QDoVI 141030.DVI

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1 Quality Investing Robert Novy-Marx just as much value investing as Buying high quality assets without paying premium prices is buying average quality assets at discount prices. Strategi es that exploit the quality dimen- r both dimensions of value sion of value can be profitable on their own, and accounting fo yields dramatic performance improvements over traditiona l value strategies. Gross prof- itability is particularly powerful among popular quality n otions, especially among large cap stocks and for long-only investors. d? Quality, unlike value, has What is quality investing, and how should quality be measure sily identified by the fact they no universally accepted definition. Value strategies are ea trast, are generally identified hold stocks with low valuations. Quality strategies, in con using something more akin to Supreme Court Justice Potter St ewart’s obscenity doctrine of Jacobellis v. Ohio, 1964). This paper attempts to identify “you know it when you see it” ( commonalities across seven of the best know quality strateg ies. It also looks for differences, running a performance horse race between alternative quali ty strategies. Quality is often marketed as an attractive alternative to tr aditional growth strategies, flation in the early 2000s. which performed terribly both during and after the NASDAQ de Its leading industry proponents include GMO’s Jeremy Grant ham, whose high quality in- dicators of “high return, stable return, and low debt” have s haped the design of MSCI’s Quality Indices, and Joel Greenblatt, whose “Little Book th at Beats the Market” has en- couraged a generation of value investors to pay attention to capital productivity, measured by return on invested capital, in addition to valuations. There has also been increased interest in incorporating aca demic measures of quality into value strategies. BlackRock, an early adopter (while s till Barclays Global Investors) of Sloan’s (1996) accruals-based measure of earnings quali ty, is currently promoting the Robert Novy-Marx is Lori and Alan S. Zekelman Professor of Bu siness Administration at the Simon Graduate School of Business at the University of Rochester, New York, and a research associate of the National Bureau of Economic Research. 1

2 benefits of integrating earnings quality into global equiti es strategies (Kozlov and Peta- formed jointly on valuations jisto, 2013). Piotroski and So (2012) argue that strategies and another accounting based measure of financial strength, the Piotroski’s (2000) F-score quality among its nine sub- (which uses both Sloan’s accruals and aspects of Grantham’s components), have dramatically outperformed traditional value strategies. Societe General n) as the primary screen it employs has appropriated Piotroski’s F-score (without attributio when constructing its Global Quality Income Index, launche d in 2012 (Lapthorne et. al., 2012). profitability (revenues Novy-Marx (2013) finds that a simpler quality measure, gross predicting stock returns minus cost of goods sold, scaled by assets), has as much power as traditional value metrics. Strategies based on gross pro fitability are highly negatively correlated with strategies based on price signals, making t hem particularly attractive to traditional value investors. Novy-Marx’s results have infl uenced the design of both DFA’s growth funds and AQR Capital Management’s core equity funds . One common recurring theme is the strong relation between qu ality and value. The two are quite similar, philosophically. Quality can even be viewed as an alternative im- aying premium prices is just plementation of value—buying high quality assets without p as much value investing as buying average quality assets at a discount. Warren Buffett, Graham’s most famous student and the most successful value i nvestor of all time, is fond of saying that it is “far better to buy a wonderful business at a fair price than to buy a fair business at a wonderful price.” In fact, Frazzini, Kabiller , and Pedersen (2012) show that the performance of the publicly traded companies held by Ber kshire Hathaway, Buffett’s primary investment vehicle, can largely be explained by his commitment to buying high quality stocks. Quality and value strategies are highly dissimilar, howeve r, in the stocks that they actu- ally hold. High quality firms tend to be expensive, while valu e firms tend to be low quality. Quality strategies are thus short value, while value strate gies are short quality. Each of these strategies consequently tends to do well precisely when the other under-performs, making 2

3 them exceptionally attractive to run together. With these c laims regarding the synergies re of strategies masquerading between quality and value, and the varied and disparate natu as “quality,” it is natural to ask which quality measures bes t help investors design success- is question, by assessing the ful investment portfolios. This paper attempts to answer th performance of the best known quality strategies. wer predicting returns, es- It finds that all of the quality measures appear to have some po pecially among small cap stocks, and when used in conjunctio n with value measures. Only gross profitability, however, generates significant excess returns as a stand alone strategy, and has the largest Fama and French (1993) three-factor alph a, especially among large cap f the other measures. stocks. Gross profitability also subsumes most of the power o The paper also shows that long-only investors need to be more careful when designing strategies to exploit quality. For these investors, whose p ortfolios are dominated by market risk, it is difficult to get large exposures to the attractive opportunities provided by value and quality by running value and quality strategies side by s ide. Long-only investors can get larger quality and value tilts, and thus achieve higher S harpe ratios, through the inte- ty stocks. grated solution of buying only reasonably priced high quali Measuring quality I will be comparing the performance of strategies based on se ven of the best known and most widely used notions of quality. These include Graham’s quality criteria from his “In- telligent Investor,” Grantham’s “high return, stable retu rn, and low debt” and Greenblatt’s return on invested capital, Sloan’s (1996) accruals-based measure of earnings quality and Piotroski’s (2000) F-score measure of financial strength, a nd Novy-Marx’s (2013) gross profitability. I also include the low volatility/low beta no tion used by “defensive equity” strategies, which look more like a traditional value but are often marketed as high qual- ity. Before comparing the ability of these measures to predi ct returns, each is discussed in greater detail below, beginning with Graham’s quality crit eria. 3

4 Graham quality Today Benjamin Graham is primarily associated with value me trics like price-to-earnings heap stocks. He believed in or market-to-book, but Graham never advocated just buying c ms cheaply. In fact, Graham buying undervalued firms, which means buying high quality fir was just as concerned with the quality of a firm’s assets as he w as with the price that one had to pay to purchase them. According to Graham, an equity in vestor should “. . . apply a e obtains (1) a minimum of set of standards to each [stock] purchase, to make sure that h on of the company, and also (2) quality in the past performance and current financial positi a minimum of quantity in terms of earnings and assets per doll ar of price” (Graham 1973, pp. 183). Graham’s seven quality and quantity criteria are: 1. “Adequate” enterprise size, as insulation against the “v icissitudes” of the economy; 2. Strong financial condition, measured by current ratios th at exceed two and net current assets that exceed long term debt; 3. Earnings stability, measured by 10 consecutive years of p ositive earnings; 4. A dividend record of uninterrupted payments for at least 2 0 years; 5. Earnings-per-share growth of at least one-third over the last ten years; 6. Moderate price-to-earnings ratios, which typically sho uld not exceed 15; and 7. Moderate price-to-book ratios, which typically should n ot exceed 1½. The first five screens attempt to ensure that one buys only high quality firms, while the last two ensure that one buys them only at reasonable prices. To turn these criteria into a trading strategy, I create a “Gr aham score” (G-score) quality index for each stock. This composite of Graham’s five quality criteria gets one point if a firm’s current ratio exceeds two, one point if net current ass ets exceed long term debt, one point if it has a ten year history of positive earnings, one po int if it has a ten year history 4

