Fundamentals of Value versus Growth Investing and an Explanation for the Value Trap

Value stocks earn higher returns than growth stocks on average, but a “value” position can turn against the investor. Fundamental analysis can explain this so-called value trap: The investor may be buying earnings growth that is risky. Both the earnings-to-price ratio (E/P) and the book-to-price ratio (B/P) come into play. E/P indicates expected earnings growth, but price in that ratio also discounts for the risk to that growth; B/P indicates that risk. A striking finding emerges: For a given E/P, a high B/P (“value”) indicates higher expected earnings growth—but growth that is risky. This finding contrasts with the standard convention that considers a low B/P to be “growth” with lower risk. A practitioner's perspective on this article is provided in the In Practice piece "Explaining Value vs. Growth Investing through Accounting Fundamentals" by Keyur Patel. Disclosure: The authors report no conflicts of interest. Editor’s Note This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the authors thanked the reviewers in their acknowledgments. Clifford S. Asness was one of the reviewers for this article. Submitted 12 December 2017 Accepted 23 July 2018 by Stephen J. Brown

"Value" and "growth" are prominent labels in the lexicon of finance.They refer to investing styles that buy companies with low multiples (value) versus high multiples (growth), though the labels sometimes simply refer to buying stocks with low price-to-book ratios (P/Bs) versus high P/Bs.Value is sometimes taken to indicate a "cheap" stock, and history shows that value outperforms growth on average.However, a value position can turn against the investor, and therein lies the "value trap."Indeed, experience with value stocks in the last few years has been disappointing.Despite the prominence of these styles, it is not clear what one is buying with value and growth stocks, and the labels are not particularly illuminating.
This article provides an understanding of these stocks in terms of the underlying fundamentals. 1When one buys a stock, one buys future earnings.Accordingly, price multiples imbed expectations of earnings growth; indeed, it is well recognized that the earnings-to-price ratio (E/P)-or, alternatively, the price-to-earnings ratio (P/E)-indicates the market's expectation of future earnings growth.However, less well recognized is that growth can be risky-it may not be realized-so price (in the E/P) discounts for that risk.Understanding the exposure to this risk is thus key for an investor buying growth in an E/P.In this article, we show that the book-to-price ratio (B/P) indicates not only growth but also the risk in buying that growth: For a given E/P, a high B/P indicates a higher likelihood that growth will not be realized.A high-B/P stock might look cheap, but it could be a trap.
A unifying theme underlies the analysis: Pricing ratios, such as E/P and B/P, involve accounting numbers; given price, they are accounting phenomena, a construction of the accounting involved.Thus, one understands the risk in buying E/P and B/P by understanding the accounting that generates earnings and book value.These accounting principles, involving the realization principle and conservative accounting for investment, are familiar to students of basic accounting Value stocks earn higher returns than growth stocks on average, but a "value" position can turn against the investor.Fundamental analysis can explain this so-called value trap: The investor may be buying earnings growth that is risky.Both the earnings-to-price ratio (E/P) and the book-to-price ratio (B/P) come into play.E/P indicates expected earnings growth, but price in that ratio also discounts for the risk to that growth; B/P indicates that risk.A striking finding emerges: For a given E/P, a high B/P ("value") indicates higher expected earnings growth-but growth that is risky.This finding contrasts with the standard convention that considers a low B/P to be "growth" with lower risk.
courses.This article applies them to understanding investment risk.
Three points emerge from our study.First, E/P and B/P are multiples to be used together.Just as earnings and book value-the "bottom line" numbers in the income statement and the balance sheet-articulate in an accounting sense, E/P and B/P articulate to convey risk and the expected return for that risk.Second, when applied jointly with E/P, high B/P-a value stock-indicates higher future earnings growth.This is surprising, because the standard labeling implies that it is "growth" (a low B/P) that buys growth, not "value."Third, the higher growth associated with high B/P is risky: High-B/P stocks are subject to more extreme shocks to growth.These are empirical findings, but our study demonstrates that they are also properties implied by the accounting for earnings and book value.
Our analysis explains some puzzling features observed in value versus growth investing-why buying B/P predicts returns for small companies but not large companies and why for large companies E/P dominates B/P in predicting returns.These differences are explained by relative exposure to growth at risk, an exposure indicated by the accounting fundamentals.Indeed, returns to investing by company size can be explained by exposure to risky growth.
We are, of course, not the first to associate the value-growth spread with fundamentals.For example, Fama and French (1995) showed that high B/P is associated with low profitability, and Cohen, Polk, and Vuolteenaho (2009) and Campbell, Polk, and Vuolteenaho (2010) calibrated the risk with fundamental ("cash flow") betas. 2 The aim here is not just to add more evidence of the risk in value stocks.Rather, it is to explain why: We show why value connects to low profitability and why that connection implies the risky outcomes documented in these papers.
First, we document the historical returns to value versus growth investing-returns that the subsequent analysis will explain.

