the U.S. and global samples. The payout factor has a positive loading in the U.S. and global sample s. As discussed above, this positive payout loading could be driven by cheap stocks endogenously choosing a low payout. Panel C of Table VI and Figure 1 report the performance of the QMJ factor across countries. Remarkably, the QMJ fa ctor delivers positive returns and alphas in all but one of the 24 countries that we study, displaying a strikingly consistent pattern (with the only small negative being in New Zealand, one of the smallest countries in market capitalization and number of stocks). Furthermore 4-factors alphas are statistically significant in 17 out of 24 countries which is striking given the fact th at many individual countries have a small cross section of securities and a short time series. the QMJ factor over time in the U.S. and Figures 2 and 3 show the performance of e cumulative return of the QMJ factor (plotted global samples. Specifically, Figure 2 shows th as the cumulative sum of excess returns to avoid compounding issues) and Figure 3 shows - Page 18 Quality Minus Junk - Asness, Frazzini, and Pedersen

19 the cumulative sum of QMJ’s 4-factor risk-adjusted returns (the sum of the monthly in- sample regression alpha plus the regression erro r). Clearly, the QMJ factor has consistently delivered positive excess returns and risk-a djusted returns over time with no subsample driving our results. We report a series of robustness checks in the appendix. In Table A3 we split the sample in 20-year subsamples and report QMJ returns by size (10 size-sorted based on NYSE-breakpoints). Table A4 and Figure A1 re port results for large and small cap stocks within each country. Finally, Table A5 reports re sults for an alternative definition of the QMJ factor: we build a factor for each of the 22 quality measures we use and simply average the resulting portfolios returns to compute our pr ofitability, growth, safety, payout and QMJ factors. All the results point in the same direct ion with consistency across size, time periods, countries and construction methodology: QMJ port folios that are long high quality stocks and short junk stocks earn large and signific ant 1- , 3- and 4-factor abnormal returns. The return evidence on the QMJ factors could potentially be consistent with both junk stocks are overpriced), or risk (quality mispricing (quality stocks are underpriced and the world). Although a full explanation of stocks underperform junk stocks in bad states of can nonetheless provide the driver of quality returns is beyond the scope of this paper, we some stylized facts that either explanation should generate in order to fit the available evidence. The evidence does not point toward compensati on for tail risk as seen in Table VII. ng recession and expansions, during severe We compute the return of the QMJ factors duri bear and bull markets (defined as st 12 months below -25% or total market returns in the pa above +25%), during periods of high and low market volatility (we measure volatility as the 1-month standard deviation of da ily returns of the CRSP-value weighted index or the MSCI- World index and split the sample in the 30% top and bottom time periods) and during periods of a large increase or drop in aggregate volatil ity ( again, we split the sample into the 30% 1-month change in volatility). We find no top and bottom time periods in terms of the evidence of compensation for tail risk, if anything quality appears to hedge (as opposed being correlated to periods) of market distress. To study further the risk of QMJ, Figure 4 plots the performance of QMJ against the is clearly visible by the downward sloping return on the market. The negative beta of QMJ - Page 19 Quality Minus Junk - Asness, Frazzini, and Pedersen

20 relation of the excess return of QMJ and the mar ket. Further, the relatively tight fit around the curve shows the limited residual risk, implying a strong and consistent historical performance of QMJ during down periods for the market. QMJ also performs well in extreme down markets; in fact, the second-ord er polynomial showed in the graph has a positive (but insignificant) quadratic term (mea ning that the fitted curve bends upward in the extreme). This mild concavity is mostly driven by the returns to the profitability subcomponent of quality. In fact, the quadratic term is marginally significant ( t -statistic of 2.0) for the profitability factor. The strong ret urn in extreme down markets is consistent with a flight to quality (or at least profitability). That is , in down markets, investors may exhibit flight to quality in the sense that prices of unp rofitable stocks drop more than the prices of profitable stocks, even adjusting for their betas. The strong performance of QMJ in down ods for the market such as down quarters or markets is robust to considering longer down peri down years (not shown). Further, looking at the al phas reveal a similar pattern of mild flight to quality. Overall, our findings present a serious challenge for risk-based explanations (to the extent that bad states of the world are related to large negative realization of market returns) as high quality stocks appear to protect inve stors from severe market downturns. Of course, alternative risk-based explan ations are always possible. The Time Variation of the Price of Quality: Predicting QMJ 6. It is interesting to consider how the price of quality varies over time. To study this, Figure 5 shows the time series of the price of quality, that is, the time series of the Fama- 8. We see that the price MacBeth regression coefficients that we esti mate above in Equation of quality varies significantly over time. As one might expect, the price of quality is lowest during the height of the internet bubble in earl y 2000 and has other large swings during time periods consistent with economics intuition as discussed in the introduction. The intuitive pattern of the price of quality suggests that the variation is not just the price of quality, it is interesting to link driven by noise. To explore further the variation in prices and subsequent returns in the time series. Sp ecifically, if this time variation is not due to mis-measurement noise, then a high price of quality should predict low subsequent returns - Page 20 Quality Minus Junk - Asness, Frazzini, and Pedersen

21 of QMJ. Table VIII provides evidence of such predictability. This table reports the regression coefficients of time-series regressions of future QMJ returns on the ex ante price of quality: Ͳ Žƒ‰‰‡†  ௟௔௚௚௘ௗொெ௃ ߚ൅ ߚ൅ ܾ (11) ߚൌ ܬܯܳ ܬܯܳ ߝ൅ ௧ ௧ିଵ ௧ିଵଶǡ௧ିଵ ௧՜௧ା௞ Said simply, ܬܯܳ is the lagged price is the return of QMJ over the future k months, ܾ ௧ିଵ ௧՜௧ା௞ of quality (the variable of interest), and ܬܯܳ controls for past returns. Let us describe ௧ିଵଶǡ௧ିଵ each of these variables in detail. We run the regression in two ways: Using the “raw” excess returns of the QMJ factor on the left hand side (“raw”) and using the al pha of the QMJ factor on the left hand side (“alpha”). The future excess return on the raw QM J factor is computed simply by cumulating ௙ ௙ ௞ ς ς returns, To compute the alphas, we regress ൌ ൯ ܬܯܳ൫ͳ൅ ൫ͳ൅ݎ ݎ൅ . ܬܯܳ ൯െ ௧ା௝ ௧ ௧՜௧ା௞ ௝ୀ଴ ௧ା௝ ௧ା௝ QMJ on the contemporaneous returns of the market, size, value, and momentum factors and compute the alpha as the regression residual plus the intercept (i.e., as the return of QMJ with ௞ ς its factor exposures hedged out). We then cumulate these alphas ܬܯܳ ൅ ൌ ൫ͳ൅ߙ ௧ା௝ ௧՜௧ା௞ ௝ୀ଴ ௙ ௙ ς ݎ and use them on the left hand side of (11). We consider alphas to ensure ൯െ ൫ͳ൅ݎ ൯ ௧ ௧ା௝ ௧ା௝ that the predictability of the price of qu ality on QMJ is not driven by any potential predictability of other factors. ܾ is the lagged Fama-MacBeth regression coefficient from The price of quality, ௧ିଵ Equation (8) that gives the connection between pr ice and quality at each time. Specifically, the price of quality is estimated as column (1) in Table III for the U.S. and column (5) for the global sample. We are interested in testing the hypothesis that a high lagged price of quality predicts lower subsequent returns, that is, ൏ͲǤ ܾ ௧ିଵ defined as the portfolio weighted average of the past 1-year Last, ܬܯܳ – is ௧ିଵଶǡ௧ିଵ returns of the stocks in the QMJ portfolio. Th is captures standard momentum effects, again to ensure that the predictability of the price of quality is a novel finding. Table VIII reports only the regression coefficient for the variable of interest, the , ܾ ௧ିଵ ex ante price of quality. We run overlapping fore casting regressions predicting returns from one month up to five years. We adjust st andard errors for heteroskedasticity and rns (Newey and West (1987)) by setting the autocorrelation induced by the overlapping retu lag length equal to the forecasting horizon. - Page 21 Quality Minus Junk - Asness, Frazzini, and Pedersen

22 Table VIII shows that a high price of quality indeed predicts lower future returns on A, all the coefficients have the expected QMJ. In our U.S. long sample shown in Panel negative sign and we are able to reject the null hypothesis of no predictability in all but one specification. Predictability rises with the for ecasting horizon, indicating slowly changing obal sample in Panel B are noisier, but we see expected returns. The results for our shorter gl ients are negative as expected. The bottom rows that all of the statistically significant coeffic of Table VIII similarly test whether the price of the separate quality characteristics predict the returns of the corresponding long/short fa ctors. While these results are noisier, the estimates tend to be negative and all of the st atistically significant coefficients are again negative, as expected. We also run these tests using cross sectional coefficients obtained from a regression of the log book-to-market (as opposed to ranks) on the quality scores, thus preserving the scale of the spread in book to ma rket ratios. Results are in general stronger for the U.S. sample and similar for our global sample. We report these results in Table A6 of the Appendix. To summarize, the results in Table VIII and Table A6 are consistent with the hypothesis that the variation of the price of quality is not pure noise but, rather, reflects changes in the market pricing of quality character istics, generating variation in QMJ returns. Quality at a Reasonable Price 7. It is interesting to consider what is the “f air” price of quality? That is, if we suppose that a stock’s fundamental value is a multiple of its quality, ݕݐ݈݅ܽݑܳ݉ൌܸ , then what is V the fair value of m ? Relatedly, if the market pays a price for quality different from m , then what is the best way to buy cheap quality stocks? To answer these questions, we construct a long-short portfolio that we call quality at a reasonable price (QARP) as follows. Using the same factor construction as for QMJ, we ௜ ௜ . െ  n for various choices of ݕݐ݈݅ܽݑܳ݊ construct a long-short portfolio based on the signal ௧ ௧ That is, QARP is based on the differ ence between a stock’s quality times n minus its price- , that is, base the signal on the ݉ൌ݊ to-book score. We should get the highest alpha if we let is of course unobservable). m quality multiple that corresponds to the fundamental value ( - Page 22 Quality Minus Junk - Asness, Frazzini, and Pedersen

23 Indeed, in this case, the portfolio is long th e highest-alpha securities and short the lowest- 11 alpha securities. If the highest-quality stocks were the most expensive, then the quality and price ranks would line up, implying that ൌͳ݉ . When we construct QARP empirically, we do find that the alpha is highest for n close to 1 both in the U.S. and globally. ly form a portfolio of quality (QMJ) and Another way to consider QARP is to simp value (HML). The combination of QMJ and HML that has the highest Sharpe ratio puts a the remaining 30% on HML) in the U.S. and weight of about 70% on QMJ (and, hence, about 60% weight on QMJ globally. The Sharpe ratio of QARP (whether c onstructed based on combining signals or combining factor returns) is naturally higher than either quality or value alone, about 0.7 in the U.S. and 0.9 globally. QARP performs well as quality strategies complement value by helping an investor avoid the “value trap,” namely the trap of buying securities that look cheap but deserve to be cheap. Instead, QARP bu ys securities that are cheap relative to their quality. Our evidence suggests that the fair price of quality is above the level paid by the market. QMJ on the Right-Hand-Side of a Factor Model 8. 11 For simplicity consider a 2-period model so that the fundamental value is the expected payoff at ாሺ௉ ሻ మ k is the required return. The alpha of the security, that , where time 2 discounted at the required return, ൌܸ ଵା௞ is, the expected excess return above the required return is then ܲ ܲെܸ ଶ ଵ ൬ܧൌߙ ሺͳ൅݇ሻ ൰െͳെ݇ൌ ܲ ܲ ଵ ଵ ܸ and the price ܲ Naturally, the alpha depends on the difference between the fundamental value . Since our ଵ ly subtract the two (rather than dividing by price as measures of quality and price are based on z-scores, we simp above). - Page 23 Quality Minus Junk - Asness, Frazzini, and Pedersen

24 We have seen that QMJ is an intuitive a nd powerful factor that has significant alpha relative to the standard factors. It is also inte resting to switch things around and put QMJ on the right-hand-side to see how it affects the alphas and interpretation of the standard factors. More broadly, QMJ is a useful factor to add to the toolbox of global factors, e.g., when researchers need to test whether new phenomena are driven by quality. Table IX reports the results of regressing each of the SMB, HML, and UMD on the other standard factors, with and without QMJ on the right-hand-side. Let us first consider SMB, that is, the size effect. SMB has a mode st, but significant, excess return in our US sample and an insignificant excess return in the global sample. In both samples, however, SMB actually has a small and insignificant alpha when controlling for the other standard factors (the market, HML, and UMD). The size ef fect could appear to be a fluke, an artifact 12 of SMB’s market exposure. Controlling for QMJ completely changes this conclusion. SMB has a very large negative exposure to QMJ. Clearly, small stocks are junky relative to big stocks. This finding be young firms that are yet to be profitable, is intuitive as small stocks could, for instance, safe, and high payout. Moreover, controlling fo r QMJ, the size effect becomes large and highly significant in both samples. The size effect is alive and well when we account for quality as small stocks outperform large stocks when we compare firms of similar quality (and market beta, value and momentum exposure). This finding in return space is the analog of the strong size effect for prices that we documented in Table III. Table IX further shows that HML has a negative loading on QMJ. This is also intuitive as cheap stocks (with high book-t o-market) are naturally lower quality than expensive stocks. This negative loading implie s that controlling for QMJ increases the alpha of HML, strengthening the value effect. Lastly, UMD has positive loading on QMJ, which is significant in the global but not U.S. sample. Controlling for this exposure to quality lowers the alpha of UMD, but the in both samples. Quality has several other momentum effect remains highly significant 12 This alpha is further reduced if we include lagged ve rsions of the market return on the right-hand-side to lication we do not pursue in this paper. account for possible illiquidity in SMB, a comp - Page 24 Quality Minus Junk - Asness, Frazzini, and Pedersen