5 of returning cash to shareholders, and one point if its earni ngs-per-share are at least a third 1 This results in a score from zero to five, with higher higher than they were 10 years ago. scores signaling higher quality firms. The quality signal em ployed for stock selection is the rank of a firm’s G-score among the applicable universe. For mo re details of the construction of all the variables employed in this paper, please see Appen dix A. Grantham quality Grantham’s views on quality investing are espoused by his fir m, GMO, which argues the for Quality—The Danger of merits of quality investing in its 2004 white paper “The Case t the criteria of low leverage, Junk.” This paper defines quality companies as those that mee ts that stocks of firms with these high profitability, and low earnings volatility, and sugges ds.” In a later study, “Profits characteristics “have always won over longer holding perio yer, 2012), GMO shows for the Long Run: Affirming the Case for Quality” (Joyce and Ma verage return on equity that since 1965 the least levered firms (lowest 25%) have had a 5% higher than the most levered firms (highest 25%), and claim s that “profitability is the ultimate source of investment returns.” These ideas have been highly influential. MSCI Quality Indic es, launched in December 2012, are based on Grantham’s basic principles. According t o MSCI, their Quality Indices ore for each security in the el- “identify quality growth stocks by calculating a quality sc ables: high return on equity igible equity universe based on three main fundamental vari (ROE), stable year-over-year earnings growth and low financ ial leverage.” The Grantham criteria of “high returns, stable returns, low leverage” al so make up half of the score (to- gether with low volatility) used by Russell when constructi ng their Defensive Indexes, and two of the three criteria (high ROE and low leverage) form the basis of the Dow Jones 1 This methodology is similar to that employed by Piotroski (2 000) to calculate his financial strength F- score, which is investigated in greater detail in later sect ions. In calculating the G-score I have reduced the required earnings history from 20 to 10 years to get more vari ation in this component of the measure. I have also relaxed the dividend condition to include net repu rchases, because share repurchases have gained popularity as a means for returning cash to shareholders. Gr aham also preferred large firms, but I have ignored this criterion, as this paper also considers the performanc e of quality strategies formed entirely within the large and small cap universes. 5

6 Quality Index. Others have argued that the benefits of incorporating qualit y concerns into equity strate- aper, “Power Couple: Quality gies accrue primarily to value investors. In a recent white p ead et. al., 2013), MFS and Value are Strong Drivers of Long-Term Equity Returns” (M Investment Management studies the performance of strategi es based on Grantham’s no- tions of quality, both as a stand-alone investment strategy and in conjunction with value. They conclude that while “. . . investing in quality without r egard for valuation is not a com- t are both high quality and pelling way to drive alpha over time. . . owning companies tha ate sustainable, long-term inexpensively valued is. . . the most compelling way to gener performance.” Return on invested capital (ROIC) Joel Greenblatt’s “Little Book that Beats the Market” has be en equally influential in getting investors, especially value investors, to pay atte ntion to quality. The logic of Green- blatt’s “magic formula investing” is clearly that of combin ing quality and value, in the spirit of Graham’s belief in buying good firms at low prices. M agic formula investing en- tails ranking firms on the basis of return on invested capital (ROIC) and earnings yield (EY, ly buying stocks with the high- defined as EBIT-to-enterprise value), respectively, and on est combined ranks. In Greenblatt’s formula ROIC serves as t he quality metric, while EY ed to ensure that investors are serves as the value metric. The formula is explicitly intend “buying good companies. . . only at bargain prices” (Greenbl att 2010, p.47). Earnings quality BlackRock has probably been the biggest proponent of incorp orating earnings quality sig- nals into value strategies. Sloan (1996) develops the best k nown and most widely used earn- ings quality measure. This accruals measure is the differen ce between cash and accounting earnings, scaled by firm assets. According to Sloan, BlackRo ck (then BGI) “. . . was the first place to really pick up on my work” (Businessweek 2007). BGI hired Sloan in 2006, presumably at least in part for his earnings quality experti se. More recently BlackRock 6

7 researchers have been promoting the benefits of trading earn ings quality in conjunction ed “Global Return Premiums with value in equity markets around the world, in a paper titl on Earnings Quality, Value, and Size” (Kozlov and Petajisto , 2013). Strategies based on vestors. The Forensic Accounting earnings quality are also readily available to long-only in ETF (FLAG), for example, is designed to track the Del Vecchio Earnings Quality Index, id companies with aggressive which “uses financial statement analysis in an attempt to avo revenue recognition while investing in companies that have high earnings quality.” Financial strength nother accounting based mea- Piotroski’s (2000) F-score measure of financial strength, a al money managers and sure of firm quality, is also commonly employed by profession widely available on internet stock screeners. Societe Gene ral uses the F-score as its pri- ex, while Morgan Stanley mary screen when constructing its Global Quality Income Ind has offered products linked to strategies that combine the F -score with Greenblatt’s magic formula (Ng 2009). The F-score is constructed by summing nine binary variables , and includes elements of both Grantham’s quality and Sloan’s earnings quality, as we ll as fundamental momentum of the variables it employs (improving earnings) and the equity issuance anomaly. Four are designed to capture profitability, three to capture liqu idity, and two to capture oper- ating efficiency. Each component takes on the value zero, ind icating weakness, or one, indicating strength. The F-score thus takes on a value from z ero to nine, with higher num- bers indicating stronger financial performance. While Piot roski (2000) originally analyzed stand-alone strategies based on the F-score, Piotroski and So (2012) shows that strategies that trade jointly on valuation and the F-score perform even better. Defensive equity Defensive equity strategies have become popular over the la st five years, partly in response to the market’s poor performance in the last quarter of 2008. These strategies promise equity like returns, delivered with less volatility and sma ller drawdowns, and are often 7

8 marketed as high quality strategies. Defensive equity strategies typically hold stocks with low volatility and low market ady performance, while low market betas. Low volatility contributes to these strategies’ ste ket betas are only weakly betas generate outperformance in down markets. Because mar correlated with average returns (Black, Jensen, and Schole s, 1972; Black, 1972, 1993; Frazzini and Pedersen, 2013), and high volatility stocks ha ve actually underperformed low volatility stocks (Ang et. al. 2006; Baker, Bradley, and Wur gler, 2011), providers typically acrificing absolute performance. claim that these strategies mitigate market risks without s Well known defensive indicies include Research Associates ’ RAFI Low Volatility, Sabri- Beta. Investable products in- ent’s Defensive Equity, and Dow Jones’ Market Neutral Anti- clude both traditional mutual funds, such as AQR’s and Russe ll’s Defensive Equity Funds, and ETFs, such as Guggenheim Defensive Equity, PowerShares S&P 500 Low Volatility Portfolio, and QuantShares U.S. Market Neutral Anti-Beta F und. Defensive equity strategies tilt towards value, and conseq uently look significantly dif- ferent than the other strategies considered here. They are i ncluded here because some de- fensive strategies sometimes select stocks using addition al themes common to other quality equity, and they are often marketed strategies, particularly low leverage and stable return on to quality oriented investors. Gross profitability Novy-Marx (2013) shows that a simple quality metric, gross p rofits-to-assets, has roughly as much power predicting the relative performance of differ ent stocks as tried-and-true value measures like book-to-price. Buying profitable firms a nd selling unprofitable firms, where profitability is measured by the difference between a fi rm’s total revenues and the costs of the goods or services it sells, scaled by assets, yie lds a gross profitability premium. Just as importantly, the performance of strategies based on gross profitability is strongly negatively correlated with value, so profitability strateg ies not only deliver high average returns, but also provide a valuable hedge to value investor s. Financial economists have long believed that profitability should forecast returns, and 8

9 puzzled over ROE’s poor performance predicting cross secti onal differences in average tter follows from the simplest of stock performance. This belief that profitability should ma economic reasoning. A stock’s current price reflects market expectations of its future pay- old it. If two companies have the outs, discounted at the rate of return investors require to h same expected future profitability (i.e., payoffs), but are priced differently, this must reflect lding the low priced stock (Ball the fact that investors require a higher rate of return for ho 1978, Berk 1995). That is, simple dividend discounting pred icts the value premium. Simi- ities, and thus different expected larly, if two firms have different expected future profitabil fact that investors require a future payoffs, but are priced the same, this must reflect the ble firm. The same economic higher rate of return for holding the stock of the more profita reasoning that predicts the value premium thus also predict s a profitability premium, sug- gesting that the quality and value phenomena are two sides of the same coin. These arguments for the value and profitability premiums are not predicated on in- vestor rationality. Differences in required rates of retur n could partially reflect mispricings (a stock is mispriced if and only if investors require the wro ng rate of return to hold it). Trading on value and profitability may thus simply be a crude b ut effective way of exploit- ing mispricings in the cross section. Fama and French (2006) use the reasoning of the dividend disc ount model to motivate their empirical investigation of profitability as a stock re turn predictor. They find that cross- sectional regressions, which identify primarily off of sma ll cap stocks, suggest that ROE is “related to average returns in the manner expected” (Fama and French 2006), but Fama and French (2008) find that portfolio tests, which better app roximate the performance of trading strategies available to investors, “do not provide much basis for the conclusion that, with controls for market cap and B/M, there is a positive rela tion between average returns and profitability.” The surprising fact, from the point of vi ew of the model, is the poor empirical performance of profitability, measured by earnin gs, predicting returns. Novy-Marx (2013) argues that gross profitability performs b etter predicting future stock returns than ROE, the profitability variable most frequentl y employed in earlier academic 9