Returns to Value vs. Growth Investing
Panel A of Table 1 reports the average annual returns to investing on the basis of E/P and B/P over 1963-2015.The sample covers all companies in the Compustat database at any time during that period, except financial companies (SIC codes 6000-6999), companies with negative book values, and companies with per share stock prices less than $0.20.Earnings and book value of common equity are from Compustat.Prices for the multiples are those three months after fiscal year-end, at which time accounting numbers for the fiscal year should have been reported (as required by law).As with earnings and book value, prices are per share, adjusted for stock splits and stock dividends over the three months after fiscal year-end.Annual returns are observed over the 12 months after this date, calculated as buyand-hold returns from monthly returns in the CRSP database with an accommodation for companies not surviving the full 12 months.A total of 176,848 company-year observations are involved. 3  Table 1 was constructed as follows.For each year, companies were ranked on their E/Ps and sorted into five portfolios from low to high E/P (along the top row in the panels).Then, within each E/P portfolio, companies were ranked on their B/P and sorted into five portfolios (down the columns).This nested sort ensured that the B/P sort is for companies with a similar portfolio E/P.E/P Portfolio 1 consists solely of loss companies. 4  The first row in Panel A reports equally weighted returns (before transaction costs) for E/P portfolios before ranking on B/P.E/P ranks returns and does so monotonically for (positive) E/P Portfolios 2-5, which is well-known and is documented, for example, in Basu (1977Basu ( , 1983) ) and Jaffe, Keim, and Westerfield (1989).Further, for a given E/P, B/P ranks returns (down columns): The "book-to-price" effect in stock returns is evident, but now for stocks with a given E/P.The mean return spread between the 1.9% return for the low-E/P and low-B/P portfolio and the 27.1% return for the high-E/P and high-B/P portfolio in Panel A is quite impressive.
The results for value-weighted portfolio returns in Panel B are similar, though there is less of a return spread over the E/P and B/P spread.We report these returns with the understanding that investors often work with value-weighted portfolios to avoid weighting small companies too heavily.However, these returns somewhat dampen those from investing on the basis of E/P and B/P because, as in Fama and French (2012), we have implicitly confirmed that the book-to-price "value" effect is much reduced in large companies.Thus, weighting toward large market capitalization moves away from the effect For Personal Use Only.Not for Distribution.
under investigation, which highlights a point that we will return to later.This strategy has presumably been trawled many times by value-growth investors, though not always with this structure.What explains the spread?The spread looks too large to be a "free lunch"; there is just too much money left on the table for a very simple strategy.It presumably cannot be explained by transaction costs.Does the return spread reflect differences for bearing risk, a trap to fall into?
Connecting E/P and B/P to Growth and Risk: The Accounting Given price, E/P and B/P are accounting phenomena; that is, they depend on how earnings and book value are measured.Thus, if E/P and B/P indicate risk, it may have something to do with the accounting.
To illustrate, consider the B/P for two investment funds, a ("risk-free") money market fund holding US government securities and a (risky) equity hedge Note: This table presents average annual percentage returns for portfolios formed by ranking companies each year on E/P and then ranking on B/P within each E/P portfolio; t-statistics are tests for significant differences between the means for high and low portfolios and are calculated as the mean annual difference relative to the standard error calculated from the time series of return differences.
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Fourth Quarter 2018 fund.In both cases, B/P = 1, even though the two funds have different risk.This, of course, is the result of mark-to-market accounting (strictly, fair value accounting) that yields a net asset value on which investors can trade (in and out of the fund).B/P does not differentiate risk: Fair value accounting takes away the ability to do so.However, for non-investment companies, so-called historical cost accounting is applied so that B/P ≠ 1 (and usually is less than 1).Does the accounting for B/P indicate risk and expected return in this case?
A standard pricing formula sets up the answer to this question.For positive earnings, P r g where P 0 is the current price, Earnings 1 is forward (one-year-ahead) earnings, r is the required return for the risk borne, and g is the expected earnings growth after the forward year (r and g are constants here just for simplicity). 5The forward E/P is thus This expression shows that the forward E/P is increasing in the required return and decreasing in expected growth (as is well recognized).Growth is typically seen as decreasing E/P (and increasing P/E), and indeed, Equation 1a shows that this is so for a given required return: Higher expected growth means a higher price and a lower E/P.But what if buying that growth were risky?Then more growth would mean a higher required return, r.The effect of growth would go into r rather than the price, yielding a higher E/P to the extent that r increases more than g.Indeed, if r increased with g, one for one, then increased growth expectations would not affect the E/P.
Here is the point: In the determination of price in Equation 1, earnings are capitalized at the rate r -g.
A given E/P indicates the difference between r and g, so the investor observing an E/P is confronted with the question of whether the E/P is due to risk or to expected growth.So, a given E/P = r -g could indicate risk with no expected growth (g = 0), high growth with high risk (high g and high r), or low growth with low risk (low g and r).Clearly, there is some sorting out to do.The value investor buying a high-E/P stock could just be loading up on risk: That stock might not be a low-growth stock at all but, rather, a stock with high but risky growth.Such a stock would be labeled a value stock because it looks cheap, but it may be a value trap.
It is not difficult to accept that buying earnings growth might be risky: A company with high growth prospects ("growth options") is typically considered risky.However, accounting principles also come into play, which introduces B/P.Dividing Equation 1a through by Earnings 1 /Book value 0 , B/P is given by