25 interesting implications for the standard fact broadly, which we ors and asset pricing more intend to explore further in future research. 9. Conclusion In this paper we define a quality security as one that has characteristics that should command a higher (scaled) price. Following from the Gordon Growth Model, quality stocks are safe, profitable, growing, and have high payout ratio. We create definitions of all four quality subcomponents, and quali ty in general, which are robust and inclusive from across the literature and test the hypothesis that high quality firms have higher scaled prices. Consistent with market efficiency, we find that high quality firms do exhibit higher prices on average. However, the explanatory power of quality on prices is low, leaving the majority of cross sectional dispersion in scaled prices unexplained. As a result, high quality firms exhibit high risk-adjusted returns. A quality-minus-junk (QMJ) factor that goes long high-quality stocks and shorts low-quality stocks earns significant risk-adjusted returns with tio above 1 after hedging its other factor an information ratio above 1 (i.e., a Sharpe ra exposures) in the U.S. and globally across 24 countries. They are consistent with quality stocks Our results present a puzzle for asset pricing. being underpriced and junk stocks overpriced or, alternatively, with quality stocks being riskier than junk stocks. However, while one can never rule out a risk explanation for the high return of quality stocks, we are unable to identify this risk; in anything, we find evidence of the opposite. We show that quality st ocks are low beta and, rather than exhibiting crash risk, if anything they benefit from “ flight to quality, ” that is , they have a tendency to perform well during periods of extreme market distress. These findings present a challenge for risk-based explanations where bad states of the world are negatively correlated to extreme return realizations of the market factor. Finally, we show that the price of quality varies over time, generating a time-varying expected return on quality-minus-junk portfolios: a low price of quality predicts a high future return of quality stocks relative to junk stocks. In summary, we document strong and cons istent abnormal returns to quality, and do ing than prior papers using all four components so in a far more inclusive and complete sett - Page 25 Quality Minus Junk - Asness, Frazzini, and Pedersen

26 implied by the Gordon Growth Model simultaneously . We also tie these results to the cross- section and time-series of the pricing of quality in novel ways. et pricing: We cannot tie the returns of Our results present an important puzzle for ass , demonstrate that prices cross-sectionally vary quality to risk, or, in a highly related finding “enough” with quality measures. At this point the returns to quality must be either a n anomaly, data mining (incredibly robust data mining - including across countries, size and istent U.S. and global correlations of quality time periods, and encompassing the strong cons to size), or the results of a still-to-be-identified risk factor not from the 4-factor model. - Page 26 Quality Minus Junk - Asness, Frazzini, and Pedersen

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30 Agency costs of free cash flow, corporate finance, and “ Jensen, Michael C. (1986), takeovers ,” The American Economic Review 76(2), 323-329. ratio test statistic of mean -variance efficiency without a Kandel, S. (1984), “The likelihood -592. riskless asset,” Journal of Financial Economics, 13, pp. 575 Karceski, J. (2002), “Returns - Chasing Behavior, Mutual Funds, and Beta’s Death,” Journal of Financial and Quantitative Analysis, 37:4, 559-594. McLean, David, Jeffrey Pontiff, and Akiko Watanabe (2009), “Share Issuance and Cross - Sectional Returns: International Evidence,” Journal of Financial Economics 94, 1 -17. Myers, Stewart, and N. Majluf (1984), “Corporate financing and i nvestment decisions when Journal of Financial Economics 13, 187– firms have information that investors do not have,” 221. Separating Winners from Losers among Low Book-to-Market Mohanram, Partha (2005), “ Stocks using Financial Statement Analysis ”, Review of Accounting Studies, 10, 133 – 170. Novy- Marx, Robert (2013), “ The Other Side of Value: The Gross Profitability Premium, ” Journal of Financial Economics 108(1), 2013, 1-28. Penman, Stephen H. (1996), The articulation of price-earnings ratios and market-to-book “ ratios and the evaluation of growth ,” Journal of Accounting Research, 34 (2), 235-259. Penman, Stephen, Scott Richardson, and Irem Tuna (2007), “The Book -to-Price Effect in Stock Returns: Accounting for Leverage,” Journal of Accounting Research, 45 (2), 427 -467. . (2000), “ Value Investing: The Use of Historical Financial Statement Piotroski, Joseph D Information to Separate Winners from Losers Journal of Accounting Research, 38, 1-41. ,” - Page 30 Quality Minus Junk - Asness, Frazzini, and Pedersen

31 - sectional returns,” Journal of Pontiff, J., W. Woodgate (2008), “Share issuance and cross Finance 63, 921-945. Richardson, Scott, Richard G. Sloan, Mark Soliman, and Irem Tuna (2005), “ Accrual Reliability, Earnings Persistence and Stock Prices, ” Journal of Accounting and Economics 39 (3), 437-485. Roll, Richard (1984), “ Orange juice and weather ,” American Economic Review, 74 (5), 861- 880. Roll, R. (1988), 566. – R2, Journal of Finance 43, 541 “ ” Scholes, M., and J. Williams (1977), “Estimating Betas from Nonsynchronous Data" Journal of Financial Economics ,5 ,309-327. - beta CAPM,” Journal of Financial Shanken, J. (1985), “Multivariate tests of the zero Economics, 14,. 327-348. Sloan, Richard G. (1996), "Do Stock Prices Refl ect Information in Accruals and Cash Flows About Future Earnings?", The Accounting Review 71, 289-315. et Rationally Reflect Fundamental ce H. (1986), “Does the Stock Mark Summer, Lawren -601. Values?,” The Journal of Finance 41, 3, 591 ,” The Journal of What Drives Firm-Level Stock Returns? Vuolteenaho, Tuomo (2002), “ Finance, 57, 1, 233-264. - Page 31 Quality Minus Junk - Asness, Frazzini, and Pedersen

32 Table I Summary Statistics This table shows summary statistics as of June of each year. The sample includes all U.S. common stocks (CRSP ” equal to 10 or 11) and all global stocks (“tcpi” equal to 0) in the merged CRSP/ Xpressfeed “ shrcd global databases. Country Average number Firm size Total number of Weight in global St art Year End Year of stocks stocks p ortfolio (Billion-USD) 2,142 660 Aust ralia 0.63 0.018 1986 2012 Austria 56 0.70 0.002 1990 2012 126 231 91 2.37 0.009 1990 2012 Belgium Canada 1,901 541 1.08 0.022 1982 2012 Switzerland 343 135 4.06 0.023 1986 2012 1,492 3.01 596 Germany 0.061 1989 2012 Denmark 85 1.08 0.004 1986 2012 227 Sp ain 212 82 4.48 0.014 1986 2012 Finland 83 1.66 0.005 1986 2012 202 France 1,088 397 2.85 0.044 1986 2012 United Kingdom 3,312 1,103 1.83 0.095 1986 2012 Greece 239 132 0.48 0.002 1995 2012 1,351 516 1.21 0.026 1989 2012 Hong Kong 106 38 1.58 0.002 1987 2012 Ireland Israel 284 97 0.64 0.003 1995 2012 Italy 129 2.37 0.018 1986 2012 356 Jap an 3,856 1,988 1.29 0.202 1986 2012 Netherlands 250 109 4.70 0.021 1986 2012 Norway 120 0.96 0.004 1986 2012 429 New Z ealand 176 69 1.26 0.003 1990 2012 Portugal 92 38 1.96 0.002 1990 2012 Singap ore 860 353 0.60 0.009 1990 2012 Sweden 677 203 1.35 0.012 1986 2012 0.399 1.31 2012 1951 19,356 3,594 United States – Page T1 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

33 Table II Persistence of Quality Measures stocks in each country in are ranked in ascending This table shows average quality scores. Each calendar month, order on the basis of their quality score. The ranked stoc n portfolios. U.S. sorts are ks are assigned to one of te based on NYSE breakpoints. This table reports the value-weighted average of quality measures across stocks in the portfolio at portfolio formation (t) up to the subsequent ten years (t + 120 months). We report the time series average of the value-weighted cross sectional means. Panel A reports results from our Long Sample of domestic Broad Sample stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our of global stocks. The sample period runs from June 1986 to December 2012. Standard errors are adjusted for heteroskedasticity and autocorrelation with a lag length of five years (Newey and West (1987)) and 5% significance is indicated in bold. P2 P3 P4 Panel A: Long Sample P6 P7 P8 P9 P10 P10 - P1 P10 - P1 P1 P5 (Lo w) t-s tat (Hig h ) U.S., 1956 - 2012 0.46 -1.38 -0.39 -0.15 Qu alit y 0.25 -0.71 0.69 1.00 1.56 2.94 47.46 0.05 t 0.63 Qu alit y -0.14 0.00 0.14 0.29 0.45 -0.29 0.86 1.31 1.92 37.42 -0.60 t + 12M 33.01 -0.33 -0.12 -0.05 0.05 0.15 0.27 0.40 0.54 0.74 1.16 1.49 Qu alit y t + 36M 0.35 Qu alit y 0.04 0.09 0.16 0.22 -0.02 0.46 0.68 1.04 1.20 20.68 -0.16 t + 60M 0.30 Qu ality 0.00 0.03 0.07 0.09 0.21 -0.09 0.38 0.62 0.89 0.98 20.70 t + 120M Profit 20.74 -0.37 -0.19 -0.10 0.05 0.12 0.18 0.29 0.35 0.59 1.08 1.44 t + 120M 6.10 0.57 -0.23 -0.19 -0.13 -0.12 Gr o w t h -0.12 -0.02 0.11 0.11 0.34 -0.10 t + 120M 0.67 0.35 0.21 0.15 0.08 -0.03 0.63 0.49 0.95 9.68 Safety -0.15 -0.28 t + 120M Payout 0.12 0.29 0.28 0.29 0.38 17.31 0.49 0.49 0.56 0.61 0.49 0.39 t + 120M P1 Panel B: Broad Sample P3 P4 P5 P6 P7 P8 P9 P10 H-L H-L P2 Glo b al, 1956 - (Low) (High) t-stat 1.04 0.72 0.47 0.25 0.04 -0.79 42.28 3.07 Qu alit y -0.19 -1.45 1.62 -0.45 t 1.87 39.05 1.28 0.85 0.60 0.44 0.27 0.13 Qu alit y 0.01 -0.59 -0.29 -0.14 t + 12M 0.06 44.95 1.37 1.07 0.70 0.48 0.36 0.23 Qu alit y 0.13 -0.30 -0.13 -0.05 t + 36M 0.93 0.20 0.13 0.32 0.42 0.61 35.22 1.03 Qu alit y 0.10 -0.10 0.00 0.04 t + 60M 0.19 35.47 -0.08 -0.01 0.07 0.07 0.10 t + 120M 0.27 0.36 0.52 0.75 0.82 Qu ality 22.77 1.19 -0.28 -0.08 0.00 0.10 0.14 0.23 0.34 0.37 0.53 0.90 Profit t + 120M 0.37 0.18 0.09 0.00 -0.07 -0.16 6.40 Gr o w t h -0.09 -0.19 -0.12 -0.15 -0.14 t + 120M 0.06 0.20 0.74 -0.22 -0.14 -0.09 0.02 Safety 0.11 0.32 0.50 0.52 13.59 t + 120M 8.15 0.51 0.31 0.49 0.42 0.42 0.57 0.40 Payout 0.35 0.17 0.28 0.48 t + 120M Asness, Frazzini, and Pedersen Page T2 – Tables and Figures – – Quality Minus Junk