10 studies, because it is a better proxy for true economic profit ability. In particular, the study mic investment (e.g., R&D, points to the fact that accountants treat many forms of econo advertisement, sales commissions, and human capital devel opment) as expenses, so these rofitability. This makes earnings activities lower net income, but increase future expected p a poor proxy for true expected economic profitability. While analysts spend a lot of time thinking about bottom line earnings, and to a lesser extent free cash flow or EBIT, empirically gross profitabilit y, which appears almost at the top of the income statement, is a better predictor of a firm’s f uture stock performance. Ac- cording to Chi and Fogdall (2012), the co-heads of portfolio management at Dimensional Fund Advisors, “the research breakthrough in this case is no t the discovery of expected thing that financial economists profitability as a dimension of expected returns per se, some have suggested for quite some time... rather, it is the disco very of reasonable proxies for s another dimension of expected expected profitability, which allow us to use profitability a returns in the creation of investment solutions.” Quality strategy performance To compare the performance of these different notions of qua lity, strategies are con- 2 ity metrics. structed by ranking firms on the basis of each of the seven qual Strategies d non-financials. Several of include both financials (firms with one digit SIC codes of 6) an -financial firms, however, so these measures look very different for financial firms and non 3 to avoid strong industry biases financials and non-financial s are ranked separately. Strate- gies are formed as value-weighted portfolios that hold (sho rt) stocks in the top (bottom) 30% by quality rank, using NYSE breaks. Portfolios are rebal anced each year at the end of June, using accounting data from the fiscal year ending in the previous calendar year. The 2 the data items used in the construction Data come from CRSP and Compustat. Detailed descriptions of of each of the measures is provided in Appendix A. 3 Financial firms typically have large financial asset bases, b ut little tangible capital. Financials conse- quently tend to look low quality when measured using Grantha m’s notion, earnings quality, or gross prof- itability, which all are, or have components, scaled by asse ts. They tend to look high quality when measured using ROIC, which has tangible assets in the denominator, or using the defensive notion of low volatility and low market beta. 10

11 Table 1: Value and quality strategy return correlations Sort variable G1 G2 ROIC EQ F D B/P -0.24 Graham’s G-score (G1) -0.38 0.47 Grantham’s quality (G2) ROIC -0.11 0.29 0.47 0.14 0.04 0.20 -0.27 Earnings quality (EQ) -0.11 Piotroski’s F-score (F) 0.38 0.56 0.06 0.18 Defensive (D) 0.24 0.57 0.54 0.18 0.40 0.20 Gross profitability (GP) -0.58 0.42 0.38 0.43 -0.26 0.17 -0.0 0 sample covers July 1963 to December 2013. Returns are calcul ated net of estimated trans- , using the Hasbrouck (2009) action costs calculated, as in Novy-Marx and Velikov (2014) lized version of the Roll (1984) Bayesian-Gibbs sampling procedure for estimating a genera effective spread measure. Trading costs are typically mode st, on the order of 0.5%/year for large cap strategies and 1.5%/year for small cap strategies , because quality is highly per- ly. sistent so strategies based on quality turnover infrequent uality strategies and a Table 1 shows correlations between the returns to the seven q traditional value strategy, which is constructed similarl y using book-to-price. The table shows some commonalities across the different measures of q uality. Eighteen of the twenty one pair-wise correlations across distinct quality measur es are positive. Two of the three negative coefficients are on correlations with Sloan’s earn ings quality strategy, which is relatively weakly correlated with all the other strategies . This suggests that the earnings quality strategy should not, despite its name, be classified as a quality strategy. The table shows mixed results on the quality strategies’ rel ation to value. The strategies based on Graham’s and Grantham’s notions of quality, and esp ecially that based on gross profitability, tilt towards growth. The strategies based on ROIC and the accounting notions of quality are only weakly correlated with traditional valu e. The defensive strategy, as is well known by practitioners, tilts strongly toward value. I nterestingly, the defensive strat- egy, despite this value tilt, still covaries positively wit h all of the quality strategies except gross profitability. It covaries particularly strongly wit h the strategy based on Grantham’s 11

12 Table 2: Quality strategy performance Three-factor model regression results e EŒr ̨ ˇ Sort variable ˇ • ˇ HML SMB MKT Panel A: Traditional value -1.54 -0.00 0.27 0.96 Book-to-price 3.49 [-0.31] [14.5] [47.5] [-2.27] [2.33] Panel B: Quality strategies -0.08 1.69 -0.10 -0.16 Graham’s G-score -0.15 [-0.08] [-6.07] [-6.70] [-5.57] [1.93] -0.55 -0.30 -0.47 -0.48 Grantham’s quality 4.84 [4.90] [-15.7] [-17.0] [-16.4] [-0.37] ROIC 2.17 -0.15 -0.49 -0.01 4.66 [2.78] [-4.42] [-10.4] [-0.27] [1.16] Earnings quality 1.17 2.13 -0.10 -0.13 0.01 [0.99] [1.83] [-3.99] [0.39] [-4.43] 2.24 -0.14 -0.29 -0.08 Piotroski’s F-score 4.33 [3.57] [-5.88] [-8.53] [-2.14] [1.69] Defensive -1.55 -0.66 -0.86 0.39 3.45 [2.09] [-20.4] [-18.9] [7.85] [-0.52] Gross profitability 2.70 5.21 -0.08 -0.02 -0.46 [2.15] [4.65] [-0.80] [-13.7] [-3.56] This table shows returns (percent per year), in excess of tho se on T-bills, to long/short strategies Notes: e of seven quality metrics. The table also shows formed by sorting stocks on the basis of book-to-price, or on three-factor model alphas and factor loadings. notion of quality, which uses low earnings volatility as one of its components. Table 2 shows the performance of the seven quality strategie s, as well as that of tradi- tional value. Of the seven quality strategies only gross pro fitability generates a significant excess return, and the gross profitability spread of 2.7%/ye ar is only three-quarters as large as the 3.5%/year value spread. Three of the quality strategi es, those based on Graham’s and Grantham’s notions of quality and the defensive strateg y, actually generate negative spreads, though these are all insignificant. All of the quality strategies look better when evaluated aga inst the Fama and French three-factor model. All of the strategies have negative mar ket loadings, ranging from -0.08 on gross profitability to -0.66 on defensive equity. All of th e strategies also tilt toward large 12

13 caps, with SMB loadings ranging from -0.02 on gross profitabi lity to -0.86 on defensive rantham’s notions of qual- equity. Four of the strategies, those based on Graham’s and G ity, have significant growth tilts, ity, that based on Piotroski’s F-score, and gross profitabil while the defensive strategy has a significant value tilt. As a result of the negative Fama and French factor loadings four of the strategies, those bas ed on Grantham’s notion of qual- ity, ROIC, Piotroski’s F-score, and gross profitability, ha ve highly significant three-factor oss profitability strategy is alphas in excess of 4%/year. The three-factor alpha on the gr 5.21%/year, with a t-stat in excess of four. Spanning Tests This section compares the performance of the seven quality s trategies head-to-head, through a series of spanning tests. These tests essentially ask whic h of the strategies generate signif- icant alpha relative to the others, by regressing the return s of a test strategy, taken from the quality strategies, onto the returns of the Fama and French f actors and a potential explana- tory strategy, also taken from the quality strategies. Sign ificant abnormal returns suggest an investor already trading the Fama and French factors and t he explanatory strategy could egy. Insignificant abnormal returns realize significant gains by starting to trade the test strat suggest that the investor has little to gain by starting to tr ade the test strategy. Table 3 shows that all of the strategies generally generate p ositive abnormal returns when evaluated against the Fama an French factors and anothe r quality strategy, but these abnormal returns are typically modest and statistically in significant. Only two of the strate- gies consistently generate significant abnormal returns re lative to all the others. The second and seventh rows of the table show that the strategies based o n Grantham’s notion of qual- ity and gross profitability generate significant alpha relat ive to all the others. The second and seventh columns also show that these two strategies basi cally subsume all the others. The insignificant alphas in these columns show that an invest or trading either of these two strategies has little to gain from starting to trade any of th e five other strategies. 13