Book value
Book value Earnings Earnings Book value ( This equation expresses B/P as the product of E/P and the (inverse of the) book return on equity, ROE 1 = Earnings 1 /B 0 .It also establishes conditions under which B/P indicates growth and the risk (and the required return) associated with growth, r and g.For a given E/P and thus a given r -g, the following statements can be made: 1. B/P is determined by the (inverse of) ROE; a lower ROE implies a higher B/P.

2.
A higher B/P is associated with a higher g if a lower ROE is associated with a higher g-that is, if a lower ROE implies higher future growth expectations.
3. If a higher B/P is associated with a higher g, a higher B/P is also associated with a higher r (with r -g unchanged for a given E/P).
In total, the three properties state that for a given E/P, B/P is positively related to both expected earnings growth and the required return for risk, r and g, if ROE is negatively associated with these features.Property 1 is just simple math, stating that for a given r -g, B/P is determined by ROE.But Properties 2 and 3 are conditional statements: If a lower ROE 1 implies higher future earnings growth, then B/P is increasing in growth and the required return.This "realization" principle, taught in any Accounting 101 class, instructs the accountant to book earnings only when the risk of actually "earning" expected earnings is largely resolved.In terms of asset pricing theory, the accountant does not recognize earnings until the company can book a low-beta asset, usually cash or a near-cash receivable.Delaying earnings recognition means more earnings in the future-that is, earnings growth.So, an expectation of future earnings that awaits "realization" is an expectation of earnings growth, and because that realization is tied to risk resolution, the expected growth is risky: It may not be realized. 6The principle potentially bears on r and g in Equations 1 and 2.
The principle is an application of so-called conservative accounting, an apt term for dealing with risk.It has its expression in recognizing revenue only when a customer has been "sold," agreeing to a legally binding contract, and even then, only if "receipt of cash is reasonably certain."(Dear reader: We hope your Accounting 101 is coming back to you!) So, expected revenues from the prospect of future customers are not booked, even though the expectation is appropriately incorporated in the stock price.Accountants see value from prospective customers as risky-the value may not be realized-and thus it is not unreasonable to conjecture that price, P 0 , in Equations 1 and 2 is also discounted for that risk.Even the receivables from actual sales are discounted (in allowances for credit losses) for the risk of not receiving cash from the sales.
Earnings are revenue minus expenses, and this conservative accounting is reinforced by the accounting for expenses: Investments that otherwise would be booked to the balance sheet are expensed on the income statement when the outcome from the investment is particularly uncertain.Doing so reduces current earnings but increases expected future earnings, because now there is the prospect of future revenues from the investment but no amortization of the cost of the investment against those future revenues.And on a lower current earnings base, there is higher expected growth.R&D investment is the typical example: It may not produce salable products (let alone customers), so it is particularly risky and expensed immediately. 7But the accounting treatment goes well beyond R&D.The same expensing of investment against earnings applies to brand building (advertising to gain future revenue), organization and store opening costs, investment in employee training, software development, and investments in distribution and supply chains-often buried in the amorphous "selling, general, and administrative expenses," or SG&A, account.This accounting lowers current earnings, but the investment produces future earnings growth if the earnings from the risky investments are realized.The "if" implies risk. 8 This brings a different perspective to the g in Equation 1a.We often think of growth abstractly, with terms like "organic growth" and "economic growth."But expected growth is an accounting phenomenon, induced by how one accounts for earnings and book value.With mark-to-market accounting, there can be no expected growth: Growth that might otherwise be expected is capitalized into the book value, as it is in price (and B/P = 1).Growth comes only with delayed recognition of earnings, and accounting principles that induce this delay tie the growth to risk.If investors price the growth as risky, the growth affects r.