34 Table III Results: Cross Sectional Regressions, the Price of Quality score of a stock’s This table reports coefficients from Fama-Macbeth regressions. The dependent variable is the z- market to book ratio (MB) in month t. The explanatory va riables are the quality scores in month t and a series of Size is the stock return in month t. R ’ s market equity (ME). ሻݐሺݐܴ݁ controls. ሻݐെͳʹǡݐሺݐ݁ is the z-score of the stock is the stock return in the prior year. All variables are rescaled to have a zero mean and a standard deviation of one. When indicated ( “Industry FE” , “Country FE” ) variables are standardized by indust ry-country pairs. Average R2 is the time series averages of the adjusted R-square of the cross sectional regression. Stan dard errors are adjusted for heteroskedasticity and autocorrelation (Newey and West (1 987)) with a lag length of 12 months. T-statistics are shown below the coefficient estimates and 5% statistical significance is indicated in bold. Panel A: The Price of Quality Broad Samp le (Global, 1986 - 2012) Long Samp le (U.S. , 1956 - 2012) (1) (3) (4) (5) (6) (7) (8) (2) 0.09 0.32 0.19 0.32 0.20 0.24 0.10 0.22 Qu alit y (23.33) (13.94) (23.92) (22.47) (15.54) (24.39) (17.20) (15.94) . Size . 0.30 . 0.29 0.31 0.31 . (19.19) (20.91) (27.08) (17.71) . . . . . Ret(t-12,t) . 0.27 . 0.28 0.27 . 0.28 (26.50) (18.60) (22.54) (21.36) . . . . Industry FE No No Yes Yes No No Yes Yes Country FE Yes Yes Yes Yes 0.25 0.05 0.30 0.31 0.26 0.11 0.06 Average R2 0.12 Panel B: The Price of Each Quality Component Broad Samp le (Global, 1986 - 2012) Long Samp le (U.S., 1956 - 2012) (1) (3) (4) (5) (6) (7) (8) (9) (10) (2) Pro fit ab ilit y 0.41 ... 0.30 0.29 ... 0.19 (26.19) ... (23.64) (33.76) ... (31.37) . . Gr o w t h .. 0.11 0.28 .. 0.08 0.38 . ( 3 1. 18 ) .. (12.25) . (35.02) .. (12.67) . . -0.08 0.14 . Safety . . 0.11 . -0.10 (8.19) -(12.59) .. (9.95) . -(11.38) .. . . . -0.13 -0.10 -0.10 -0.06 .. Payout .. ... -(18.41) ... -(4.69) -(11.23) -(11.11) . . ... Size 0.28 ... 0.31 ... (26.22) ... (21.67) . . 0.28 ... 0.28 Ret(t-12,t) ... ... ... (23.33) (28.69) Industry FE No No No No Yes No No No No Yes Country FE Yes Yes Yes Yes Yes 0.02 0.01 0.08 0.31 0.40 0.09 Average R2 0.18 0.15 0.03 0.01 – Tables and Figures – – Page T3 Asness, Frazzini, and Pedersen Quality Minus Junk

35 Table IV Quality-Sorted Portfolios This table shows calendar-time portfolio returns. Each calendar month, stocks in each country in are ranked in nked stocks are assigned to one of ten portfolios. U.S. ascending order on the basis of their quality score. The ra sorts are based on NYSE breakpoints. Portfolios are value-weighted, refreshed every calendar month, and s. We form one set of portfolios in each country and rebalanced every calendar month to maintain value weight compute global portfolios by weighting each country’s portfolio by the country’s total (lagged) market capitalization. The rightmost column report s returns of a self-financing portfolio that is long the high quality is table includes all available common stocks on the portfolio and shorts the low quality portfolio. Th CRSP/Xpressfeed merged database for the markets listed in Table I. Alpha is the intercept in a time-series riables are the monthly retu rns from the market portfolio regression of monthly excess return. The explanatory va t (HML), and momentum (UMD) factor-mimicking portfolios. Panel A (MKT) and size (SMB), book-to-marke reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December Broad Sample 2012. Panel B reports results from our of global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Returns and alphas ar e in monthly percent, t-statistics are shown below the coefficient estimates, and 5% statistical significance is indicated g on the market portfolio. Information in bold. Beta is the realized loadin e standard deviation of the estimated residuals in the time- ratio is equal to 4-factor alpha (intercept) divided by th d information ratios are annualized. series regression. Sharpe ratios an Panel A: Long Sample P3 P4 P5 P6 P7 P8 P9 P10 H-L P1 P2 (Lo w) U.S. , 1956 - 2012 (High) Exces s return 0.36 0.39 0.45 0.45 0.57 0.47 0.58 0.61 0.15 0.47 0.38 (2.75) (1.90) (2.51) (2.60) (3.42) (2.04) (3.48) (3.68) (2.80) (0.55) (1.56) -0.53 -0.24 0.01 -0.12 -0.02 -0.01 0.13 0.71 0.14 0.18 -0.15 CAPM alpha (-2.85) (-2.25) (-0.33) (-0.18) (2.41) (0.23) (2.71) (2.86) (4.92) (-4.62) (-2.01) -0.38 0.01 -0.21 -0.08 -0.06 0.12 -0.67 0.16 0.29 0.97 -0.25 3-factor alpha (0.12) (-4.11) (-1.44) (-1.09) (2.26) (-4.47) (3.37) (5.24) (9.02) (-7.83) (-5.47) -0.56 -0.42 -0.26 -0.29 -0.14 -0.12 0.04 -0.05 0.19 0.41 0.97 4-factor alpha (-6.24) (-4.26) (-5.39) (-2.37) (-2.22) (0.68) (-1.08) (3.62) (7.10) (8.55) (-5.73) 0.97 Beta 1.08 1.09 1.03 1.01 1.22 1.00 0.95 0.90 -0.38 1.28 Sharpe Ratio 0.07 0.21 0.25 0.27 0.33 0.35 0.46 0.37 0.46 0.49 0.37 In fo rmatio n Ratio -0.90 -0.82 -0.61 -0.77 -0.34 -0.32 0.10 -0.15 0.52 1.02 1.23 A d ju s ted R2 0.90 0.92 0.93 0.90 0.91 0.91 0.93 0.92 0.90 0.60 0.91 Panel B: Broad Sample P10 P4 P5 P6 P7 P8 P9 P3 H-L P1 P2 (Lo w) (High) Glo b al , 1986 - 2012 Exces s return 0.35 0.43 0.38 0.52 0.46 0.57 0.52 0.61 0.65 0.68 -0.03 (1.01) (1.85) (1.25) (-0.08) (1.74) (2.29) (2.08) (2.54) (2.78) (3.22) (1.42) -0.61 0.17 -0.06 -0.12 0.07 0.03 -0.20 0.11 0.22 0.28 0.89 CAPM alpha (-3.20) (-0.42) (-0.90) (0.53) (0.25) (-1.19) (1.05) (2.05) (2.44) (5.00) (1.52) 1.12 -0.73 -0.33 -0.18 -0.24 -0.02 -0.04 0.10 0.11 0.24 0.39 3-factor alpha (-4.14) (-1.33) (-1.98) (-0.17) (-0.35) (0.92) (0.98) (2.17) (3.49) (7.68) (-2.08) -0.46 -0.04 -0.09 -0.23 0.01 -0.24 0.10 0.11 0.23 0.47 0.93 4-factor alpha (-2.49) (-0.63) (-1.75) (0.06) (-0.36) (-1.44) (0.95) (1.97) (3.96) (6.06) (0.91) Beta 1.14 1.12 1.00 1.03 0.94 0.91 0.85 0.87 0.82 0.78 -0.36 0.44 Sh arp e Ratio 0.27 0.24 0.36 0.33 0.20 0.40 0.49 0.53 0.62 -0.01 1.28 -0.53 -0.30 -0.13 -0.37 0.01 -0.08 0.19 0.20 0.41 0.84 In fo rmatio n Ratio 0.82 0.84 0.82 0.81 0.82 0.56 0.79 0.80 A d ju s ted R2 0.79 0.80 0.81 – Page T4 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

36 Table V Quality Minus Junk: Correlations This table shows correlation of monthly returns. Quality minus Ju nk (QMJ) factors are constructed as the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigned to two size-sorted portfolios based on their market capitalization. For U.S. securi ties, the size breakpoint is the median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, first sorting on size , then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the lar two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a simi by weighting each c manner. We form one set of portfolios in each country and compute global portfolios ountry’s portfolio by country’s total (lagged) market capitali zation. This table includes all availab le common stocks on the CRSP/Xpressfeed the merged database for the markets listed in Ta ble I. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the ma rket portfolio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor-mimicking portfolios. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our Broad Sample of global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Abnormal returns are constructed as the intercept plus the residual of a time-series are the monthly returns from the market portfolio (MKT) and regression of monthly excess return. The explanatory variables size (SMB), book-to-market (HML), and momentum (UMD) factor-mimicking portfolios. 1956 - 2012) Pan el B: Bro ad Samp le (Glo b al, 1986 - 2012) Panel A: Long Sample (U.S. , QM J Pro fit ab ilit y yout Safet y Gro wt h Pa yout QMJ Profitab ilit y Safet y Gro wt h Pa Ret u rn s Ret u rn s 1.00 1.00 QMJ Pro fit ab ilit y 0.82 1.00 0.79 1.00 0.88 0.64 1.00 0.86 0.84 1.00 Safety 0.24 0.52 0.15 1.00 0.28 0.36 0.27 1.00 Gr o w t h 0.76 0.69 0.53 -0.34 1.00 1.00 0.46 0.51 -0.19 0.35 Payout Abnormal Returns (4-factor) Abnormal Returns (4-factor) 1.00 QMJ 1.00 1.00 1.00 Pro fit ab ilit y 0.70 0.82 0.43 Safety 0.71 0.76 1.00 0.72 1.00 0.42 0.49 0.18 1.00 0.35 0.30 0.15 1.00 Gr o w t h -0.09 0.62 0.30 -0.06 1.00 0.69 0.36 0.33 0.44 1.00 Payout – Page T5 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

37 Table VI Quality Minus Junk: Returns rns and factor loadings. Quality minus Ju nk (QMJ) factors are constructed as the This table shows calendar-time portfolio retu intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigne d to two size-sorted portfolios based on their market capitalizati on. For U.S. securities, the size breakpoint is the median NYSE rst market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, fi sorting on size, then on quality. Portfolios are value-weigh h, and rebalanced every calendar ted, refreshed every calendar mont month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each c ountry and compute global portfolios by weighting each country’s portfolio by the country’s total (lagged) market capitalization. This table includes all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor-mimic king portfolios. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our of Broad Sample global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Returns and alphas are in m onthly percent, t-statistics are shown below the coefficient estim ates, and 5% statistical significance is indicated in bold. Information ratio is equal to 4-fa ctor alpha (intercept) divided by the standard deviation of the estima ted residuals in the time-series regression. Sharpe ratios and information ratios (i.e., the Sharpe ratio of the regression residual) are annualized. Panel A: Long Sample (U.S. , Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) 1956 - 2012) QM J Pro fit ab ilit y Gro wt h Pa yout QMJ Profitab Safet y Safet y Gro wt h Pa yout ilit y 0.38 0.40 0.27 0.23 0.12 0.31 0.38 0.34 0.19 0.02 Excess Returns (4.38) (2.06) (1.63) (3.37) (3.22) (3.30) (1.33) (0.24) (3.41) (3.81) 0.52 0.55 0.42 0.08 0.46 0.33 0.43 0.34 0.02 0.49 CAPM-alpha (7.27) (4.78) (4.76) (1.06) (6.10) (5.75) (4.61) (3.07) (0.18) (5.29) 0.44 0.45 0.59 0.20 0.43 0.61 0.53 0.50 0.14 0.68 3-factor alpha (11.10) (7.82) (8.68) (3.32) (6.86) (7.68) (6.11) (5.40) (1.92) (5.17) 0.29 0.39 0.19 0.49 0.66 0.53 0.57 0.38 0.21 0.45 4-factor alpha (10.20) (6.13) (3.43) (5.50) (5.34) (4.00) (3.91) (2.26) (8.71) (7.97) -0.16 -0.25 0.05 -0.20 -0.24 -0.34 -0.28 0.00 -0.18 MKT -0.11 (-8.08) (-20.77) (3.35) (-14.47) (-14.36) (-8.33) (-13.74) (-0.06) (-10.50) (-17.02) -0.38 -0.21 -0.41 -0.05 -0.30 -0.33 -0.20 -0.31 -0.18 -0.23 SMB (-17.50) (-17.00) (-2.53) (-14.82) (-9.46) (-5.07) (-7.48) (-5.62) (-6.58) (-10.21) 0.36 -0.12 -0.28 -0.23 -0.44 0.39 -0.01 -0.16 -0.22 -0.38 HML (-5.03) (9.89) (-11.62) (-5.23) (-12.16) (-8.50) (-18.81) (16.68) (-0.31) (-3.95) 0.15 0.02 0.01 -0.17 0.21 -0.07 0.03 0.10 -0.14 0.24 UMD (0.82) (-3.80) (0.64) (-8.55) (10.79) (5.54) (1.01) (3.07) (-5.64) (8.57) 0.45 Sharpe Ratio 0.58 0.51 0.27 0.22 0.62 0.63 0.26 0.05 0.66 1.16 Information Ratio 1.14 0.88 0.49 1.25 1.13 0.84 0.83 0.48 1.46 0.52 0.57 0.37 0.63 0.40 0.60 0.60 0.34 0.58 0.35 A d ju s ted R2 Page T6 – – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