14 Table 3: Spanning tests Explanatory strategy ( ) x y ) G2 ROIC EQ F D GP Test strategy ( G1 1.06 1.33 1.36 -0.23 0.29 Graham’s G-score (G1) 1.42 [1.60] [1.49] [1.53] [-0.28] [0.34] [1.20] 4.06 3.82 4.13 3.95 3.07 Grantham’s quality (G2) 4.41 [4.38] [4.11] [4.25] [3.16] [4.17] [3.96] 3.21 ROIC 4.58 1.58 2.83 -0.70 1.32 [1.90] [3.12] [1.02] [1.76] [-0.50] [0.80] 1.50 2.62 1.69 1.57 2.86 Earnings quality (EQ) 1.14 [0.95] [2.57] [1.43] [1.34] [2.50] [1.27] Piotroski’s F-score (F) 3.32 2.21 3.48 3.16 2.37 2.69 [2.17] [2.00] [2.85] [2.59] [1.94] [2.71] Defensive (D) 2.23 -0.72 0.98 2.44 1.68 0.54 [1.33] [-0.46] [1.48] [1.01] [0.33] [0.62] 4.26 4.62 3.56 5.35 4.40 Gross profitability (GP) 3.34 [3.03] [4.06] [4.88] [3.87] [4.13] [3.80] Notes: This table shows alphas (percent per year) from five-factor t ime-series regressions of the form y D ̨ C ˇ ; MKT C ˇ C SMB C ˇ x HML C ˇ ˇ UMD C UMD x SMB MKT HML y are the returns to a test strategy and an explanatory strateg x where y, and in each case these are both and taken from the seven quality strategies. Quality performance within the large and small cap universe s Several of the quality strategies, especially defensive eq uity and that based on Grantham’s notion of quality, have strong size biases that are well know n by practitioners. In these cases the quality metrics work in part by picking stocks across cap italization universes, which raises concerns regarding the power that these metrics have predicting performance within a given universe. This section addresses this issue by analyz ing strategies constructed within the the Russell 1000 and Russell 2000 universes, which make u p time series averages of 86.2% and 11.7% of total market capitalization over the samp le, respectively. Table 4 shows the performance of the seven quality strategie s, as well as traditional value, constructed entirely within the Russell 1000 and Rus sell 2000. Panel A shows that among large caps none of the strategies, including value, ge nerated significant excess re- 14

15 Table 4: Value and quality strategy performance by size Three-factor model regression results e EŒr ̨ ˇ Sort variable ˇ • ˇ HML SMB MKT Panel A: Large cap results (Russell 1000) Book-to-price 2.06 -2.29 -0.01 0.15 0.91 [-1.04] [8.12] [44.2] [1.43] [-3.34] 1.18 -0.13 -0.15 -0.30 Graham’s G-score -1.33 [-6.91] [-10.6] [1.26] [-1.29] [-5.80] -0.75 -0.22 -0.28 -0.42 Grantham’s quality 3.29 [3.78] [-13.1] [-11.6] [-16.2] [-0.65] 0.66 ROIC -0.01 -0.09 -0.36 2.62 [2.17] [-0.59] [-10.1] [0.52] [-2.80] 1.85 0.02 -0.07 1.27 Earnings quality -0.08 [-3.68] [-2.29] [0.66] [1.18] [1.72] 1.36 2.67 -0.11 Piotroski’s F-score -0.07 -0.11 [1.18] [-4.93] [-3.53] [-2.16] [2.36] -2.43 -0.60 Defensive -0.50 0.39 1.02 [0.67] [-20.1] [-11.8] [8.52] [-0.98] Gross profitability 1.95 4.99 -0.10 0.00 -0.57 [1.49] [4.60] [0.13] [-17.6] [-4.70] Panel B: Small cap results (Russell 2000) Book-to-price -0.00 -0.11 0.87 4.56 1.18 [-0.25] [39.8] [1.62] [3.09] [-5.43] 2.75 -0.13 -0.12 -0.04 Graham’s G-score 4.10 [3.92] [-6.42] [2.53] [-1.43] [-4.10] Grantham’s quality 3.58 -0.23 -0.31 -0.33 -0.20 [3.93] [-12.3] [-0.17] [-12.2] [-12.8] ROIC 2.73 -0.06 -0.22 0.03 1.81 [1.35] [2.08] [-2.18] [-6.02] [0.73] Earnings quality 2.02 -0.01 -0.03 0.14 1.59 [1.96] [-1.45] [5.79] [2.45] [-0.71] 2.11 3.68 -0.14 Piotroski’s F-score 0.03 -0.27 [1.72] [3.38] [-6.69] [-8.91] [1.02] Defensive -1.50 3.44 -0.64 -0.76 0.29 [-0.56] [-22.3] [-18.8] [6.70] [2.36] Gross profitability 3.32 3.85 0.02 0.05 -0.19 [2.99] [3.53] [0.90] [1.81] [-5.87] 15

16 turns. Four strategies, those based on Grantham’s notion of quality, ROIC, Piotroski’s F- s among large cap stocks, though score, and gross profitability, generate three factor alpha these alphas, with the exception of that on gross profitabili ty, are 1-2%/year lower than re cross-section. those observed on the strategies constructed using the enti Panel B shows stronger results within the small cap universe . Among small caps, in ad- m’s notion of quality and Sloan’s dition to gross profitability, the strategies based on Graha earnings quality also generate significant excess returns. Among small caps all the strate- gies generate significant three-factor alpha, though this s ignificance is only marginal in the case of earnings quality. These significant three-factor al phas come despite generally at- s generate higher returns in the tenuated size and value loadings, because all the strategie small cap universe. Table 5 shows results of spanning tests, like those performe d in Table 3, for the large and small cap quality strategies. Here the results are strik ing. Panel A shows that in the large cap universe, which accounts for almost 90% of total ma rket capitalization, only gross profitability generates consistently significant abn ormal returns relative to the Fama and French factors and the other notions of quality. The rela tively weak performance of rom mitigating the size bias that the strategy based on Grantham’s notion of quality results f arises from sorting on Grantham quality metric. In Table 3, w hich shows results for strate- gies formed using the entire cross section of stocks, the Gra ntham strategy’s large alpha was driven disproportionately by the short side, which tilt ed strongly to small stocks where the effects were stronger. Panel B shows that in the small cap s three strategies generate consistently significant abnormal returns relative to the F ama and French factors and the other notions of quality, the strategy based on Graham’s not ion of quality (first row), which had almost no power in the whole cross-section, the strategy based on Grantham’s notion of quality, and gross profitability (last row). Graham’s qua lity does little to explain the per- formance of the other small cap quality strategies (first col umn), while gross profitability subsumes the power of all the other strategies except for ear nings quality, to which it is negatively correlated (last column). 16