But how does B/P come into play?
Conservative accounting reduces earnings in the E/P, but those earnings are also the numerator of ROE, so the accounting also reduces ROE, the relevant fundamental in Equation 2. That ties ROE to growth: The conditional if in Property 2 is satisfied by accounting principles.Thus, B/P is positively related to expected growth by the mathematical Property 1. Further, according to Property 3, B/P also indicates the required return if the risk that growth may not be realized is priced.In buying a high-B/P "value" stock, an investor takes on this risk.
There is a flip side to conservative accounting that further connects ROE to growth and risk: If the deferred For Personal Use Only.Not for Distribution.
cfapubs.org Fourth Quarter 2018 earnings are recognized when risk is resolved, ROE is higher.Earnings (in the numerator of ROE) are higher, not only because earnings have been realized but also because there are no depreciation or amortization charges against that revenue; the investments were written off.Further, the earlier expensing of the investments means that book values in the denominator of ROE are lower; the assets generating the earnings are missing from the balance sheet.Thus, with higher realized earnings on a lower book value base, ROE is particularly high.A high ROE thus indicates risk that has been resolved. 9And for a given E/P, B/P is correspondingly lower, according to Equation 2.
In sum, for a given E/P, a low ROE because of conservative accounting implies higher growth and risk, and a high ROE results from earnings (growth) being realized and a lowering of risk.And according to Equation 2, B/P distinguishes whether a given E/P (= r -g) is one with high r and high g or with low r and low g.Properties 2 and 3 stand as a matter of accounting principles.