38 Table VI (Continued) Quality Minus Junk: By Country rns and factor loadings. Quality minus Ju nk (QMJ) factors are constructed as the This table shows calendar-time portfolio retu intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigne d to two size-sorted portfolios based on their market capitalizati on. For U.S. securities, the size breakpoint is the median NYSE rst market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, fi sorting on size, then on quality. Portfolios are value-weighted , refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each c ountry and compute global portfolios by weighting each country’s portfolio by the country’s to tal (lagged) market capitalization. This table includes all available comm on stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor-mimicking por tfolios. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our Broad Sample of global stocks. Panel C reports results by country. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are abov e the U.S. Treasury bill rate. Returns and alphas are in monthly percent, t-statistics are shown below the coefficient es timates, and 5% statistical significance is indicated in bold. Information ratio is equal to 4-factor alpha (intercept) divided by the standard deviation of the estimated residuals in the ti me- series regression. Sharpe ratios and information ratios are annualized. Sharp e Date Range T-stat 4-factor Number of Factor Loadings Excess T-stat Information months Ratio Alpha return Alpha Excess Ratio UMD HML SMB MKT return 0.55 0.75 210 1995-2012 0.34 Aust ralia 2.73 -0.40 0.10 0.00 0.36 1.51 -0.17 0.16 1996-2012 198 0.11 Austria 0.21 0.66 0.38 1.42 -0.33 -0.04 -0.15 0.36 -0.16 0.27 210 1995-2012 -0.16 -0.09 0.41 1.57 0.36 1.59 0.43 Belgium 0.38 0.21 0.59 0.43 306 1987-2012 Canada 0.61 2.98 0.39 2.05 -0.19 -0.07 0.28 0.39 0.08 210 1995-2012 -0.33 Switzerland 0.79 1.41 0.64 3.17 -0.35 -0.31 0.34 0.05 0.56 0.92 210 1995-2012 Germany 0.48 2.35 0.59 3.56 -0.24 -0.11 -0.19 0.17 -0.25 204 1996-2012 -0.20 1.90 0.49 2.08 0.66 0.50 Denmark -0.34 0.48 -0.25 0.18 210 1995-2012 -0.06 -0.08 0.22 0.88 0.20 0.58 0.15 Sp ain 0.14 -0.01 0.34 0.48 210 1995-2012 Finland 0.53 1.40 0.59 1.93 -0.08 -0.17 -0.51 0.16 0.45 0.76 210 1995-2012 France 1.86 0.53 2.96 -0.27 -0.04 -0.17 0.45 -0.27 -0.15 0.33 246 1992-2012 -0.16 0.15 1.35 0.32 0.69 0.17 United Kingdom 0.08 -0.19 0.34 0.79 0.98 126 2002-2012 Greece 1.35 2.54 1.06 3.07 -0.07 -0.21 -0.18 -0.42 1.04 210 1995-2012 -0.27 4.15 1.02 1.72 0.61 Hong Kong 0.08 0.41 0.12 0.04 208 1995-2012 -0.53 1.59 0.84 0.85 0.53 Ireland 0.20 -0.17 0.39 -0.13 0.51 2001-2012 0.07 0.85 -0.12 138 -0.33 2.67 0.85 1.72 0.66 Israel Italy 0.91 198 1996-2012 0.72 2.54 0.69 3.60 -0.21 -0.12 -0.22 0.26 0.62 Jap an 0.23 0.59 246 1992-2012 0.22 1.02 0.38 2.40 -0.31 -0.28 -0.15 0.10 -0.15 0.08 0.35 210 1995-2012 Netherlands 0.10 0.33 0.34 1.43 -0.37 -0.08 0.04 -0.19 0.18 0.61 210 1995-2012 -0.23 0.47 2.47 0.68 1.95 0.61 Norway -0.13 -0.14 0.16 0.05 -0.04 210 1995-2012 New Zealand 0.07 0.22 -0.05 -0.17 -0.15 -0.06 0.18 -0.26 150 2000-2012 -0.08 -0.26 2.30 0.89 1.87 Portugal 0.86 0.53 0.67 -0.31 0.06 210 1995-2012 -0.11 0.22 0.60 -0.22 2.38 0.44 0.90 0.26 Singap ore Sweden 0.32 0.53 256 1991-2012 0.40 1.49 0.50 2.36 -0.22 -0.26 -0.22 0.15 -0.12 0.02 0.58 1.46 678 1956-2012 Unit ed St at es 0.40 4.38 0.66 10.20 -0.25 -0.38 0.38 -0.01 0.62 1.16 324 1986-2012 -0.33 -0.24 5.50 0.45 3.22 0.15 Global – Page T7 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

39 Table VII QMJ: Recessions, Severe Bear and Bull Markets and Volatility Environment This table shows calendar-time portfolio returns of QMJ factors in different macroeconomic environments. Quality minus Junk ighted portfolios formed on size and quality. At the end of ea (QMJ) factors are constructed as the intersection of six value-we ch calendar month, stocks are assigned to two size-sorted portfolios based on their market capitalization. For U.S. securities, th e size breakpoint is the median NYSE market equity. For Internat ional securities the size breakpoint is the 80th percentile by dar country. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calen month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, nner. We form one set of portfolios in each country and compute growth, safety and payout score are constructed in a similar ma country’s total (lagged) market capitalization. This table inc ludes global portfolios by weighting each country’s portfolio by the all available common stocks on the CRSP/Xpressfeed merged databas e for the markets listed in Table I. Alpha is the intercept planatory variables are the monthly returns from the market in a time-series regression of monthly excess return. The ex mentum (UMD) factor-mimicking portfolios. Panel A reports portfolio (MKT) and size (SMB), book-to-market (HML), and mo results from our Long Sample of domestic stocks. The sample pe riod runs from June 1956 to December 2012. Panel B reports results from our Broad Sample of global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are abov e the U.S. Treasury bill rate. Returns and alphas are in timates, and 5% statistical significance is indicated in bold. monthly percent, t-statistics are shown below the coefficient es Information ratio is equal to 4-factor alpha (intercept) divided by the standard deviation of the estimated residuals in the ti me- series regression. Sharpe ratios a nd information ratios are annualized. “Recession” indicates NBER recessions. “Expansion” indicates all other months. “Severe bear (bull) market” is defined as a total market return in the past 12 -month below (above) - 25% (25%). of low (high) market volatility. We measure volatility as the 1-month “Low (high) volatility” indicated periods standard deviation of daily returns of the CRSP-value weighted index or the MSCI-World index and split the sample in the top and bottom 30% high and low periods . “Spike Up (down) in Volatility” indicate periods of large increases or drops in market volatility. We measure volatility changes as the 1-month change in market volatility and split the sample into the top and bott om 30% high and low periods. t-statistics Return Panel A: Long Samp le Number Excess 4-Factor CAPM 3-Factor 3-Factor CAPM 4-Factor Excess U.S., 1956 - 2012 Alpha Alpha Alpha Alpha Return Alpha Return of months Alpha 0.40 7.27 0.68 0.66 4.38 All Periods 11.10 10.20 678 0.55 Recession 0.73 0.96 0.95 2.77 3.55 5.76 5.61 110 0.76 Exp ansion 0.33 0.52 0.63 0.60 3.48 6.30 9.81 8.63 568 Severe Bear market 0.39 0.76 0.87 0.07 0.57 1.52 1.65 21 0.07 Severe Bull M arket 0.42 0.42 0.56 0.68 2.39 2.67 4.49 5.07 135 Low Volat ilit y 0.52 0.78 0.88 0.83 2.37 4.64 6.42 5.93 227 227 8.60 7.64 0.43 High Volat ilit y 0.25 4.20 0.60 0.73 2.24 0.49 0.65 0.67 2.68 3.97 5.48 5.39 226 0.57 Sp ike Up in Volat ilit y 0.30 0.60 0.87 0.73 1.90 4.42 8.36 6.62 226 Sp ike Down in Volat ilit y t-statistics Return Broad Samp le Excess 3-Factor 4-Factor Excess CAPM CAPM 3-Factor 4-Factor Number Global, 1986 - 2012 Alpha Alpha Alpha Return Alpha Alpha of months Alpha Return 0.38 0.52 0.45 3.22 5.75 7.68 5.50 324 All Periods 0.61 0.84 0.89 0.92 1.70 1.60 3.84 4.51 37 Recession 0.46 0.32 0.51 0.59 0.41 2.74 7.01 4.67 287 Exp ansion 5.36 0.15 0.52 0.59 0.13 0.89 2.30 2.18 15 Severe Bear market 0.32 0.73 Severe Bull M arket 2.95 3.13 3.17 3.15 55 0.59 0.71 0.61 0.69 0.61 2.73 4.65 5.61 4.87 144 0.62 Low Volat ilit y 0.75 0.26 0.36 0.45 0.45 1.89 High Volat ilit y 2.95 75 0.07 2.85 0.34 0.45 0.35 1.52 2.97 3.15 2.48 114 Sp ike Up in Volat ilit y 0.48 0.56 0.77 0.52 2.12 3.65 5.74 3.91 120 Sp ike Down in Volat ilit y 0.40 Page T8 – Tables and Figures – – Asness, Frazzini, and Pedersen Quality Minus Junk

40 Table VIII Time Variation of the Price of Quality: High Price of Quality Predicts Low QMJ Returns factor returns on the lagged price of quality. The left hand side This table shows the time series regression of future quality is the cumulative excess return of the QMJ factor (or profitability, growth, safety and payout factor) over the future 1, 12, 36, or 60 months. Each regression is run in two ways: Using the “raw” quality factor returns on the left hand the market, size (SMB), book-to-market (HML), and momentum (UMD) side (“raw”) or using the quality factor with its exposures to The right hand hedged out (denoted “alpha”). side variables are the lagged price of quality and past quality returns. The lagged price of quality is the cross-sectional reg ression coefficient of market to book score on quality (Table III, Panel A column (1) and (5) and Panel B columns (1)-(4) and (6)-(9)). The past quality return is defined as the port folio – weighted average of the past 1-year returns of the stocks in the quality portfolio. Panel A reports results from our Long Sample of U.S. stocks from June 1956 to December 201 2. Panel B reports results from our Broad Sample of global stocks from June 1986 to December 2012. We report onl y the coefficient on the variable of interest, the lagged price of quality. T-statistics are shown below the coefficient estimates, and 5% statistical significance is indicated in bold. Standard errors are adjusted for heteroskedasticit y and autocorrelation (Newey and West (1987)) with lag length equal to the forecasting horizon. “ Mean Adj R2 ” is the average adjusted R-squared across all the regression above. The in tercept and prior returns are included in all regressions but not reported. Panel A: Long Samp le (U.S. , 1956 - 2012) Panel B: Broad Samp le (Global, 1986 - 2012) Return (t, t+12) Return (t) Return (t, t+60) Return (t, t+36) Return (t, t+12) Return (t) Return (t, t+60) Return (t, t+36) Left-hand side Alp ha Alp ha Raw Alp ha Raw Alp ha Raw Alp ha Raw Raw Raw Alp ha Raw Alp ha Alp ha Raw -0.41 -0.01 -0.67 -0.52 -1.01 -1.32 -0.02 0.00 -0.17 0.05 -0.69 0.14 -1.06 -2.14 -0.02 -0.27 QMJ (-2.50) (-1.73) (-2.61) (-2.08) (-2.27) (-2.77) (-1.02) (0.40) (-2.70) (0.34) (-2.04) (0.35) (-2.40) (-4.33) (-2.06) (-2.31) -0.02 -0.20 -0.16 -0.58 -0.49 -0.86 -1.01 0.00 -0.01 -0.17 0.07 -0.41 0.02 -1.36 -1.63 Pro fit ab ilit y 0.01 (-2.87) (-3.03) (-2.30) (-3.54) (-2.79) (-2.91) (-3.58) (0.21) (0.95) (-0.86) (0.41) (-0.73) (0.04) (-1.64) (-2.17) (-3.06) -0.01 Gro wth 0.00 -0.12 0.18 0.49 -0.20 -0.05 -0.04 -0.55 -0.53 -0.94 -1.21 -1.92 -0.61 0.00 -0.07 (-0.79) (-2.66) (-0.37) (0.68) (0.95) (-0.37) (-2.09) (-2.07) (0.23) (-2.62) (-1.37) (-2.81) (-3.16) (-0.81) (-0.92) (-0.02) 0.01 -0.03 -0.11 -1.10 -0.67 -1.30 -1.84 -0.03 -0.37 -0.38 0.07 -0.65 0.27 0.28 -0.53 Safety 0.00 (-0.35) (-3.27) (-1.29) (-3.85) (-1.46) (-1.38) (-3.11) (-1.41) (0.67) (-2.44) (1.14) (-2.76) (1.76) (0.75) (-1.55) (-2.62) -0.01 -0.03 -0.06 -0.66 -0.28 -0.91 -1.58 -0.05 -0.30 -0.37 0.02 -0.19 0.14 -0.77 -1.02 -0.02 Payout (-1.54) (-2.06) (-0.64) (-1.53) (-1.26) (-1.91) (-2.29) (-2.08) (-0.87) (-1.59) (0.21) (-0.34) (0.31) (-1.68) (-2.36) (-2.04) 0.12 0.01 0.08 0.07 0.19 0.15 0.17 0.22 0.01 0.00 0.10 0.05 0.22 0.00 0.25 0.25 Mean A d j R2 – Page T9 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