17 Table 5: Spanning tests, by universe Explanatory strategy ( ) x y ) G2 ROIC EQ F D GP Test strategy ( G1 Panel A: Large cap results (Russell 1000) -0.19 1.09 1.03 -1.00 0.30 Graham’s G-score (G1) 1.00 [1.13] [1.07] [-1.20] [0.34] [-0.21] [1.04] 1.88 2.81 2.59 2.67 1.09 Grantham’s quality (G2) 2.32 [3.20] [2.39] [3.31] [1.36] [2.88] [2.93] 0.75 2.49 2.09 2.00 -0.83 ROIC 3.15 [2.93] [1.74] [2.03] [-0.89] [1.75] [0.68] 1.12 1.52 2.26 1.36 Earnings quality (EQ) 2.30 1.19 [1.02] [2.36] [1.25] [1.11] [2.14] [1.39] 1.74 1.36 1.84 1.69 1.29 Piotroski’s F-score (F) 1.17 [1.05] [1.12] [1.48] [1.19] [1.52] [1.63] 0.07 -0.27 0.52 0.05 -1.05 Defensive (D) -1.75 [-1.23] [-0.17] [0.34] [0.03] [0.04] [-0.68] Gross profitability (GP) 2.97 3.00 4.80 4.35 4.47 3.87 [2.99] [3.95] [4.48] [4.10] [4.12] [3.63] Panel B: Small cap results (Russell 2000) Graham’s G-score (G1) 3.95 4.50 4.02 4.19 3.12 3.41 [3.26] [3.74] [4.22] [3.77] [3.99] [3.03] Grantham’s quality (G2) 2.37 3.67 2.04 3.06 1.65 2.11 [2.82] [4.04] [3.47] [1.99] [2.60] [2.53] 0.07 2.49 0.67 1.95 -0.84 ROIC 3.86 [3.21] [0.63] [2.00] [-0.92] [1.46] [0.07] 1.52 1.94 2.07 Earnings quality (EQ) 1.36 2.23 1.46 [1.82] [2.78] [1.77] [1.66] [2.80] [2.39] 2.48 3.18 1.50 Piotroski’s F-score (F) 2.65 1.38 0.99 [1.03] [1.72] [2.87] [2.57] [1.34] [2.22] Defensive (D) 0.17 -0.39 0.11 1.60 -0.12 0.17 [0.12] [-0.28] [-0.09] [0.12] [0.08] [1.13] 2.31 4.75 3.04 4.01 2.81 2.39 Gross profitability (GP) [3.21] [2.62] [2.94] [3.68] [2.34] [4.48] This table shows alphas (percent per year) from five-factor t ime-series regressions of the form Notes: D ̨ C ˇ ; MKT C ˇ SMB C ˇ HML C ˇ UMD C ˇ x C y HML x UMD SMB MKT where y and x are the returns to a test strategy and an explanatory strateg y, and in each case these are both taken from the seven quality strategies. 17

18 Long-only investors Long-only investors face a fundamentally different invest ment problem than long/short in- rough leverage, which separates vestors. Unconstrained investors can control their risk th ncentrate solely on finding op- the opportunity and exposure decisions, allowing them to co portunities that provide the highest reward-to-risk ratio . Long-only investors do not have this luxury. They cannot separate the opportunity and expos ure decisions, so must evaluate risk and reward jointly, and may rationally choose to pass up an investment with a higher risk/reward tradeoff for an investment that allows them to g et greater exposure to another attractive opportunity with a lower risk/reward tradeoff. This is not merely a theoretical concern for long-only quali ty investors. Much, and sometimes all, of the observed quality strategy three-fact or alpha in Table 2 came from negative loadings on the Fama and French factors. In these ca ses the strategies do not raise expected returns, but simply provided an attractive hedge f or market investors with small cap and value tilts. The value of this hedge is only large if th e small cap and value tilts contribute significantly to the investors’ portfolio risk. Most of a well diversified, long-only equity investor’s risk comes from the market, how- versified, long-only strategies ever, not from tracking error relative to the market. Well di can only achieve modest size and value loadings. With small t racking errors even rela- tively tracking error reductions have little impact on port folio volatility. Adding quality to a value strategy can thus improve the strategy’s informat ion ratio while simultaneously reducing the strategy’s Sharpe ratio. If adding quality red uces the tracking error more than it reduces expected active return, then it improves the info rmation ratio, but if there is little associated reduction in portfolio volatility it lowers the Sharpe ratio. Combining value and quality portfolios Table 6 shows the stand-alone performance of the long-only q uality and traditional value strategies, which are just the long sides of the long/s hort strategies considered in Table 2. All of the quality strategies generate positive CAPM alph as, ranging from 0.03%/year for 18

19 Table 6: Long-only quality strategy performance Three-factor model regression results e EŒr ̨ Sort variable ̨ ˇ • ˇ ˇ SMB MKT HML CAPM Panel A: Value strategy 3.36 -0.72 1.01 0.18 Book-to-price 8.70 0.68 [3.15] [-1.34] [96.8] [12.4] [42.7] [3.77] Panel B: Quality strategies 5.66 0.03 0.26 0.98 -0.07 Graham’s G-score -0.02 [2.61] [1.34] [262.0] [-12.5] [-2.92] [0.14] 5.74 1.39 0.94 -0.12 -0.16 Grantham’s quality 0.25 [0.57] [4.02] [138.8] [-12.9] [-15.9] [2.67] ROIC 6.11 1.53 0.98 -0.08 -0.20 0.26 [0.49] [3.32] [109.1] [-6.12] [-14.8] [2.65] Earnings quality 6.13 0.22 0.78 1.00 -0.02 -0.10 [2.57] [0.30] [69.1] [-0.84] [-4.37] [1.06] 6.22 1.34 0.94 -0.08 -0.08 Piotroski’s F-score 0.77 [1.74] [3.15] [112.6] [-6.69] [-5.96] [2.91] Defensive 5.21 0.14 0.80 -0.16 0.22 0.99 [1.44] [0.25] [72.7] [-10.5] [13.0] [2.97] Gross profitability 7.10 1.44 2.74 0.94 -0.06 -0.22 [3.11] [2.03] [73.4] [-3.08] [-11.1] [4.17] nly gross profitability’s CAPM Graham’s strategy, to 1.44%/year for gross profitability. O e quality strategies do, however, alphas is statistically significant at the 5% level. All of th with the exception of the earnings quality and defensive str ategies, generate highly signifi- cant Fama and French three-factor alphas. Table 7 shows the performance of strategies that run quality side-by-side with value. The table shows the difficulties long-only investors face ex ploiting quality’s benefits. The table shows information ratio gains, but Sharpe ratio losse s. In every case, except for the earnings quality and defensive strategies, combining v alue and quality yields active returns relative to the market that have a better risk/rewar d trade-off than that provided by value alone (last line of Panel C). This results, however, fr om a dramatic decrease in the CAPM tracking error, coupled with a smaller decrease in the a verage active returns. Market exposure plus moderate exposure to the attractive opportun ity provided by the pure value 19

20 Table 7: Combining value and quality portfolios Specification (2) (3) (5) (6) (7) (8) (1) (4) Panel A: Portfolio weights (%) 100 50 50 Book-to-price 50 50 50 50 50 50 Graham’s G-score Grantham’s quality 50 ROIC 50 50 Earnings quality 50 Piotroski’s F-score 50 Defensive 50 Gross profitability Panel B: Portfolio performance 8.70 7.18 7.22 7.40 7.41 7.46 Average annual return 7.90 6.95 Volatility 16.2 15.2 15.0 15.4 15.7 15.0 13.9 15.2 Sharpe ratio 0.54 0.47 0.48 0.48 0.47 0.50 0.50 0.52 Panel C: Benchmarked performance CAPM alpha 1.69 1.80 1.81 1.79 2.06 2.18 2.40 3.36 7.46 3.63 3.22 3.31 4.25 3.77 5.13 3.52 Tracking error Information ratio 0.45 0.47 0.56 0.55 0.42 0.55 0.42 0.68 tilt turns out to be superior, in a Sharpe ratio sense, to mark et exposure plus a minimal 4 . exposure to the more attractive joint value and quality tilt Selecting stocks using value and quality Greenblatt (2006, ROIC), Piotroski and So (2012, the F-scor e) and Novy-Marx (2013, gross profitability) all consider strategies that combine v alue and quality to select stocks. These strategies, instead or running value and profitabilit y side-by-side, select stocks that look attractive on both the value and quality dimensions. Tr ading quality with value in this manner yields similar information ratio improvements to tr ading quality along side value, but generates these improvements primarily by increasing r ewards, as opposed to reducing 4 The 50/50 mixes are considered here because in every case exc ept gross profitability the long-only ex- post mean-variance efficient portfolio of value and each of t he quality strategies is fully invested in value. 20