Some Case Studies
. This growth rate accommodates small and negative denominators and ranges between 2 and -2.For each portfolio in each year of the sample period, the median two-yearahead realized growth rate was calculated, and the annual mean is reported in the table.
For Personal Use Only.Not for Distribution.future growth for a given E/P?And regarding the issue at hand, is B/P positively correlated with future growth for a given E/P?For a Given E/P, B/P Is Positively Associated with Subsequent Earnings Growth at Risk.Property 3 connects B/P to both growth and risk.Tables 3 and 4 report that the portfolios in Table 1 and 2 are associated not only with expected growth but also with the risk that the growth may not be realized.They validate not only that accounting principles connect ROE to growth but also that buying that growth also comes with risk.
Table 3 shows that the E/P-B/P sort of Tables 1 and  2 is also a sort on the variation in earnings outcomes.
For each portfolio, Panels A and B report the standard deviation and interdecile range (IDR) of realized earnings one year ahead (relative to price).Panels C and D report the same statistics for realized earnings growth rates two years ahead.The IDR, the 90th percentile minus the 10th percentile of realizations, focuses on extreme (tail) realizations, a risk the investor is particularly concerned about.Both the standard deviation and the IDR are calculated from the time series of earnings outcomes for portfolios over the sample period.
There is some variation in the volatility of earnings outcomes across E/P portfolios (across the top row in the panels), mainly owing to significantly high volatility in the negative E/P portfolio, Portfolio 1. Regarding the issue at hand, however, both the standard deviation and the IDR increase over B/P for a given E/P (down columns): A higher B/P indicates that one is buying riskier forward earnings and subsequent earnings growth, more so for the earnings growth rates.This is so for all levels of E/P, including high E/P (value) and low E/P (growth).It also is so for negative E/P (loss) companies, which are often associated with particularly strong expensing of investment.
To connect the variance of growth rates to that of stock returns, we calculated the correlation between the standard deviation of earnings growth rates for the B/P portfolios (down columns in Panel C) and the standard deviation of returns in the same year as the growth realizations.These correlations are reported at the bottom of Panel C. The variance of realized returns is associated with the variance of realized growth rates.The correlation across the whole spread on E/P-B/P portfolios is 0.69. 17 In short, B/P indicates not only expected growth (in Table 2) but also the variance around that expectation.In terms of Equation 1a, B/P indicates whether a given E/P is one with high growth and risk or low growth and risk.The finding for the interdecile range is pertinent, for therein is the trap the investor is particularly concerned about: B/P indicates a higher chance of a high-growth outcome but also a higher chance of growth falling in the lower tail.The reward to that risk shows up in the return spread in Table 1.
Under asset pricing theory, risk is priced only if it pertains to sensitivity to risk that cannot be diversified away.So, risk to earnings is associated with shocks to marketwide earnings.Accordingly, Table 4 reports earnings betas from estimating the following regression for each portfolio: The regression is estimated in time series over all years, t, in the sample period.The earnings realizations are for the forward year-that is, the same year during which portfolio returns are observed in Table 1-so the betas are not historical betas but those experienced during the holding period.To align realizations in calendar time, the regression is estimated for companies with 31 December fiscal years only.The portfolio earnings yield is the mean for the portfolio, and the marketwide earnings yield is the For Personal Use Only.Not for Distribution.aggregate earnings for all companies in the sample in that year relative to aggregate price at the beginning of the period. 18  The betas in Panel A of Table 4 are increasing in B/P for a given E/P portfolio.The average R 2 for the regressions is 60.7%, which indicates that marketwide earnings explain a significant part of portfolio earnings.Separating years in which the marketwide earnings yield was higher than in the previous year (up markets) from years when it was lower (down markets), the conditional betas in Panels B and C indicate that higher-B/P portfolios have higher up-market betas-delivering higher earnings in good times-but also higher down-market betas, a trap that is compensated with higher upside potential.Correspondingly, low-B/P portfolios have considerably lower betas in down markets, but their upside betas are also lower.In sum, the variation in earnings outcomes across B/P portfolios in Table 4 is due, in part, to economy-wide shocks. 19  If the market prices the fundamental risk documented in these tables, the spread of average portfolio returns in Table 1 can be interpreted as reward for bearing that risk.Of course, the returns in Table 1 represent reward for risk only if the market prices risk efficiently.They could be abnormal returns (alpha) because the market does not price the earnings growth appropriately.We take no stand on this; we (collectively) do not have a generally accepted asset pricing model that delivers an expected return benchmark.But for those inclined to see the returns as alpha, the analysis brings caveat emptor into play: In trolling for alpha, you are taking on risk, and you may be falling into a value trap.
One might suggest that the return spreads in Table 1 are just too large to be explained by risk.But the period covered, 1963-2015, was one of significant corporate earnings growth and a bull market in stocks.Buying growth is risky, but in this happy period, the bet paid off handsomely; it was, after all, the "American Century."Koijen, Lustig, and Van Nieuwerburg (2017) showed that value pays off when economic activity increases, and that appears to be the case here.Results are similar over 10-year subperiods during 1963-2015.
The trap is there, however, as the correlations between the variation in realized growth rates and variation in returns in Panel C of Notes: This table documents the fundamental risk that an investor faces in investing in the portfolios in Table 1.Panels A and B report the standard deviation and interdecile range of realized portfolio earnings one year ahead (relative to the current price), calculated from the time series of portfolio earnings over the sample period.Panels C and D report the same statistics for realized earnings growth rates two years ahead.Earnings growth rates are calculated as in Table 2.

Company Size and Value vs. Growth Investing
In Table 1, the return spreads for value-weighted returns are lower than those for equally weighted returns, suggesting that the phenomena that we have documented are stronger in small companies than in large companies.That makes sense.Small companies are more likely to be growth prospects, but with growth that is at risk: Consider the biotech startup investing in R&D with little revenue against the mature pharmaceutical company with a product line realizing earnings from past R&D.Several papers-including Loughran (1997); Asness, Frazzini, Israel, and Moskowitz (2015); and Kok, Ribando, and Sloan (2017)-have documented that the book-toprice premium is absent from large-cap stocks.Is this because large companies are those with lower growth prospects with less risk?
Figure 1 suggests so.It depicts the difference between high-and low-B/P portfolio returns within the five E/P groups in Table 1-but now differentiated by size.Small companies are the smallest 30% by market cap, large companies the highest 30%, and medium companies the rest.There are some differences in return spreads across E/P portfolios, but for a given E/P, the return spread between highand low-B/P portfolios is decreasing in company size.The B/P return spread is negligible for large companies in all E/P portfolios (and similar to that for small companies in the high-E/P portfolio).The same pattern holds for 10-year subperiods between 1963 and 2015.Notes: This table reports returns for the same portfolios as in Table 1 but for the 2 years with the lowest market returns in the last 10 years of the sample period.In 2015 and 2008, the S&P 500 returned 1.38% and -37.0%, respectively.
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Weights are fitted using the Theil-Sen robust estimator; that is, the weights are the median values of w 1 and w 2 from fitting for all possible combinations of observations within the portfolio for each year, with the reported weights being the mean over years.
The mean weights on E/P increase with company size.
average.That accords with the observations in other papers that the book-to-price premium is absent in large-cap stocks.However, we provide an explanation: B/P plays no role (incremental to E/P) when there is little expected growth at risk.As Table 6 moves through medium cap to small cap (from right to left in the table), the weight shifts from E/P to B/P.Smaller companies are likely to have higher risky growth, and that must be weighed in.Indeed, the table also reports that the mean realized earnings growth two years ahead (t + 2) is decreasing in company size, as are the other metrics reported in Table 3 that indicate risk around mean growth, the standard deviation and the IDR of earning growth rates: Smaller companies have not only higher expected growth but also growth more likely to considerably deviate from expectation.Notes: This figure reports Table 1 returns by company size.Within each E/P portfolio in that table, the high -low return spread for B/P is depicted for three size portfolios.Small companies are the lowest 30% by market capitalization, and large companies are the highest 30%.
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cfapubs.org Fourth Quarter 2018 earnings growth beta, which measures the sensitivity of earnings growth to variation in marketwide growth rates.These betas, too, are decreasing in company size.The mean and median ROEs in the table are increasing in size and are also negatively correlated with growth and the variability of growth realizations-as expected under the accounting principles.
These findings raise the specter that the so-called size effect in returns is really a discount to price for expected growth that may not be realized, not a "factor" separate from B/P.