41 Table IX Pricing HML, SMB and UMD This table shows calendar-time portfolio retu rns and factor loadings. Quality minus Ju nk (QMJ) factors are constructed as the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigne d to two size-sorted portfolios based on their market capitalizati on. For U.S. securities, the size breakpoint is the median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, fi rst sorting on size, then on quality. Portfolios are value-weigh h, and rebalanced every calendar ted, refreshed every calendar mont month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each c ountry and compute global portfolios by weighting each le includes all available common stocks on t country’s portfolio by the country’s total ( lagged) market capitalization. This tab he CRSP/Xpressfeed merged database for the markets listed in Table I. Alpha is the intercept in a time-series regression of monthly excess return. The other variables are the monthly retu rns from the market portfolio (MKT) and size (SMB), book-to- market (HML), and momentum (UMD) factor-mimicking portfolios. We run a regression of the SMB, HML and UMD factors of the remaining ones excluding and including the QMJ factor. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our Broad Sample of global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Returns and alphas are in monthly percent, t-statistics are shown below t he coefficient estimates, and 5% statistical significance is indicated in bold. Information ratio is equal to 4-factor alpha (inte rcept) divided by the standard deviation of the estimated residuals in the time-series regression. Sharpe ratios and information ratio s are annualized. Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) Panel A: Long Sample (U.S. , 1956 - 2012) Left-hand side SMB SMB HML HML UMD UMD SMB SMB HML HML UMD UMD 0.11 0.28 0.34 0.70 0.70 0.11 0.34 0.45 0.45 0.58 0.58 0.28 Excess Returns (2.54) (2.66) (2.66) (4.52) (4.52) (0.92) (0.92) (2.77) (2.77) (2.69) (2.69) (2.54) 0.08 0.13 0.77 0.94 1.05 1.01 0.64 0.36 0.79 0.81 1.07 0.72 Alpha (0.62) (1.16) (8.01) (9.35) (9.11) (8.05) (6.39) (3.02) (6.62) (6.39) (6.90) (4.44) -0.12 -0.04 -0.20 MKT 0.19 -0.08 -0.16 -0.23 -0.20 -0.18 0.06 -0.09 -0.09 (7.38) (-3.06) (-8.74) (-7.39) (-5.61) (2.09) (-3.90) (-3.27) (-2.73) (-6.04) (-0.94) (-7.04) . 0.08 -0.03 0.04 0.07 -0.01 -0.02 0.02 0.21 SMB . (2.34) (-0.86) (1.05) (1.33) (-0.24) (-0.36) (0.34) (2.80) -0.03 -0.81 -0.80 -0.01 -0.02 -0.89 -0.81 0.10 HML (2.34) (-0.86) (-23.24) (-22.10) (-0.24) (-0.36) (-16.81) (-15.23) 0.04 0.04 -0.55 -0.53 0.02 0.11 -0.53 -0.52 UMD (1.05) (1.33) (-23.24) (-22.10) (0.34) (2.80) (-16.81) (-15.23) -0.83 0.06 -0.67 -0.03 0.58 -0.29 QMJ (-5.03) (-9.46) (-0.31) (5.54) (-17.50) (0.82) 0.34 0.34 0.35 Sharpe Ratio 0.60 0.60 0.18 0.18 0.53 0.53 0.52 0.52 0.35 Information Ratio 0.17 0.96 1.10 1.36 1.23 1.18 0.13 0.66 1.31 1.33 1.36 0.95 0.46 A d ju s ted R2 0.36 0.45 0.47 0.46 0.07 0.01 0.22 0.47 0.46 0.50 0.55 Page T10 – – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

42 Figure 1 QMJ: 4-Factor Adjusted Information Ratios This figure shows 4-factor adjusted information ratios of Qual ity minus Junk (QMJ) factors. This figure includes all available rkets listed in Table I. Alpha is the intercept in a time- common stocks on the CRSP/Xpressfeed merged database for the ma riables are the monthly returns from the market portfolio (MKT) series regression of monthly excess return. The explanatory va factor-mimicking portfolios. Returns are in USD, do not and size (SMB), book-to-market (HML), and momentum (UMD) easury bill rate. Information ratios are equal to alpha divid include currency hedging, and excess returns are above the U.S. Tr ed residuals in the time-series regression. Information ratios are annualized. by the standard deviation of the estimated 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 Italy Israel Spain Japan Global France Ireland Austria Greece Finland -0.20 Canada Norway Sweden Belgium Australia Portugal Denmark Germany Singapore Hong Kong Switzerland Netherlands New Zealand United States United Kingdom Page T11 – Tables and Figures – Asness, Frazzini, and Pedersen – Quality Minus Junk

43 Figure 2 QMJ: Cumulative Returns This figure shows cumulative returns of Quality minus Junk (QMJ) factors. This figure includes all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Panel A reports results of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B from our Long Sample reports results from our Broad Sample of global stocks. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging. Panel A: Long Sample (U.S. , 1956 - 2012) 350% 300% 250% 200% 150% 100% 50% 0% 1986 2007 2001 2004 1995 1998 1992 2010 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1989 -50% QMJ Cumula tive Re turn, L ong Sa mp le (U .S. ) Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) 140% 120% 100% 80% 60% 40% 20% 0% 1987 2009 2010 2011 2007 2005 2012 1986 2008 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2006 -20% QMJ Cumulative Return , B road Sample (Global) – Page T12 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

44 Figure 3 QMJ: Cumulative 4-Factor Alphas s of Quality minus Junk (QMJ) factors. This figure includes This figure shows 4-factor adjusted cumulative return all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December Broad Sample of global stocks. The sample period runs from June 1986 to 2012. Panel B reports results from our regression of monthly excess return. The explanatory December 2012. Alpha is the intercept in a time-series variables are the monthly returns from the market portfo lio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor-mimicking portfolios. Returns ar e in USD, do not include currency hedging, and excess returns are above the U.S. Treasury b ill rate. We plot cumulative abnormal returns (alpha plus regression residual) from the time series regression. Panel A: Long Sample (U.S. , 1956 - 2012) 500% 450% 400% 350% 300% 250% 200% 150% 100% 50% 0% 1971 2010 1998 1995 2007 2004 2001 1980 1956 1959 1962 1965 1968 1992 1974 1977 1989 1983 1986 -50% Cumulative 4-Factor Alpha, Long Sample (U.S.) Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) 160% 140% 120% 100% 80% 60% 40% 20% 0% 1987 2011 2007 2005 2008 2009 2010 1986 2012 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2006 -20% Cumulative 4-Factor Alpha , Broad S ample (Global) – Page T13 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

45 Figure 4 QMJ: Flight to Quality This figure shows monthly excess returns and 4-factor alpha of Quality minus Junk (QMJ) factors. This figure includes all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to of global stocks. The sample period runs from December 2012. Panel B reports results from our Broad Sample June 1986 to December 2012. Alpha is the intercept in a time-series regression of monthly excess return. The market portfolio (MKT) and size (SMB), book-to-market explanatory variables are the monthly returns from the (HML), and momentum (UMD) factor-mimicking portfo lios. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury b ill rate. Monthly excess returns and alphas on the y-axes and market excess returns on the x-axes. Panel A: Long Sample (U.S. , 1956 - 2012) 12.00% 15.00% 10.00% 8.00% 10.00% 6.00% 4.00% 5.00% QMJ - 4-factor alpha QMJ - excess returns 2.00% 0.00% 0.00% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 10% -15% -25% 20% 15% -10% -5% 0% 5% -30% -20% -2.00% -5.00% -4.00% -6.00% -10.00% -8.00% -10.00% -15.00% Market Excess Return Market Excess Return Panel B: Broad Sample (Global, 1986 - 2012) 8.00% 10.00% 8.00% 6.00% 6.00% 4.00% 4.00% 2.00% QMJ - 4-factor alpha QMJ - excess returns 2.00% 0.00% 0.00% -10% -15% -20% -25% 15% 10% 5% 0% -5% -25% 10% 15% 5% 0% -5% -10% -20% -15% -2.00% -2.00% -4.00% -4.00% -6.00% -6.00% -8.00% -10.00% -8.00% Market Excess Return Market Excess Return – Page T14 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

46 Figure 5 Cross Sectional Regressions Coef ficient, the Price of Quality This figure reports coefficients from Fama-Macbeth regressions. The dependent variable is the z- score of a stock’s market to book ratio (MB) in month t. The explanatory variab les are the quality scores in month t. We plot the time om table III, panel A, column (1) and (7). series of the cross sectional coefficients fr Time Series of FMB Coefficients 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1998 2001 2004 1995 2007 2010 1956 1959 1992 1965 1968 1971 1974 1977 1980 1983 1986 1989 1962 Long Sample (U.S.) Broad Sample (Global) – Page T15 – Tables and Figures – Asness, Frazzini, and Pedersen Quality Minus Junk

47 Appendix A A1: Variable Definitions In this section we report details of each variable used on our quality score. Our variable s’ definitions are based on Altman (1968 ), Ohlson (1980), Ang, Hodrick, Xing, and Zhang (2006), Danile and Titman (2006), Penma n, Richardson, and Tuna (2007), Campbell, vy-Marx and Zhang (2011), Novy-Marx (2012), Hilscher, and Szilagyi (2008), Chen, No nd Frazzini (2013). Variable names correspond to Frazzini and Pedersen (2013) and Asness a CRSP/XpressFeed data items and we omit the time subscript ݐ for contemporaneous variables. Finally, unless specified, XpressFe ed data items refer to annual items and time subscripts refer to years. Profitability We compute a profitability z-score by averag ing z-scores of gross profits over assets (GPOA), return on equity (ROE), return on a ssets (ROA), cash flow over assets (CFOA), gross margin (GMAR) and low accruals (ACC): ൅œ ൅œ ൅œ ൅œ ൅œ ൯ ”‘ˆ‹–ƒ„‹Ž‹›ൌœ൫œ ୰୭ୣ ୥୮୭ୟ ୥୫ୟ୰ ୰୭ୟ ୟୡୡ ୡ୤୭ୟ ሺ ܣܱܲܩ is equal to revenue minus costs of goods sold divided by total assets െܸܶܧܴ ሻ ܧܤȀܤܫ ܵܩܱܥ . ܶܣȀ . ܧܱܴ is net income divided by book-equity is net income divided ܣܱܴ ܶܣȀܤܫ by total assets ܣܱܨܥ is net income plus depreciation minus changes in working . ሻ ሺ s divided by total assets: ܶܣȀ capital and capital expenditure . ܺܲܣܥെܥܹെȟܲܦ൅ܤܰ ሺ ሻ ܴܣܯܩ ܵܩܱܥെܸܶܧܴ ܧܮܣܵȀ . is revenue minus costs of goods sold divided by total sales: ሻ ሺ is depreciation minus changes in working capital െ ܥܥܣ ܲܦെܥܹȟ ܶܣȀ . Working capital ܥܹ rrent liabilities minus cash and short term is defined as current assets minus cu instruments plus short term debt and income taxes payable ൅ܥܮܦ൅ܧܪܥെܶܥܮെܶܥܣ ܲܺܶ . Book equity ܧܤ is defined as s hareholders’ equity minus preferred stock. To obtain shareholders’ equity we use we use stockholders’ e quity ( ܳܧܵ ) but if not available, we use are ܳܧܥ the sum of common equity ( ܳܧܥ ) and preferred stocks ( ܭܶܵܲ ). If both ܳܧܵ and ) minus the sum of total ܶܣ by total assets ( unavailable, we proxy shareholders’ equity – Page A1 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

48 ܶܮ ). To obtain book equity (BE), we subtract from liability ( ܤܫܯ ) and minority interest ( ܮܭܶܵܲ or ܭܶܵܲ depending on shareholders’ equity the preferred stock value ( ܸܴܭܶܵܲ , availability). Growth growth z-score by averaging z-scores of five-year growth in gross We compute a ܲܩെ , five-year growth in ܶܣሻȀ ܵܩܱܥെܸܶܧܴൌ ܲܩ where profits over assets ܲܩሺ ௧ିହ ௧ିହ ௧ return on equity ܤܫሺ ܤܫെ ܧܤሻȀ , five-year growth in return over assets ܤܫሺ െ ௧ିହ ௧ ௧ ௧ିହ ܨܥെ ܤܫ ܶܣሻȀ where , five-year growth in cash flow over assets ܨܥሺ ܶܣሻȀ ௧ିହ ௧ିହ ௧ ௧ିହ ௧ିହ ܺܲܣܥെܥܹെȟܲܦ൅ܤܫൌܨܥ , five-year growth in gross margin ܲܩሺ , ܧܮܣܵሻȀ ܲܩെ ௧ିହ ௧ ௧ିହ where ൌ ܦܲܥܹܯ and five-year growth in (low) accruals ܦܲܥܹܯሺ ܣሻȀ ܦܲܥܹܯെ ௧ିହ ௧ ௧ିହ ሺ ሻ ܲܦെܥܹȟ  : െ ”‘™–Šൌœ൫œ ൅œ ൯ ൅œ ൅œ ൅œ ൅œ ୼ୡ୤୭ୟ ୼୥୫ୟ୰ ୼୰୭ୣ ୼ୟୡୡ ୼୥୮୭ୟ ୼୰୭ୟ Safety We compute a safety z-score by averaging z-scores of low beta (BAB), low idiosyncratic volatility (IVOL), low leverage (LEV), low bankruptcy risk ( Ohlson’s O and Altman’s Z ) and low earnings volatility (EVOL): ሻ ሺ  ൅œ œ ൅œ ƒˆ‡–›ൌœ ൅œ ൅œ ൅œ ୪ୣ୴ ୸ ୠୟୠ ୣ୴୭୪ ୭ ୧୴୭୪ . Betas are estimated as in Frazzini and Pedersen ܤܣܤ is equal to minus market beta ߚȂ (2013) based on the product of the rolling one-year daily standard deviation and the rolling , we use three-day returns to account for five-year three-day correlations. For correlations nonsynchronous trading and a longer horizon because correlations are more stable than ௜ ܮܱܸܫ is minus a stock ’s idiosyncratic volatility ߪെ volatilities. . Idiosyncratic volatility is equal to the rolling one-year standard deviation of daily beta-adjusted excess return, skipping the most recent trading day. ܸܧܮ is minus total debt (the sum of long term debt, short term red stock) over total assets ൅ܶܤܫܯ൅ܥܮܦ൅ܶܶܮܦെሺ debt, minority interest and prefer O-Score as ’s . We compute Ohlson ܶܣሻȀܭܶܵܲ – Page A2 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