21 risk. For example, Novy-Marx (2013) finds that a long/short s trategy based on combined y the 500 largest non-financial book-to-price and gross profitability ranks that trades onl firms earned excess returns of 7.4%/year from July 1963 to Dec ember 2011. This is signif- onstructed strategies trading icantly more than the 3.2 and 3.8%/year earned on similarly c on gross profitability or book-to-price alone, or the 3.5%/y ear one would have gotten trad- e strategy that selects stocks on ing the pure strategies side-by-side. This is because the th the basis of both profitability and valuations achieves larg er exposures to profitability and . If a stock has moderately high value than the strategy that runs profitability next to value o an investor attempting to get loadings on both factors, then the stock is more attractive t g on one factor but a low load- exposures to both factors than a stock with a very high loadin ing on the other. A 50/50 combination of pure factor strategi es will nevertheless ignore this stock, because it does not achieve a sufficiently high exposu re to either factor individually. The increase in tilts that results from buying stocks with hi gh combined exposures can be further illustrated with a simple example. Panel (a) of Fi gure 1 shows stocks’ loadings on two factors, assuming the loadings on each factor are norm ally distributed with mean zero, and uncorrelated across stocks. Panel (b) shows that t he portfolio that holds only ve loading on the first factor stocks with positive loadings on the first factor has a positi factor. Panel (c) shows similar (arbitrarily scaled to one), but a zero loading on the second ve loadings on the second factor. results for the portfolio that holds only stocks with positi factors (i.e., the portfolio that Panel (d) shows that a portfolio designed to tilt toward both holds stocks for which the sum of the loadings on the two facto rs in positive) achieves p 2=2 on each factor, 71% of the loading one could achieve on either loadings of only variable attenuation” that factor individually. Fama and French (2013) emphasize the “ occurs when one goes from selecting stocks on the basis of a si ngle predictive variable to selecting stocks on the basis of multiple predictors. In t heir words, “getting the average return benefits of an additional variable involves losing so me of the gains from the variables already in the mix.” The integrated solution, which selects stocks on the basis o f the combined factor sig- 21

22 Figure 1: Factor loadings from single and combined characte ristic sorts (b) Stocks with > 0 (a) All stocks ˇ 1 ! ! ˇ .1;0/ ; ˇ / . D .0;0/ . ˇ D ; ˇ / 2 1 1 2 (c) Stocks with ˇ > 0 > 0 (d) Stocks with ˇ ˇ C 1 2 2 ! ! p p 2=2/ ; ˇ / / D .0;1/ . ˇ 2=2; ; ˇ . ˇ D . 2 2 1 1 nals, achieves significantly higher factor loadings, howev er, than the portfolio solution. An investor that puts half of her money into each of two uncorrel ated pure factor strategies only tilts half way towards each. These tilts are much smalle r than the 0.71 loadings on each factor achieved by the combined sort. By selecting stoc ks directly to maximize both exposures, an investor is able to achieve combined factor lo adings that are 40% higher. The advantage of the integrated solution is even more pronou nced when the univariate 22

23 factor loadings are negatively correlated, such as value an d profitability. At first glance end to have high valuations, so this may be somewhat surprising. High profitability stocks t Fama and French’s (2013) variable attenuation problem is pa rticularly acute when adding alue stocks are not nearly as cheap profitability metrics to value signals. High profitability v as pure value stocks, so including profitability considerat ions results in a bigger reduction s, however, more than offset in value exposures. This attenuation in the value exposure i by gains in the profitability exposure. Portfolios selected purely on the basis of value sig- nals are significantly short profitability, so incorporatin g profitability considerations yields disproportionately large gains in the profitability dimens ion. Appendix B analyzes these oadings obtained by selecting effects in more detail, deriving predicted gains in factor l stocks on the basis of value and quality jointly, relative to those obtained by holding equal ue and quality characteristics are positions in pure value and quality strategies, when the val noisy signals of the true value and quality factor loadings. These results suggest that larger value and quality tilts ca n be achieved sorting on a combined quality and value signal than can be obtained runni ng value and quality strate- gies side-by-side, which should translate into higher acti ve returns. Table 8 shows the per- quality and value signals, the formance of the long-only strategies sorted on the combined average book-to-price and quality metric ranks, and confirm s this hypothesis. Panel A gives large cap results, and shows that combining valuations with ROIC, Piotroski’s F-score, or gross profitability, yields higher returns than using valua tion alone. In the case of gross profitability this improvement is almost 2%/year. In every c ase, with the exception of earn- ings quality, incorporating quality concerns leads to impr ovements in the Sharpe ratios and CAPM information ratios, though with the exception of gross profitability these improve- ments are quite marginal. Panel B gives small cap results, wh ere traditional value already delivered stellar performance over the sample, yielding a C APM alpha of 5.35%/year, and should consequently be difficult to beat. The table shows tha t while only incorporating gross profitability concerns actually yielded a strategy th at generated higher excess returns (12.3 vs. 11.7%/year), all of the joint quality and value str ategies with the exception of 23

24 Table 8: Long-only joint quality and value strategy perform ance Three-factor model regression results e Sort variable ̨ EŒr ̨ ˇ • ˇ ˇ SMB HML CAPM MKT Panel A: Large cap results (Russell 1000) 2.38 -0.78 -0.01 0.59 7.49 Traditional value 0.99 [-1.76] [114.1] [-1.01] [44.1] [3.47] [2.60] 1.89 -0.01 0.96 -0.04 0.36 Graham value 6.99 [-0.03] [22.3] [-2.78] [2.54] [3.34] [89.3] 6.90 1.01 0.89 -0.13 0.27 Grantham value 2.20 [3.13] [1.79] [80.8] [-8.35] [16.0] [3.57] 8.15 Magic formula 0.94 1.00 -0.01 0.33 2.75 [3.72] [1.61] [-0.65] [19.1] [3.71] [86.7] 1.77 -0.07 0.94 6.76 0.33 Sloan value 0.09 [0.13] [72.8] [-3.93] [17.0] [3.26] [2.18] 7.83 2.94 1.29 Piotroski and So -0.08 0.33 0.92 [3.80] [1.79] [65.1] [-4.00] [15.3] [3.41] 6.42 0.83 0.11 Cheap defensive -0.17 0.48 2.35 [2.43] [0.17] [65.4] [-9.44] [24.6] [3.51] Profitable value 9.20 3.68 1.70 1.00 0.08 0.33 [4.10] [4.86] [82.4] [4.92] [18.0] [2.75] Panel B: Small cap results (Russell 2000) Traditional value -0.74 1.07 0.87 0.79 11.7 5.31 [-1.18] [49.9] [3.19] [42.1] [3.96] [87.1] 11.8 0.67 0.98 0.78 0.65 Graham value 5.81 [3.88] [1.00] [4.32] [42.1] [32.9] [75.4] Grantham value 5.56 1.36 0.95 0.70 0.51 11.4 [4.21] [74.2] [4.40] [38.6] [26.3] [2.09] Magic formula 4.68 0.05 1.05 0.80 0.55 11.2 [3.83] [3.07] [0.06] [67.0] [36.2] [23.0] Sloan value 11.4 -0.59 1.09 0.85 0.67 4.76 [2.93] [71.6] [39.7] [28.8] [3.78] [-0.76] 11.7 5.64 0.75 Piotroski and So 0.76 0.62 1.00 [4.22] [3.70] [0.91] [62.5] [33.3] [25.2] Cheap defensive 10.0 5.15 0.63 0.83 0.58 0.61 [4.43] [0.92] [62.2] [30.6] [30.2] [3.99] Profitable value 12.3 5.73 1.19 1.03 0.89 0.50 [4.16] [3.67] [1.62] [71.8] [43.7] [23.0] 24