(Mis)Labeling Value and Growth
Our analysis challenges the standard labels of value and growth for low pricing multiples versus high multiples.Truth in advertising would demand that "growth" mean higher expected earnings growth.That is so with E/Ps, as The confusion in labeling increases when it is said that growth yields lower returns, a common attribution.That seems odd, on the face of it, because one typically sees growth as risky, requiring a higher return.An understanding of the accounting further .The table also reports ROE, earnings growth, and measures of the risk in growth for the quintiles.IDR is the interdecile range.
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points to growth as risky; the mantra of the fundamentalist-beware of buying growth, for growth is risky-takes on added meaning when one appreciates the accounting for earnings and book value.Labeling presumably is supposed to convey meaning.The labels "value" and "growth" confound.
The value label is sometimes applied to just B/P, with the interpretation that price (in the denominator) discounts for risk, yielding a higher B/P when expected payoffs are risky.We consider B/P along with E/P to introduce both earnings and book value and thus ROE that then conveys the risk that discounts the price.Earnings and book value "articulate" in the double-entry system-the accounting for book value also affects earnings-so one cannot consider the B/P without the E/P.Stated differently, if one is to understand B/P, one must understand the earnings associated with the book value (ROE).The doubleentry accounting system of Luca Pacioli from 1494 that proved so useful to the Venetian merchants and many merchants since is also useful for conveying the risk of investing in those merchants.
With respect to the unconditional correlation of B/P with stock returns, note that the cross-sectional correlation between B/P and E/P is 0.25, on average, and E/P predicts returns in Table 1 (and strongly so for large companies in Table 6).Further, conditional on E/P, B/P further predicts returns, contributing to the unconditional correlation of B/P with returns.We make this assertion not to dismiss other possible explanations for the B/P effect but to point out that part of the explanation centers on the accounting and what it reveals about risk.

Conclusion
This article explains the value trap in terms of accounting fundamentals.In buying "value" companies with low multiples, the investor may be taking on the risk of buying earnings growth that may not materialize.A relatively high-E/P stock, a so-called value stock, is typically viewed as one with low growth expectations but in fact could be one with high growth expectations but growth that is risky.By adding the B/P, the investor understands that risk, because earnings together with book value yield the book rate of return-ROE, which indicates not only expected growth but also the risk in buying that growth.This phenomenon is due to accounting principles for measuring earnings and book value that evaluate risk.
In this article, we lay out this accounting and bring it to bear on assessing the risk in buying E/P and B/P-the risk of falling into the value trap.
Value investors screen on high E/P and B/P with the idea that low prices relative to earnings and book value indicate cheap stocks.There may be alpha in this strategy, but the analysis here provides a warning: Buying "value" may be buying risky earnings growth.