49 ൌെሺെͳǤ͵ʹെͲǤͶͲ͹כŽ‘‰ሺ Ȁ ሻ൅͸ǤͲ͵כȂͳǤͶ͵כ൅Ͳ ǤͲ͹͸ כȂͳǤ͹ʹכ െʹǤ͵͹כ െͳǤ ͅ͵כ ൅ͲǤʹ ͅͷ כ െͲǤͷʹͳכ ሻǢ where is adjusted total assets equal to to tal assets plus 10% of the difference ܶܧܵܵܣܬܦܣ . ܫܲܥ is the consumer price between book equity and market equity ሻܧܤെܧܯሺכ൅Ǥͳܶܣ ܣܶܮܶ is equal to book value of debt ( ܶܶܮܦ൅ܥܮܦ ) divided by ܶܧܵܵܣܬܦܣ . ܣܶܥܹ is index. ities scaled by adjusted assets ܶܧܵܵܣܬܦܣሻȀܶܥܮെܶܥܣሺ current assets minus current liabil . ܣܥܮܥ vided by current assets ܶܥܣȀܶܥܮ . ܩܧܰܧܱ is a dummy equal to is current liabilities di 1 if total liabilities exceed total assets ሻܶܣ൐ܶܮͳሺ . ܣܶܫܰ is net income over assets ܶܣȀܤܫ . ܮܷܶܨ is pre-tax income over total liabilities ܶܮȀܶܲ . ܱܹܶܰܫ is a dummy equal to one if net ሼ ሽ ܺܣܯͳሺ income is negative for the current and prior fiscal year ܤܫ ܤܫǡ ൏Ͳሻ is ܰܫܪܥ . ௧ ௧ିଵ ȁ ȁ ȁ ȁ ሻ ’s Z-Score is a changes in net income defined as ܤܫሺ . Altman ൅ ሻȀሺ ܤܫ ܤܫെ ܤܫ ௧ ௧ିଵ ௧ିଵ ௧ weighted average of working capital, retained earnings, earnings before interest and taxes, market equity and sales, all over total assets: ൌሺͳǤʹ൅ͳǤͶ൅͵Ǥ͵ ൅ͲǤ͸൅ሻȀ is the standard deviation of quarterly ܧܱܴ over the past 60 quarters. We require at ܮܱܸܧ least twelve non missing quarters. If quarterly data is unavailable we use the standard 1 . ܧܱܴ deviation of annual over the past 5 years and we require five non missing fiscal years Payout We compute a payout z-score by averagin g z-scores of net equity issuance ( ܵܵܫܧ ), net debt issuance ( ܵܵܫܦ ) and total net payout over profits ( ܱܲܲܰ ): ƒ›‘—–ൌœ൫œ ൅œ ൯ ൅œ ୢ୧ୱୱ ୣ୧ୱୱ ୬୮୭୮ 1 Quarterly data is unavailable for some of our international sample. – Page A3 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

50 split-adjusted number of shares ܵܵܫܧ is minus one-year percent change in ܬܦܣ̴ܷܱܴܶܪܵȀ where ܬܦܣ̴ܷܱܴܶܪܵ ሻ is split-adjusted shares ܬܦܣ̴ܷܱܴܶܪܵሺ‰‘Žെ ௧ିଵ ௧ outstanding. ܵܵܫܦ is minus one-year percent change in total debt ܦܱܶܶሺ‰‘Žെ ܦܱܶܶȀ ሻ ௧ ௧ିଵ m debt, minority interest and preferred is the sum of long term debt, short ter ܦܱܶܶ where ܭܶܵܲ൅ܶܤܫܯ൅ܥܮܦ൅ܶܶܮܦ . ܱܲܲܰ is equal the sum of total net payout (net stocks ) over the past 5 years divided by total income minus changes in book equity ܧܤെȟܤܫ profits ( ܵܩܱܥെܸܶܧܴ ) over the past 5 years. Book-to-Market Book-to-market ratios follow Asness and Fraz zini (2013). We require stocks to have a positive book equity and compute book-to-market as book equity divided by the most recent market equity ܧܯȀܧܤ . – Page A4 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

51 A2: Global Factor Returns truction of the market (MKT), size (SMB), In this section we report details of the cons book-to-market (HML), and momentum (UMD) port folios used on the analysis. The data can be downloaded at http://www.econ.yale.edu/~af227/data_library.htm . The portfolio construction follows Fama and French ( 1992, 1993 and 1996) and Asness and Frazzini (2013). We form one set of portfolios in each co untry and compute global factor portfolios by weighting each country’s portfolio by the co untry’s total (lagged) market capitalization. The market factor MKT is the value-weighted re turn on all available stocks minus the one- month Treasury bill rate. The size, value and momentum factors are constructed using six rket value of equity value-weighted portfolios formed on size (ma ME) and book-to-market (book equity divided by the most recent market equity ) and 1-year return (return ܧܯȀܧܤ over the prior 12 months, skipping the most recent month) . At the end of each calendar portfolios based on their market capitalization. month, stocks are assigned to two size-sorted For U.S. securities, the size breakpoint is th e median NYSE market equity. For International securities the size breakpoint is the 80th percen tile by country. We use conditional sorts, first sorting on size, then on the second variable. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar m onth to maintain value weights. The size factor SMB is the average return on the 3 small portfolios minus the average return on the 3 big portfolios: ሻ݄ݐݓ݋ݎܩ݈݈ܽ݉ܵ൅݈ܽݎݐݑ݈݈݁ܰܽ݉ܵ൅݁ݑ݈ܸ݈݈ܽܽ݉ܵሺͳȀ͵ൌܤܯܵ ሻ݄ݐݓ݋ݎܩ݃݅ܤ൅݈ܽݎݐݑ݁ܰ݃݅ܤ൅݁ݑ݈ܸܽ݃݅ܤሺͳȀ͵െ The value factors HML is the average return on the two value portfolios minus the average return on the two growth portfolios: ܩ݃݅ܤ൅݄ݐݓ݋ݎܩ݈݈ܽ݉ܵሺͳȀʹെሻ݁ݑ݈ܸܽ݃݅ܤ൅݁ݑ݈ܸ݈݈ܽܽ݉ܵሺͳȀʹൌܮܯܪ ሻ݄ݐݓ݋ݎ The momentum factor UMD is the average return on the two high return portfolios minus the average return on the two low return portfolios: ሻݓ݋ܮ݃݅ܤ൅ݓ݋ܮ݈݈ܽ݉ܵͳȀʹሺെሻ݄݃݅ܪ݃݅ܤ൅݄݃݅ܪ݈݈ܽ݉ܵሺͳȀʹൌܦܯܷ – Page A5 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

52 Portfolio returns are in USD and do not include any currency hedging. Excess returns are above the U.S. Treasury bill rate. Quality Minus Junk – Asness, Frazzini, and Pedersen – Appendix – Page A6

53 Table A1 Persistence of Quality Measures h, stocks in each country in are ranked in ascending This table shows average quality scores. Each calendar mont order on the basis of their profitability, growth, safety and payout. The ranked stocks are assigned to one of ten portfolios. U.S. sorts are based on NYSE breakpoints. We form one set of portfolios in each country and compute global portfolios by weighting each country’s portfolio by the country’s total (lagged) market capitalization. Portfolios are v alue-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. This table reports the value-weighted average of quality measures across stocks in the portfolio at portfolio formation (t) up to th e subsequent ten years (t + 120 months). We report the time series average of the value-weighted cross sectional means. Panel A reports results from our Long Sample 1956 to December 2012. Panel B reports results from our of domestic stocks. The sample period runs from June of global stocks. The sample period runs from June 1986 to December 2012. Standard errors are Broad Sample adjusted for heterskedasticity and autocorrelation with a lag length of five years (Newey and West (1987)) and 5% significance is indicated in bold. P2 P3 P4 Panel A: Long Sample (U.S.) P6 P7 P8 P9 P10 H-L H-L P1 P5 (Lo w) t-stat 1956 - 2012 (High) 0.76 -0.80 -0.20 0.03 -1.44 0.49 -0.46 1.11 1.76 3.20 63.62 Profit (t) 0.25 -0.90 -0.49 -0.28 -0.05 0.10 0.27 0.44 0.66 0.99 1.51 2.41 41.39 Pro fit (t + 12M) -0.65 -0.40 -0.03 0.11 0.23 0.37 0.56 0.82 1.40 2.05 31.26 -0.24 Pro fit (t + 36M) 0.50 -0.17 -0.03 0.13 0.22 0.32 -0.56 0.76 1.34 1.90 24.06 -0.36 Pro fit (t + 60M) -0.39 -0.22 -0.14 0.02 0.11 0.19 Pro fit (t + 120M) 0.37 0.65 1.14 25.58 0.30 1.53 0.68 -1.48 -0.38 -0.12 0.13 0.39 -0.66 1.03 1.67 3.15 101.83 Gro wth (t) -0.97 -0.78 -0.60 -0.41 -0.21 -0.04 0.13 0.30 0.58 0.80 1.25 2.03 30.85 Gro wth (t + 12M) 21.52 -0.43 -0.38 -0.28 -0.17 -0.07 0.02 0.18 0.36 0.51 0.93 1.36 Gro wth (t + 36M) -0.10 -0.09 -0.08 -0.03 0.02 -0.12 0.25 0.52 0.51 4.15 0.01 0.15 Gro wth (t + 60M) 0.12 -0.25 -0.14 -0.12 -0.06 0.12 -0.10 0.35 -0.14 5.89 -0.23 Gro wth (t + 120M) 0.58 -0.85 -0.48 -0.21 0.01 0.22 0.44 Safety (t) 0.99 1.45 2.95 49.61 -1.49 0.69 -1.11 -0.34 -0.14 0.04 0.23 -0.66 0.65 0.93 1.28 2.39 44.71 0.44 Safety (t + 12M) 0.58 -0.74 -0.07 0.06 0.24 0.42 -0.22 0.81 1.04 1.78 20.97 -0.49 Safety (t + 36M) 0.39 -0.56 -0.11 -0.02 0.11 0.23 -0.38 0.55 0.75 0.91 1.46 16.01 Safety (t + 60M) 0.45 Safety (t + 120M) 0.03 0.12 0.25 0.35 -0.03 0.65 0.71 -0.20 9.67 -0.28 0.98 -1.46 -0.82 -0.46 -0.17 0.07 0.30 0.54 0.80 1.11 1.57 3.03 70.25 Payout (t) 0.50 -0.67 -0.20 0.00 0.20 0.36 -0.39 0.66 0.81 0.95 1.63 38.22 Payout (t + 12M) -0.38 0.52 0.06 0.17 0.26 0.38 -0.19 0.61 0.71 0.80 1.18 38.26 Payout (t + 36M) 0.32 27.71 -0.15 0.02 0.19 0.25 0.68 0.41 0.49 0.59 0.71 0.86 Payout (t + 60M) Payout (t + 0.12 0.22 0.33 0.26 0.40 0.43 0.49 0.53 0.57 0.58 120M) 14.43 0.46 Panel B: Broad Sample (Global) P3 P4 P5 P6 P7 P8 P9 P10 H-L H-L P1 P2 (High) (Lo w) t-stat 1986 - 2012 -0.86 -0.50 -0.22 0.02 0.26 0.51 0.78 1.13 1.72 3.19 68.73 Profit (t) -1.48 0.65 -0.49 -0.08 0.08 0.27 0.45 -0.24 0.94 1.45 2.36 50.94 -0.91 Pro fit (t + 12M) -0.63 -0.36 -0.18 -0.03 0.09 0.24 0.37 0.56 0.78 1.29 1.91 44.82 Pro fit (t + 36M) 0.36 -0.10 0.02 0.13 0.25 -0.27 0.50 0.69 1.19 1.65 34.78 -0.46 Pro fit (t + 60M) 0.41 -0.31 0.08 0.15 0.24 0.35 -0.02 0.58 0.98 Pro fit (t + 120M) 17.41 -0.12 1.29 -1.50 -1.01 -0.69 -0.41 -0.15 0.11 0.37 0.66 1.03 1.68 3.18 57.38 Gro wth (t) 0.54 -0.71 -0.21 -0.07 0.13 0.29 -0.40 0.75 1.23 1.94 41.03 -0.53 Gro wth (t + 12M) 0.15 -0.29 -0.24 -0.13 -0.06 0.07 -0.27 0.30 0.48 0.80 1.08 23.00 Gro wth (t + 36M) 4.35 0.19 -0.04 -0.11 -0.08 -0.09 -0.04 0.03 0.11 0.19 0.38 0.18 Gro wth (t + 60M) Gro wth (t + 120M) -0.21 -0.14 -0.11 -0.15 -0.14 -0.12 0.04 0.11 0.18 -0.19 5.83 0.37 0.69 -0.54 -0.25 0.00 0.22 0.45 -0.92 1.01 1.51 3.09 62.54 Safety (t) -1.58 -1.06 -0.66 -0.38 -0.15 0.02 0.23 0.39 0.61 0.89 1.25 2.31 61.28 Safety (t + 12M) 0.31 -0.45 -0.26 -0.10 0.02 0.17 -0.63 0.47 0.72 0.93 1.55 37.58 Safety (t + 36M) 26.36 -0.45 -0.34 -0.17 -0.07 0.03 0.11 0.23 0.39 0.60 0.79 1.24 Safety (t + 60M) Safety (t + 120M) -0.17 -0.09 -0.02 0.05 0.12 0.18 0.29 0.49 0.55 -0.21 13.00 0.77 Payout (t) -0.86 -0.48 -0.19 0.06 0.30 -1.51 0.81 1.13 1.60 3.12 54.93 0.54 54.37 -0.54 -0.27 -0.12 0.07 0.24 0.34 0.52 0.64 0.76 0.90 1.43 Payout (t + 12M) 32.25 -0.25 -0.05 0.11 0.21 0.31 0.39 0.50 0.58 0.65 0.73 0.98 Payout (t + 36M) 18.32 -0.02 0.15 0.25 0.35 0.38 0.68 0.50 0.54 0.60 0.65 0.43 Payout (t + 60M) 0.59 0.51 0.45 0.50 0.49 0.42 7.42 Payout (t + 120M) 0.16 0.26 0.36 0.31 0.43 – Page A7 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