25 Figure 2: Long-only joint value and quality performance Performance of $1 (log scale), large cap strategies Profitable value Magic formula Traditional value $100 Large cap universe T−Bills $10 $1 2000 2005 2010 1975 1990 1995 1985 1970 1980 1965 p universe Worst cumulative underperformance relative to the large ca 0% −10% −20% −30% Profitable value Magic formula −40% Traditional value −50% 1995 2000 2005 1965 1970 1975 1980 1985 1990 2010 Performance of $1 (log scale), small cap strategies Profitable value $1,000 Piotroski and So Traditional value Small cap universe $100 T−Bills $10 $1 1990 1995 2000 2005 2010 1965 1970 1975 1980 1985 p universe Worst cumulative underperformance relative to the small ca 0% −10% −20% −30% Profitable value Piotroski and So −40% Traditional value −50% 1995 2000 2005 2010 1980 1975 1970 1965 1985 1990 25

26 those incorporating ROIC or earnings quality concerns had h igher Sharpe ratios, and higher CAPM information ratios, than traditional value. The top panel of Figure 2 shows the growth of a dollar invested at the end of June gy, and the two large cap joint 1963 in T-bills, the Russell 1000, the large cap value strate urns, those based on ROIC and value and quality strategies that generated the highest ret gross profitability. The second panel shows the value and joi nt value and quality strategies’ ive under-performance relative drawdowns relative to the large cap universe (i.e., cumulat to the benchmark). The third and fourth panel show similar re sults for small caps, using the two small cap joint value and quality strategies generat ing the highest returns, those based on Piotroski’s F-score and gross profitability. The mo st striking feature of the figure requencies Table 9: Growth of a dollar, drawdowns, and outperformance f Growth of $1 Max. drawdown One-year Five-year (value at end (% cumulative outperformance outperformance of sample, $) frequency (% ) underperformance) frequency (%) Panel A: Large cap strategies (benchmarked to Russell 1000) 111 Benchmark (R1000) 269 -43.0 55.7 67.5 Traditional value 218 -43.9 58.8 62.3 Graham value 226 -34.8 57.1 66.8 Grantham value Magic formula 364 -29.8 69.0 75.3 Sloan value 196 -41.2 58.9 57.4 Piotroski and So 335 60.8 71.2 -37.7 187 48.8 54.0 Cheap defensive -52.2 Profitable value 595 -18.9 72.2 81.3 Panel B: Small cap strategies (benchmarked to Russell 2000) Benchmark (R2000) 269 1,294 -36.9 65.3 72.2 Traditional value 1,561 -37.1 61.3 74.9 Graham value Grantham value 1,401 -38.1 62.1 73.9 Magic formula -48.6 63.8 64.8 1,022 Sloan value 1,055 -27.5 62.0 73.7 Piotroski and So 1,462 -40.6 66.8 75.3 Cheap defensive -55.4 53.5 55.4 870 Profitable value 1,690 -28.3 68.4 76.9 26

27 is the marked improvement in the drawdown performance that r esults in value strategies ides end of sample values for by incorporating gross profitability concerns. Table 9 prov a dollar invested in the start of the sample for all of the join t value and quality strategies, over the sample, and the as well as the largest drawdowns experienced by each of these frequencies with which these strategies outperform their b enchmarks at one- and five-year horizons. Conclusion Quality investing exploits another dimension of value. Val ue strategies endeavor to acquire productive capacity cheaply. Traditional value strategie s do this by buying assets at bar- gain prices; quality strategies do this by buying uncommonl y productive assets. Strategies bnormal returns, but the real based on either of value’s dimensions generate significant a benefits of value investing accrue to investors that pay atte ntion to both price and quality. Attention to quality, especially measured by gross profitab ility, helps traditional value in- vestors distinguish bargain stocks (i.e., those that are un dervalued) from value traps (i.e., those that are cheap for good reasons). Price signals help qu ality investors avoid good firms that are already fully priced. Trading on both signals b rings the double benefit of nd drawdowns. Cheap, profitable increasing expected returns while decreasing volatility a firms tend to outperform firms that are just cheap or just profit able. Quality tends to per- form best when traditional value suffers large drawdowns, a nd vice versa, so strategies that trade on both signals generate steadier returns than do stra tegies that trade on quality or price alone. These benefits are available to long-only inves tors as well as long/short in- vestors. Accounting for quality also significantly improve s the performance of strategies that incorporate momentum as well as price signals. Several practical considerations make joint quality and va lue strategies look even more attractive. The signal in gross profitability is extremely p ersistent—even more persistent than that in valuations—and works well in the large cap unive rse. Joint quality and value strategies thus have low turnover, and can be implemented us ing liquid stocks with the ca- 27

28 pacity to absorb large trades. The joint profitability and va lue signal is also less susceptible k returns. Both the value and to industry biases that are uninformative about future stoc na, reducing the informativeness profitability premiums are largely intra-industry phenome of simple, univariate measures of value and profitability. T his is less of a problem for strate- ause industry capital intensity gies that trade on the combined quality and value signal. Bec k values in the numerator) but is positively correlated with value signals (which have boo negatively correlated with profitability signals (which ha ve book values in the denomina- tor), systematic industry variation in the value and qualit y metrics tend to cancel in the joint signal. Joint quality and value strategies can thus be imple mented effectively while paying less attention to industry controls. ly traditional value investors, The basic message is that investors, in general but especial leave money on the table when they ignore the quality dimensi on of value. All of the best known notions of quality contribute, at least marginally, t o investment performance. Gross profitability generally contributes the most, however, esp ecially among large caps stocks and for long-only investors, and largely subsumes the power of other notions of quality. Keywords: Value Investing, Quality Investing, Gross Profitability, G ARP, Asset Pricing. 28

29 Appendix A: Variable Definitions Variables employed in this paper are constructed primarily from Compustat data, which calendar year following that is assumed to be publically available by the end of June in the in which each firms’ fiscal year ends. Detailed definitions, as well as the Compustat data iven below. items employed in the construction of these variables, are g  Book equity scaled by market equity, where market equity is Book-to-price (B/P): lagged six months in the strategies that do not trade momentu m to avoid taking un- der equity, plus deferred intentional positions in momentum. Book equity is sharehol nents of shareholder taxes, minus preferred stock, when available. For the compo those used by Fama and equity, I employ tiered definitions largely consistent with French (1993) to construct their high minus low factor (HML) . Stockholders equity is as given in Compustat (SEQ) if available, or else common eq uity plus the carry- ing value of preferred stock (CEQ + PSTX) if available, or els e total assets minus total liabilities (AT - LT). Deferred taxes is deferred taxe s and investment tax credits (TXDITC) if available, or else deferred taxes and/or invest ment tax credit (TXDB and/or ITCB). Preferred stock is redemption value (PSTKR) i f available, or else liq- e (PSTK). uidating value (PSTKRL) if available, or else carrying valu Earnings-to-price (E/P): Net income (NI) scaled by market equity.   Earnings before interest and taxes (EBIT) scaled by enterpr ise Earnings yield (EY): value (EV). Enterprise value is market equity, plus long ter m debt (DLTT), plus debt in current liabilities (DLC), plus preferred stock (as defin ed above), minus cash and short term investments (CHE). Graham G-score: The G-score gets one point if current assets (ACT) exceeds tw ice  current liabilities (LCT) , one point if net current assets ( WCAP) exceed long term debt (DLTT), one point if net earnings have been positive eac h of the last ten years, one point if dividends plus buy-backs have been positive eac h of the last ten years, and one point if current earnings per share are at least 33% hi gher than 10 years ago. 29