Editor's Note
This article was externally reviewed using our double-blind peer-review process.When the article was accepted for publication, the authors thanked the reviewers in their acknowledgments.Clifford S.  2018)-papers that connect earnings growth to risk.We apply the ideas and some empirical results from those papers to the issue of value versus growth investing.
2. In addition, La Porta, Lakonishok, Shleifer, and Vishny (1997) reported that the value-growth spread over the three days surrounding quarterly earnings announcements accounts for about 30% of the annual return spread.Doukas, Kim, andPantzalis (2002, 2004) tested whether the return spread is due to bias in analysts' earnings forecasts (it is not) and whether it is related to risk indicated by higher dispersion of analysts' forecasts for value stocks (it is).Piotroski and So (2012) indicated that return differences for value versus growth companies are concentrated in companies where market expectations differ from those indicated by a fundamental scoring metric.
3. Earnings are before extraordinary items and special items, with an allocation of taxes to special items at the prevailing statutory tax rate for the year.The findings in Table 1 are similar when the return period begins four months after fiscal year-end and when we eliminate companies with stock prices less than $1.00.For companies that are delisted during the 12-month holding period, we calculated the return for the remaining months by first applying the CRSP delisting return and then reinvesting any remaining proceeds at the risk-free rate.Doing so mitigates concerns about potential survivorship bias.Companies that are delisted for poor performance (delisting codes 500 and 520-584) often have missing delisting returns.We applied delisting returns of -100% in such cases, but the results are qualitatively similar when we make no such adjustment.
4. There are also a few loss companies in E/P Portfolio 2. Results are similar when we strictly confined all loss For Personal Use Only.Not for Distribution.8.The focus on conservative accounting is not to deny that earnings and book values might be manipulated, as entertained in Kok, Ribando, and Sloan (2017).But the accounting principles invoked here are pervasive and dominating, subject to audit, with determining effects on earnings and book value.
9. The effect of conservative accounting on ROE is simply due to the constriction of the accounting-the accounting principles invoked along with the debits and credits of the double-entry system.Feltham and Ohlson (1995) and Zhang (2000)  12. Chapter 5 of Penman (2012) lays out the Starbucks case in more detail.
13.Although earnings are purged on obvious transitory items (Note 3), there may be concerns that one year's trailing earnings may still contain transient components and are thus not a good indicator of forward earnings in Equation 1. So, we repeated the analysis in Tables 1-3 with E/P as the sum of the past three years of E/P (with dividends reinvested) and found similar results.
14. Earnings growth two years ahead is hardly sufficient to capture the complete stream of future earnings in the growth rate in Equation 1, although growth for that year likely is a forecast of subsequent growth; results for growth three, four, and five years ahead are similar.However, survivorship frustrates the observation of long-run ex post growth as an indication of ex ante growth.That, of course, raises the question of whether the results are affected by such bias, because companies do disappear within two years.The returns in Table 1 include delisting returns, but there is no accommodation for the growth findings here.So, we ascertained the fraction of companies that ceased to exist in the second year for performance-related reasons indicated by CRSP delisting codes.The delisting rate was higher for high-B/P companies, an average of 8.9% over all high-B/P portfolios in the first year ahead versus 7.7% for low-B/P portfolios.The corresponding delisting rates over the next two years were 20.8% and 16.9%.This result reinforces, rather than qualifies, our inferences; pertinent to the risk discussion that follows, delisted companies are those that had either low payoffs with company failure or high payoffs in being acquired; that is, they exhibit a wider spread of outcomes.
15. So, mean ROE for the low-B/P portfolio in E/P Portfolio 3 is 24.1%, compared with 4.8% for the high-B/P portfolio, and is similar for other E/P portfolios.The exception is Portfolio 1, with negative earnings, where the low-B/P portfolio has a lower negative ROE than the (negative) ROE for the high-B/P portfolio, as is also implied by Equation 2 when earnings are negative.
16.Because added investment from retention in the first year ahead adds to earnings growth two years ahead, we also calculated the residual earnings growth rate two years ahead to subtract for the added investment.Residual earnings were calculated as earnings with a charge against beginning-of-period book value at the prevailing yield on the 10-year US government note.Results were similar.
Portfolios were formed on the basis of reported E/P (before extraordinary and special items), not the forward E/P in Equation 1a, because we wished to discern the information conveyed by the accounting, not forward estimates, and the trailing E/P (purged of the transitory items) is a good indicator of forward E/P.The mean rank correlation between trailing E/P (as we have measured it) and realized forward For Personal Use Only.Not for Distribution.
E/P is 0.63.Of course, Equation 1 can also be expressed in terms of trailing earnings, with earnings growth, g, forecast from the current year onward rather than after the forward year.Doing so recasts the analysis as investing on the basis of trailing E/P and B/P, with no loss of insight.17.The connection of return realizations to earnings realizations accords with the observation in La Porta et al. (1997) that the value-growth spread over the three days surrounding quarterly earnings announcements accounts for about 30% of the annual return spread.
18.For the portfolios, means are arithmetic means.Similar results were obtained with weighted means-that is, with portfolio earnings calculated as the total earnings for the portfolio relative to price.The market earnings are total earnings for all companies relative to price.
19.The earnings betas here are consistent with the findings of Cohen et al. (2009) and Campbell et al. (2010), who attributed the higher returns of value stocks to higher "cash flow betas"-that is, the sensitivity to news about future cash flows.20.A similar table (with decile portfolios) can be found in Penman et al. (forthcoming).
21.In Table 2, B/P is positively correlated with subsequent earnings growth conditional on E/P.However, Penman et al. (forthcoming) reported that B/P is unconditionally positively correlated with subsequent earnings growth.Chen (2017) reported that low-B/P stocks do not have significantly higher dividend growth than high-B/P stocks.