54 Table A2 Quality Minus Junk Components This table shows calendar-time portfolio returns and factor lo adings. Quality minus Junk (QMJ) factors are constructed as the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigned to two size-sorted portfolios based on their market cap italization. For U.S. securities, the size breakpoint is the median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each country and compute global portfolios by we ighting each country’s portfolio by the country’s total (lagged) market capitalization. This rkets listed in Table I. table includes all available common stocks on the CRSP/Xpressfe ed merged database for the ma Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to- market (HML), and momentum (UMD) factor-mimicking portfolios. Panel A reports results from our of domestic stocks. The sample period runs from June 1956 to Long Sample of global stocks. Panel C report results by country. The Broad Sample December 2012. Panel B reports results from our sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess rate. Returns and alphas are in monthly pe rcent, t-statistics are shown below the returns are above the U.S. Treasury bill coefficient estimates, and 5% statistical significance is ind icated in bold. Information ratio is equal to 4-factor alpha (intercept) divided by the standard deviation of the estimated residuals in the time-series regression. Sharpe ratios and information ratios are annualized. Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) 956 - 2012) Panel A: Long Sample (U.S. , 1 Low Quality High Quality Low Quality QMJ QMJ High Quality Small Big Small Big Small Big Small Big 0.38 0.92 0.56 0.36 0.30 0.40 0.75 0.50 0.19 0.30 Excess Returns (4.70) (1.51) (4.38) (2.95) (2.10) (0.54) (0.96) (3.22) (3.44) (1.30) 0.08 0.43 -0.24 0.55 0.32 -0.31 -0.38 -0.24 0.52 0.12 CAPM-alpha (2.80) (-2.23) (-4.57) (7.27) (3.37) (1.35) (-2.45) (-3.22) (5.75) (4.85) 0.25 0.21 -0.59 -0.32 0.68 0.21 0.17 -0.52 -0.32 0.61 3-factor alpha (5.79) (-9.70) (-6.71) (11.10) (3.55) (3.10) (-5.10) (-4.50) (7.68) (6.05) 0.45 0.31 0.27 -0.40 -0.34 0.66 0.25 0.14 -0.23 -0.26 4-factor alpha (7.56) (5.50) (-3.43) (-2.33) (6.91) (2.51) (-6.67) (-6.83) (10.20) (4.00) 1.11 MKT -0.25 0.85 0.90 1.14 1.13 -0.24 1.19 0.93 0.90 (86.43) (99.31) (-17.02) (87.91) (75.37) (53.65) (71.27) (-14.36) (64.43) (115.82) 0.70 -0.18 1.15 0.12 -0.38 0.61 -0.20 1.00 0.06 -0.33 SMB (46.84) (-15.27) (57.17) (7.32) (-17.50) (22.42) (-8.22) (23.61) (1.94) (-9.46) -0.01 0.12 0.07 -0.18 -0.02 0.16 -0.12 0.10 -0.13 -0.13 HML (3.67) (-0.31) (-2.89) (4.23) (-13.21) (-0.87) (8.51) (-5.03) (3.54) (-5.26) 0.02 0.15 -0.06 -0.17 0.02 -0.06 -0.04 0.02 -0.27 -0.06 UMD (5.54) (-4.15) (-5.28) (-9.14) (1.49) (0.82) (-1.88) (1.05) (-7.98) (-2.18) 0.20 0.58 Sharpe Ratio 0.63 0.46 0.17 0.62 0.19 0.57 0.40 0.10 1.46 -0.72 0.99 1.08 -0.96 -0.98 Information Ratio (4-factor) 0.84 0.53 -0.49 1.16 Adjusted R-square 0.95 0.60 0.95 0.96 0.96 0.95 0.57 0.95 0.95 0.93 – Page A8 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

55 Table A3 Robustness Checks: QMJ by Time Period and by Size adings. Quality minus Junk (QMJ) factors are constructed as This table shows calendar-time portfolio returns and factor lo the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are italization. For U.S. securities, the size breakpoint is the assigned to two size-sorted portfolios based on their market cap median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The QMJ factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each country and (lagged) market capitalization. This compute global portfolios by weighting each co untry’s portfolio by the country’s total rkets listed in Table I. ed merged database for the ma table includes all available common stocks on the CRSP/Xpressfe Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to- market (HML), and momentum (UMD) factor-mimicking Long Sample portfolios. Panel A reports results from our of domestic stocks. The sample period runs from June 1956 to of global stocks. Panel C report results by country. The Broad Sample December 2012. Panel B reports results from our sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rcent, t-statistics are shown below the rate. Returns and alphas are in monthly pe coefficient estimates, and 5% statistical significance is ind icated in bold. Information ratio is equal to 4-factor alpha (intercept) divided by the standard deviation of the estimated residuals in the time-series regression. Sharpe ratios and information ratios are annualized. Panel A: QM J by Universe Samp le Period Number of Sharp e Excess T-stat T-stat 4-factor Information Firm return Alpha months alp ha Sub-p eriod Ratio Excess Ratio Size (4-factor) return 0.72 United States All 0.34 3.35 1956 - 1985 9.70 0.62 2.01 354 Long Sample 240 1.28 1986 - 2005 All 0.50 2.82 0.67 5.22 0.63 United States Long Sample United States Long Sample 0.37 1.13 0.55 3.26 All 1.27 84 2006 - 2012 0.43 Global Broad Sample All 0.32 2.54 1986 - 2005 2.99 0.57 0.76 240 0.31 0.69 2006 - 2012 All 0.54 1.97 84 7.62 0.74 3.07 Global Broad Sample Panel B : QM J by Number of Universe Samp le Period Excess Information T-stat Sharp e T-stat 4-factor alp ha Alpha Excess Ratio return Ratio Siz e Decile months return P1 (small) United States 1956 - 1985 0.86 5.41 0.90 6.87 0.72 0.98 678 5.82 1956 - 1985 0.51 3.83 0.61 0.51 0.83 678 United States P2 P3 United States 0.43 1957 - 1985 0.43 3.26 0.60 5.48 0.79 678 4.41 0.70 6.93 0.59 0.99 678 1958 - 1985 0.52 United States P4 1959 - 1985 0.86 3.49 0.60 6.00 0.46 0.39 678 United States P5 0.28 0.22 2.14 0.40 4.21 1960 - 1985 0.60 678 United States P6 P7 United States 0.33 3.22 0.52 5.37 0.43 0.77 678 1961 - 1985 United States P8 0.36 3.66 0.59 6.03 0.49 0.86 678 1962 - 1985 678 1963 - 1985 0.25 2.87 0.48 5.34 0.38 0.77 United States P9 United States P10 (Large) 0.33 3.26 0.66 7.22 0.43 1.04 678 1964 - 1985 0.77 0.77 1986 - 2012 0.91 3.98 324 3.64 0.77 Glo b al P1 (s mall) Global P2 1.15 2.50 0.58 1.20 0.48 0.25 324 1987 - 2012 1.27 1988 - 2012 0.73 4.89 0.73 324 0.94 6.03 Global P3 1989 - 2012 0.63 0.65 5.55 0.86 1.17 324 4.47 Global P4 324 0.84 1990 - 2012 0.45 3.32 0.44 3.97 0.64 Global P5 0.73 4.55 0.46 3.79 0.48 324 1991 - 2012 0.96 P6 Global P7 Global 1992 - 2012 0.44 3.60 0.46 4.38 0.69 0.93 324 1993 - 2012 0.33 2.52 0.44 3.54 0.49 0.75 324 P8 Global 324 0.52 4.13 1994 - 2012 0.29 2.71 0.41 0.87 Global P9 1.83 0.24 1995 - 2012 5.03 0.53 324 1.06 0.35 Global P10 (Large) – Page A9 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

56 Table A4 Robustness Checks: QMJ among Small and Large by Country adings. Quality minus Junk (QMJ) factors are constructed as This table shows calendar-time portfolio returns and factor lo the intersection of six value-weighted portfolios formed on size and quality. At the end of each calendar month, stocks are assigned to two size-sorted portfolios based on their market cap italization. For U.S. securities, the size breakpoint is the median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and QMJ factor return is the average return on the two high rebalanced every calendar month to maintain value weights. The quality portfolios minus the average return on the two low quality (junk) portfolios. Portfolios based on profitability, growth, safety and payout score are constructed in a similar manner. We form one set of portfolios in each country and compute global portfolios by we ighting each country’s portfolio by the count ry’s total (lagged) market capitalization. This table includes all available common stocks on the CRSP/Xpressfe ed merged database for the ma rkets listed in Table I. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to- market (HML), and momentum (UMD) factor-mimicking Long Sample portfolios. Panel A reports results from our of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our of global stocks. Panel C report results by country. The Broad Sample sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Returns and alphas are in monthly pe rcent, t-statistics are shown below the coefficient estimates, and 5% statistical significance is ind icated in bold. Information ratio is equal to 4-factor alpha (intercept) divided by the standard deviation of the estimated residuals in the time-series regression. Sharpe ratios and information ratios are annualized. Pan el A : Small Cap Pan el B: Larg e Cap T-stat Excess Information 4-factor Information Sharp e Sharp e Excess T-stat 4-factor T-stat T-stat Ratio return Alpha Ratio Alpha return Alpha Excess Ratio Alpha Excess Ratio return return (4-factor) (4-factor) 2.81 0.73 1.66 0.49 0.37 0.77 0.17 1.35 0.37 0.73 0.40 0.19 Aust ralia 0.28 0.41 0.16 Austria 0.63 0.16 0.27 0.78 0.49 1.62 0.19 0.08 0.34 0.03 0.85 2.75 0.66 3.56 0.87 0.71 -0.01 0.13 0.05 -0.02 -0.01 Belgium 0.53 2.59 0.60 0.55 0.67 0.38 0.88 0.25 1.93 0.56 Canada 3.04 0.19 0.45 1.75 0.55 2.40 0.42 0.60 Switzerland 0.33 0.76 0.72 2.10 0.18 0.52 0.45 0.82 -0.03 -0.11 0.46 1.74 -0.03 Germany 1.00 4.01 0.72 3.18 0.96 1.16 -0.06 0.94 0.92 1.07 3.72 Denmark 0.16 0.31 -0.10 -0.23 0.08 3.79 -0.11 0.36 -0.16 -0.46 -0.04 -0.12 Sp ain -0.03 0.47 1.42 0.43 1.47 0.34 0.70 0.49 0.59 0.24 0.61 2.37 0.16 0.95 0.48 0.69 0.45 Finland 2.05 0.48 2.06 0.46 2.25 0.49 0.58 France 0.42 1.25 0.59 2.19 0.30 0.56 -0.06 0.21 0.87 0.39 0.98 0.32 0.22 1.33 0.26 -0.26 -0.06 United Kingdom 0.41 0.50 1.53 2.93 1.22 3.35 0.90 1.07 Greece 1.18 1.59 0.89 1.58 0.49 1.04 Hong Kong 0.26 2.24 0.84 1.08 0.50 0.56 0.45 4.17 1.20 1.90 0.72 0.40 0.30 0.17 1.62 1.22 0.09 0.09 Ireland 0.02 0.47 0.69 0.97 1.26 0.68 Israel 0.57 2.14 0.72 1.93 0.68 0.64 0.63 1.14 0.98 2.02 0.34 0.63 2.42 0.61 2.43 1.60 0.61 0.78 0.55 Italy 0.89 2.51 0.60 0.39 0.68 2.77 0.45 1.47 0.35 0.34 0.32 1.39 0.31 0.38 0.09 Jap an 0.08 0.51 1.56 0.61 2.01 0.37 0.50 Netherlands -0.32 -0.80 0.07 0.20 -0.19 0.05 0.68 0.72 Norway 0.50 1.21 0.50 1.24 0.29 0.30 1.94 0.87 2.78 0.46 0.18 -0.65 0.37 0.76 0.24 0.47 New Zealand 0.12 -0.25 -0.16 -0.98 -0.35 -0.23 1.85 1.09 1.95 0.52 0.57 Portugal 0.62 1.09 0.69 1.37 0.31 0.40 1.10 0.17 Singap ore -0.47 0.22 0.69 -0.11 -0.21 0.73 2.65 0.66 2.69 0.63 0.68 2.03 0.52 0.46 0.34 0.55 Sweden 0.10 0.26 0.45 1.51 0.06 2.42 0.71 1.18 0.71 0.63 8.23 4.77 0.55 1.18 0.36 8.23 0.61 2.70 0.25 Unit ed St at es 1.60 0.20 Global 0.56 0.92 4.36 3.98 0.41 0.31 0.97 0.49 4.60 0.77 – Page A10 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