30  Grantham quality rank: Average ranks of returns-on-equity (ROE), asset-to-book to-book equity. ROE equity, and the inverse of ROE volatility. ROE is net income- volatility is the standard deviation of ROE over the precedi ng five years. EBIT-to-tangible capital, where tangible capi- Return on invested capital (ROIC):  pital (WCAP). tal is property, plant and equipment (PPEGT) plus working ca Measured as the year-over-year change in current assets (AC T)  Sloan’s accruals: hange in long term lia- excluding cash and short term liabilities (CHE), minus the c bilities (LCT) excluding debt in current liabilities (LCT) and income taxes payable (TXP), minus the depreciation and amortization (DPC). Foll owing Sloan (1996), ac- ets lagged one year. cruals are scaled by the average of total assets and total ass Piotroski’s F-score:  Constructed as the sum of nine binary variables that take the th). The F-score can get value zero (indicating weakness) or one (indicating streng ve earnings before extraor- gets one point for each of four profitability signals [positi dinary items (IB), positive cash flows from operations (OANC F), increasing returns- d negative accruals]; one on-assets (IB/AT that exceeds that of the previous year), an point for each of three liquidity signals [decreasing debt, increasing current ratio, and no equity issuance]; and one point for each of two efficien cy signals [increas- ing gross margins (revenues (REVT) minus cost of goods sold ( COGS) scaled by revenues) and increasing asset turnover (revenues scaled b y assets)].  Gross profits-to-assets (GP/A): Revenues minus cost of goods sold (REVT - COGS) scaled by total book assets (AT). Appendix B: Factor loadings from selecting stocks on value a nd quality oss stocks and normally Suppose stocks’ exposures to two factors are correlated acr j to factor i 2 distributed. That is, suppose the exposure of stock is distributed .1; 2/ 2 ˇ  N.0;  .ˇ  / and corr . Suppose further that these loadings are not di- D ; ˇ / ij 2j 1j ˇ rectly observable, but investors see publicly available si gnals S , where the D ˇ  C ij ij ij 30

31 2 / are normally distributed noise independent across stocks a nd factors. De-   N.0;  ij  2 2 2 . Then the D   C , where  fine  = z as the z-scores for the signals S S ij ij ij S  ˇ S of a portfolio that holds the fraction of stocks with the highest signal i loading on factor ̨ for that factor is     1 1 .1 z ̨/ > N D  ̨/ E ˇ ˇ = .1 j z E > N j ij ij S ij ij S !  2 1  N . ̨/ n ˇ D ;  ̨ S n.  / and N.  / are the standard normal probability density function and cu mula- where quality follows from the facts that tive distribution function, respectively, and the second e   2 2 = ˇ = contributes a fraction  of the total variance of z > x and E D z z j ij ij ij ij S ˇ S x/=N. x/ for any x . The portfolio also has a loading  n. times as large on the other of the individual factor signals factor, so a 50/50 mix of the portfolios selected on the basis C /=2 times as large on each factor. had loadings .1 i of a portfolio that holds the fraction ̨ of stocks with the highest The loading on factor combined z-scores is # "   ˇ ˇ  z C z ˇ ˇ z C z C S C S 1j ˇ 2j 1j 1j 2j 2j ˇ 1 1 2 1 > N .1 ̨/ > N E ̨/ D .1 ˇ E ˇ ˇ ij  2   C z z z C z 2 1 2 1 S S C 1 2 !  2 1  n . ̨/ N C ˇ ˇ 1 1 D  ̨ S S C 1 2 !  2 1  . ̨/ n N C  1 ˇ r D ;    ̨ S 2 2 =  C 1 2 ˇ S from the fact that .ˇ C where the first equality follows from symmetry and the second 1j 2 2 of the total variance of z C z . =  contributes a fraction ˇ /= 1j 2j 2j C S S ˇ ˇ C C S S 1 2 2 1 2 1 The ratio of the factor loadings of the portfolio that trades on the combined signal to 31

32 2 signal−to−noise = 1 signal−to−noise = 1/2 1.9 signal−to−noise = 1/3 1.8 1.7 1.6 1.5 Loading ratio 1.4 1.3 1.2 1.1 1 1 −1 −0.2 −0.6 0 0.2 0.4 −0.4 0.6 0.8 −0.8 ρ ) Correlation between factor loadings ( Factor loadings from integrated solution, relative to thos Figure 3: e from portfolio solution. the portfolio that holds a 50/50 mix of the portfolios that tr ade on the pure signals is thus s 2 : 2 2  1 = C ˇ S This is bounded from below be one, so there are always gains to trading on the combined  , so it is less important to trade on the combined characteristic, but a decreasing function of p characteristic when the factors are more correlated. It als o tends toward 2=.1 C / when the factor loadings are directly observable (i.e., when  ), and tends toward D 0 , so S D ˇ  p 2 as the signal becomes uninformative regarding factor loadi ngs (i.e., as  = ! 0 ). ˇ  This ratio is shown in Figure 3 as a function of  , the correlation in the true factor 32

33 Table 10: Performance of long/short joint value and quality strategies Four-factor model regression results Quality measure e ̨ ˇ ̨ ˇ • ˇ EŒr ˇ FF 4 used with B/M VMG SMB MKT SMI -1.54 0 0 0 1 0 None 3.49 [-2.27] [2.33] Graham value 0.07 -0.07 -0.19 0.69 0.61 2.17 0.58 [1.43] [-5.93] [-11.4] [39.8] [21.1] [0.71] [1.64] 2.79 Grantham value 0.08 -0.08 0.00 0.74 0.52 2.35 [2.13] [1.60] [-5.83] [0.26] [37.6] [21.3] [2.63] 5.74 0.17 -0.04 0.15 0.67 0.48 Magic formula 3.31 [2.84] [2.50] [-2.27] [5.84] [29.0] [23.4] [3.82] Sloan value 3.09 -0.00 -0.01 0.01 0.76 0.45 -0.21 [-0.21] [-0.04] [-1.26] [0.41] [46.1] [21.5] [2.13] Piotroski and So 3.50 0.59 -0.00 -0.01 -0.03 0.77 0.45 [2.36] [0.58] [-0.83] [-1.48] [35.0] [16.7] [-0.04] 1.32 0.03 -0.11 0.01 0.67 0.47 Cheap defensive 0.85 [0.76] [0.42] [-6.00] [0.53] [32.5] [26.5] [0.61] 6.55 3.66 0.09 -0.04 0.26 0.82 0.75 Profitable value [3.62] [4.98] [-3.16] [14.0] [36.0] [28.6] [1.63] Notes: This table shows alphas (percent per year) from four-factor time-series regressions of the form y D ̨ C ˇ ; MKT C ˇ C SMB C ˇ SMI VMG C ˇ SMI MKT SMB VMG y is formed on the basis of average value and quality ranks, and the the explanatory where the test strategy ality strategies, VMG (value-minus-growth) and strategies include similarly constructed pure value and qu SMI (superior-minus-inferior), respectively. 2 2 ) of one, 1/2, and 1/3 (solid, dashed, and dotted loadings, for signal-to-noise ratios ( =   ˇ lines, respectively). The figure shows that the magnitude of the increase in the tilts that can be obtained by selecting stocks on the basis of the combin ed signals is greater when the true factor loadings are negatively correlated, and tha t the impact of the correlation is increasing in the quality of the signal. Whenever the true fa ctor correlation in negative, however, the tilts that can be obtained by combining the sign als is at least 40% higher than those that can be obtained by combining the pure strategy por tfolios. Table 10 shows empirical results consistent with this predi ction. The table shows the performance of long/short strategies formed on the basis of joint value and quality signals, 33

34 and these strategies loadings on pure value and quality stra tegies (controlling for market and ality loading is 0.53. The SMB loadings). The mean value loading is 0.73, and the mean qu total loadings on value and quality thus average 1.27, 27% hi gher than the total loadings one would get by trading a 50/50 mix of the pure quality and val ue strategies side-by-side. One could somewhat mitigate these differences by holding mo re concentrated pure fac- e portfolios sorted on the indi- tor portfolios. If one holds only half as many positions in th ce as many positions (though vidual signals, on the theory that the 50/50 mix will hold twi of course some positions will be common across the two strate gies), the ratio becomes v  u 1 . ̨/ N n 1 u   : t 1 2 . ̨=2// n.N 2 C 2 1  = ˇ S ve negatively correlated load- This ratio is still always bigger than one for factors that ha ings across stocks when portfolios hold less than about 40% o f stocks. This suggests that even with highly diversified portfolios investors can obtai n larger tilts toward value and profitability selecting stocks on the basis of valuations an d profitability metrics jointly than they can with an equally well diversified combination of pure value and profitability strate- gies. This difference is more pronounced for more concentra ted strategies. 34

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