Figure
Figure 1.Mean Equally Weighted Returns between High-and Low-B/P Portfolios within Five E/P Portfolios, by Company Size

Table 2 . Mean Earnings Growth Rates (%) Two Years Ahead for Portfolios Formed by Ranking Companies Each Year on E/P and B/P, 1963-2015
Notes: This table reports the mean of median earnings growth rates two years ahead for the same portfolios as in Table1.Earnings growth rates are percentages and are calculated as

Table 2
supplies the answer: Yes.E/P predicts subsequent earnings growth (across rows in the table), as one expects of a P/E.But for a given E/P, B/P is positively correlated with growth (down columns), with the difference in growth rates particularly strong for lower-E/P portfolios with higher growth expectations.Because B/P is inversely related to ROE, the conditional if in Property 2 is satisfied empirically, in line with the accounting.16Thus, the return spread for the same portfolios in Table1is explained by buying future earnings growth-and by buying earnings and book values governed by accounting principles that indicate the growth.But is the expected earnings growth associated with high B/P growth that is at risk?Only after answering this question could the returns in Table1be attributed to reward for risk bearing.

Table 3 . Standard Deviation and IDR of Realized E/P One Year Ahead and Realized Earnings Growth Rates Two Years Ahead for Portfolios Formed by Ranking Companies on
For Personal Use Only.Not for Distribution.cfapubs.orgFourthQuarter 2018 Table 3 indicate.Growth expectations have been shocked in recent years, with consequent shocks to stock prices.
So, in Table5we report portfolio returns during the two years when total returns for the S&P 500 Index were lowest in the last 10 years of the sample period, 2008 (-37.0%) and 2015 (1.38%).Returns

Table 3 . Standard Deviation and IDR of Realized E/P One Year Ahead and Realized Earnings Growth Rates Two Years Ahead for Portfolios Formed by Ranking Companies on E/P and B/P, 1963-2015 (continued)
For Personal Use Only.Not for Distribution.arefromAprilthrough March of the following year for 31 December fiscal year companies, the 12 months after earnings and book values are available with a three-month reporting lag.In the 2015 period, the spread of returns over B/P portfolios was positive for the low-E/P portfolios (albeit considerably lower than in Table1) but negative for E/P Portfolios 3-5.In the financial crisis year, 2008, when growth expectations took a large hit, the spreads were negative for all E/P portfolios: For a given E/P, high B/P (and low ROE) earned lower returns than low B/P (and high ROE).

Table 4 . Unconditional Earnings Betas and Up-Market and Down- Market Earnings Betas for Portfolios Formed by Ranking Companies on E/P and B/P, 1963-2015
This table reports (fundamental) earnings betas from regressing realized portfolio earnings yields in the time series on the aggregate market earnings yield.Panel A reports these betas over all conditions, and Panels B and C report the betas in up markets and down markets, respectively.
Notes:For Personal Use Only.Not for Distribution.cfapubs.orgFourthQuarter 2018

Table 5 . Annual Returns (%) in Two Recent Down Markets for Portfolios Formed by Ranking Companies Each Year on
Table 6 adds another measure, the

Table 6 . Results by Size Quintiles, Including Weights on E/P and B/P for Forecasting Forward Returns
Asness was one of the reviewers for this article.
Twitter reported positive quarterly earnings for the first time in 2018, with a large jump in its share price-uncertainty (somewhat) resolved.11.See also Greg Bensinger, "Amazon Sales Boost Stock: Investors Focus on 24% Jump in Revenue Even as Bottom Line Remains in Red," Wall Street Journal (25 October 2013): B3, Eastern Edition; and Barney Jopson, "Amazon Pays for Keeping Up Sales Momentum," Financial Times (24 October 2013): 13.The Wall Street Journal also reported on a study by Citigroup that found 90% of a present value calculation on Amazon related to cash flow forecasts for 10 years in the future.See Liam Denning, "Here to Eternity for Tesla," Wall Street Journal (25 October 2013): C1, Eastern Edition.