57 Table A5 QMJ, Alternative Definition, Averaging Portfolios ings. Portfolios are constructed as the intersection of six This table shows calendar-time portfolio returns and factor load At the end of each calendar month, stocks are assigned to value-weighted portfolios formed on size and a quality measure. two size-sorted portfolios based on their market capitalization. For U.S. securities, the size breakpoint is the median NYSE market equity. For International securities the size breakpoint is the 80th percentile by country. We use conditional sorts, first sorting on size, then on quality. Portfolios are value-weighted, refreshed every calendar month, and rebalanced every calendar month to maintain value weights. The factor return is the average return on the two high quality portfolios minus the average return on the two low quality (junk) portfoli os. We build one portfolio for each measure and average the portfolio return to obtain a QMJ factor ሻȀͶݐݑ݋ݕܽܲ൅ݕݐ݂݁ܽܵ൅݄ݐݓ݋ݎܩ൅ݕݐ݈ܾ݅݅ܽݐ݂݅݋ݎܲሺൌܬܯܳ where ൌݕݐ݈݅݅ Ȁ͸ሻܥܥܣ൅ܴܣܯܩ൅ܣܱܨܥ൅ܣܱܴ൅ܧܱܴ൅ܣܱܲܩሺ , ൅ܣܱܴȟ൅ܧܱܴȟ൅ܣܱܲܩሺȟൌݕݐ݈ܾ݅݅ܽݐ݂݅݋ݎܲൌ݄ݐݓ݋ݎܩ Ȁ͸ሻܥܥܣ൅ȟܴܣܯܩ൅ȟܣܱܨܥȟ , ሻȀ͸ܼ൅ܱ൅ܸܧܮ൅ܮܱܸܫ൅ܤܣܤሺൌݕݐ݂݁ܽݏ and ሻܱܲܲܰ൅ܵܵܫܦ൅ܵܵܫܧሺൌݐݑ݋ݕܽ݌ . country and compute global We form one set of portfolios in each portfolios by weight ing each country’s portfolio by the country’s total (lagged) market capitalization. This table includes all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor-mimicking portfolios. Panel A reports results from our Long Sample of domestic stocks. The sample period runs from June 1956 to December 2012. Panel B reports results from our Broad Sample of global stocks. Panel C report results by country. The sample period runs from June 1986 to December 2012. Returns are in USD, do not include currency hedging, and excess returns are above th e U.S. Treasury bill rate. Returns and alphas are in monthly percent, t-statistics are shown below th e coefficient estimates, and 5% statistical significance is indicated in bold. Information ratio is equal to 4-factor alpha (intercept) divide d by the standard deviation of the estimated residuals in the time-series regression. Sharpe ratios and information ratios are annualized. Pan el B: Bro ad Samp le (Glo b al , 1986 - 2012) Panel A: Long Sample (U.S. , 1956 - 2012) QM J Pro fit ab ilit y Safet y Gro wt h Pa yout QMJ Profitab ilit y Safet y Gro wt h Pa yout 0.16 0.14 0.12 0.21 0.19 0.25 0.13 0.06 0.33 0.17 Excess Returns (4.01) (1.91) (2.44) (3.49) (3.49) (4.37) (1.51) (0.99) (4.11) (3.96) 0.41 0.22 0.21 0.27 0.10 0.31 0.25 0.31 0.24 0.06 CAPM-alpha (6.37) (4.70) (2.00) (6.23) (5.01) (6.11) (3.45) (0.99) (6.35) (5.69) 0.37 0.28 0.28 0.36 0.19 0.29 0.30 0.38 0.32 0.15 3-factor alpha (6.28) (8.42) (8.00) (4.69) (10.32) (8.37) (9.20) (5.71) (3.08) (6.97) 0.19 0.22 0.37 0.26 0.26 0.27 0.15 0.30 0.33 0.31 4-factor alpha (9.46) (6.63) (7.55) (3.63) (6.77) (8.41) (3.85) (5.19) (3.30) (9.19) -0.11 MKT -0.22 0.02 -0.14 -0.06 -0.10 -0.18 -0.01 -0.14 -0.10 (-14.98) (-7.90) (-19.87) (2.19) (-14.39) (-13.31) (-10.69) (-14.88) (-0.75) (-11.94) -0.16 -0.15 -0.30 -0.05 -0.20 -0.20 -0.19 -0.30 -0.13 -0.17 SMB (-18.13) (-12.44) (-18.81) (-4.07) (-14.43) (-11.89) (-9.96) (-11.86) (-6.26) (-6.82) 0.28 -0.06 -0.28 -0.12 -0.06 -0.16 -0.06 -0.30 0.26 -0.04 HML (-5.84) (-3.19) (-19.61) (16.50) (-11.96) (-6.26) (-2.18) (-12.74) (11.32) (-2.63) 0.17 0.01 -0.04 0.04 -0.11 0.14 0.04 0.01 0.09 -0.10 UMD (9.05) (-6.01) (4.54) (0.83) (-3.56) (2.91) (-8.70) (10.41) (3.20) (0.44) 0.46 0.79 0.53 0.25 0.32 0.53 0.67 0.84 0.29 0.19 Sharpe Ratio 1.08 Information Ratio 1.36 1.32 0.95 0.52 1.43 1.78 0.81 1.10 0.70 0.39 0.58 0.64 A d ju s ted R2 0.56 0.40 0.63 0.42 0.60 0.59 0.52 Page A11 – – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

58 Table A6 Time Variation of the Price of Quali w QMJ Returns. Using raw Book-to-Market ty: High Price of Quality Predicts Lo rns on lagged cross sectional regression coefficients. The left ha nd side is the future cumulative excess return (or This table shows time series regression of future factor retu cumulative 4-factor alphas) of the QMJ factor out factor). Alpha is the intercept in a time-series regression of monthly excess return. The (or profitability, growth, safety and pay explanatory variables are the monthly returns from the market portf olio (MKT) and size (SMB), book-to-market (HML), and momentu m (UMD) factor-mimicking portfolios. The right hand side variables are the lagged cross sectional regression coefficient of log of market to book on quality z-score. Th e prior return is defined as the portfolio – weighted average of the past 1-year returns of the stocks in the portfol cks. The sample period runs from June 1956 to io. Panel A reports results from our Long Sample of domestic sto December 2012. Panel B reports results from our Broad Sample of global stocks. The sample period runs from June 1986 to Decembe r 2012. We report the coefficient on the lagged cross sectional regression slope. T-statistics are shown be low the coefficient estimates, and 5% statistical significanc e is indicated in bold. Standard errors are adjusted for heteroskedasticity and autocorrelation (Newey and West (1987)) with lag length equal to the forecasting horizon. “ Mean Adj R2 ” is the average adjusted r -squared across all the regression above. The intercept and prior returns ar e included in all regressions but not reported. Panel B: Broad Samp le (Global, 1986 - 2012) Panel A: Long Samp le (U.S. , 1956 - 2012) Return (t, t+60) Return (t, t+36) Return (t, t+12) Return (t, t+36) Return (t, t+12) Return (t) Return (t, t+60) Return (t) Left-hand side Raw Raw Alp ha Raw Alp ha Raw Alp ha Raw Alp ha Raw Alp ha Raw Alp ha Raw Alp ha Alp ha 0.01 -0.04 -0.24 -1.19 -0.79 -1.83 -2.50 -0.02 -0.42 -0.27 0.12 -0.46 0.37 -0.69 -2.09 QMJ -0.01 (-1.68) (-3.22) (-2.19) (-4.05) (-2.35) (-3.11) (-4.79) (-0.67) (-2.63) (-1.79) (1.24) (-1.58) (1.47) (-2.23) (-5.30) (1.34) Pro fit ab ilit y -0.01 -0.37 -0.22 -1.28 -0.81 -1.65 -2.35 -0.03 0.03 -0.10 0.20 -0.42 0.36 -1.20 -2.59 0.01 (-2.58) (-1.63) (-3.64) (-2.36) (-6.22) (-3.07) (-3.55) (-6.81) (0.39) (2.53) (-0.63) (2.06) (-0.85) (1.12) (-2.41) (-5.22) Gr o w t h -0.03 -0.44 -0.12 -1.32 -0.16 0.15 -1.67 -0.03 0.01 -0.40 -0.07 -1.26 -0.66 -1.65 -1.67 0.00 (-0.14) (0.48) (-0.99) (-3.10) (-0.37) (0.20) (-2.19) (-1.28) (-2.14) (-2.48) (-0.48) (-2.20) (-1.35) (-3.40) (-4.89) (-3.13) -0.04 Safety -0.48 -0.17 -1.42 -0.81 -1.64 -2.38 0.00 0.00 -0.35 0.05 -0.68 0.24 0.21 -0.84 -0.04 (-2.37) (-0.50) (-3.44) (-1.69) (-4.82) (-1.57) (-1.36) (-3.33) (-1.33) (0.45) (-2.43) (0.95) (-3.26) (1.97) (0.66) (-3.42) -0.06 Payout -0.49 -0.13 -0.95 -0.46 -1.35 -2.06 -0.02 -0.01 -0.48 0.01 -0.39 0.11 -0.66 -1.23 -0.05 (-2.31) (-1.61) (-2.85) (-0.95) (-2.07) (-1.87) (-2.66) (-2.80) (-2.11) (-0.83) (-1.89) (0.10) (-0.68) (0.26) (-1.53) (-4.08) 0.26 Mean A d j R2 0.00 0.12 0.07 0.28 0.16 0.19 0.33 0.01 0.00 0.09 0.03 0.01 0.11 0.21 0.37 – Page A12 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

59 Figure A1 QMJ: 4-Factor Adjusted Information Ratios by Size This figure shows 4-factor adjusted info rmation ratios of Quality minus Junk ( QMJ) factors. This figure includes all available common stocks on the CRSP/Xpressfeed merged database for the markets listed in Table I. For U.S. securities, the size breakpoint is the median NYSE market equity. For Internation al securities the size breakpoint is the 80th percentile by country. Alpha is the intercept in a time-series regression of monthly excess return. The explanatory variables are the monthly returns from the market portfolio (MKT) and size (SMB), book-to-market (HML), and momentum (UMD) factor- mimicking portfolios. Returns are in USD, do not include currency hedging, and excess returns are above the U.S. Treasury bill rate. Information ratios are equal to alpha divided by the standard deviation of the estimated residuals in the time-serie s regression. Information ratios are annualized. 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 Italy Israel Spain Japan Global France Ireland Austria Greece Finland Canada Norway Sweden Belgium Australia Portugal Denmark Germany -0.20 Singapore Hong Kong Switzerland Netherlands New Zealand United States United Kingdom -0.40 Panel B: Large Cap Panel A: Small Cap – Page A13 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

60 Figure A2 ficient, the Price of Quality Cross Sectional Regressions Coef This figure reports coefficients from Fama-Macbeth regr essions. The dependent variable is the z-score of a anatory variables are the quality scores in month t stock’s market to book ratio (MB) in month t. The expl . We plot the time series of the cross sectional coeff icients from table III, panel A, column (1) and (7) . Time Series of FMB Coefficients - Long Sample (U.S.) 0.800 0.600 0.400 0.200 0.000 -0.200 -0.400 1989 2010 2007 1992 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 2004 2001 1995 1998 Profitability Growth Safety Payout Time Series of FMB Coefficients - Broad Sample (Global) 0.500 0.400 0.300 0.200 0.100 0.000 -0.100 -0.200 -0.300 2011 2009 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Profitability Payout Safety Growth – Page A14 – Appendix – Asness, Frazzini, and Pedersen Quality Minus Junk

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Networks, Crowds, and Markets: Reasoning about a Highly Connected World David Easley Jon Kleinberg Dept. of Economics Dept. of Computer Science Cornell University Cornell University Cambridge Universi...

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