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Reports of Value's Death May Be Greatly Exaggerated
August 2020
Read Time: 60 min
Key Points
  • Value investing has underperformed relative to growth investing over the last 13.5 years.  The authors examine several popular narratives to explain this relative underperformance, including technological revolution, crowded trade, low interest rates, growth of private markets, and traditional measures of value that ignore internally generated intangible assets. These narratives purport to explain why “this time may be different” and why value’s poor relative performance may be the “new normal.”

  • The authors demonstrate that the primary driver of value’s underperformance post-2007 was growth stocks getting more expensive relative to value stocks.

  • The authors explore whether book value is the right denominator for value. In today’s economy, intangible investments play a crucial role yet are ignored in book value calculations. They show that a measure of value calculated with capitalized intangibles outperforms the traditional price-to-book measure, particularly post-1990. [Data for our iHML factor can be downloaded here.]

  • With today’s value vs. growth valuation gap at an extreme (the 100th percentile of historical relative valuations), the stage is set for potentially historic outperformance of value relative to growth over the coming decade.

Cam Harvey is the corresponding author.

This article was first published in January 2020.
The current version incorporates data through June 30, 2020.

An investment strategy, style, or factor can suffer a period of underperformance for many reasons. The style may have been a product of data mining, only working during its backtest because of overfitting. The trade can get crowded, which distorts asset prices and leads to low or negative expected returns. Structural changes in the market could render the factor newly irrelevant. Structural changes in the economy can make a particular accounting-based expression ineffective in capturing the factor premium. Recent performance may disappoint because the style or factor is becoming cheaper as the factor plumbs new lows in relative valuation. Finally, flagging performance might be a result of a left-tail outlier or simple bad luck. While the first three reasons (among others) might imply the style no longer works, the last three reasons have no such implications.

Many investors are reexamining their exposure to value investing, given the extraordinary span of underperformance—from 2007 to mid-2020, and counting—relative to growth investing. The book to price (B/P)–based standard HML (high-minus-low) factor of Fama and French (1993) experienced a drawdown of -55%. As of June 2020, the current drawdown is the largest drawdown observed since June 1963.1 Given the long historical record of value investing and its solid economic foundations (dating back to the 1930s and, less formally, dating back centuries), it is unlikely that the strong performance up to 2007 was a result of overfitting.

Our analysis suggests that the last three reasons (from the list above) contributed the most to value’s travails. Specifically, we observe that B/P, as the standard value definition, tends to misclassify stocks as value and growth by failing to capture a company’s investments in intangible assets. Further, in the last 13½ years, the relative valuation of value stocks relative to growth has become cheaper than ever before in history.2 Just as a stock can become cheap relative to its fundamentals, so can an investment style, strategy, or factor. As it becomes cheaper, its performance is bad, but that weak performance has nothing to do with future performance; indeed, if any mean reversion occurs in valuations, the poor performance can presage excellent future results. As the relative valuation for the value factor plumbed the lowest levels of the last 57 years, eclipsing even the peak of the tech bubble in 2000, this revaluation is by far the largest contributor to value’s underperformance. Finally, part of the underperformance cannot be distinguished from an extreme left-tail event.

We start our analysis with the examination of the question of the adequacy of the price-to-book (P/B) measure to capture the value effect in today’s economic environment. The economy has rapidly moved from agriculture, to manufacturing, to a service and knowledge economy. As such, there are economic reasons to believe that simple measures of value, such as the B/P ratio, are problematic. For example, a company presumably undertakes the creation of intangibles (e.g., research and development, patents, and intellectual property) because management expects these investments to enhance shareholder value. These investments, however, are typically treated as an expense and are not accounted for as an amortizable asset on the balance sheet, effectively lowering—we would argue understating—book value by the amount invested in intangibles. The fact that some of these investments in intangibles fail to deliver future profits is no different from an oil company drilling a dry hole or a new manufacturing plant becoming obsolete before it can turn a profit. Mistakes are a normal part of the business world. This accounting treatment leads the stocks of many companies to be classified as growth stocks because of low—sharply understated—book values. Many of these stocks would have been classified as neutral or value stocks if the value of the internally generated intangible investments had instead been capitalized, increasing book value.

Penman and Reggiani (2018) suggest that book to market is not a sufficient statistic for determining whether an investor invests in value or growth: “...when applied jointly with E/P, high B/P... indicates higher future earnings growth.” That is, a strategy that looks like a value strategy sometimes tilts toward growth. Lettau, Ludvigson, and Manoel (2019) suggest that the issue identified by Penman and Reggiani (2018) is important for the asset management industry. They show that, of the funds that call themselves “value funds,” few rely on B/P to define value. According to this definition, many of them hold more growth than value stocks in their portfolios.3

Absent an agreed-upon industry-wide measure of value, it may be unwise to select a single measure, such as book to market value, for use in valuation, especially when a company’s book value is a materially incomplete measure of its financial position. We also believe it makes sense to capitalize intangible investments in order to have a more realistic measure of a company’s capital. Our empirical work shows that if companies had capitalized these intangibles, the average annual return of the standard HML (high-minus-low) factor of Fama–French (1993) would have improved by 2.7% per year over the last 13½ years. Our results, together with those of Lettau et al. (2019), imply that some of these value funds performed surprisingly well during value’s current drawdown because they adjusted, in due course, their approach away from a flawed definition.

Next, we explore the influence of relative valuations on the recent value drawdown. The performance of value versus growth naturally disaggregates into three components: revaluation, migration, and profitability. Revaluation is the change in relative valuation of growth versus value. If growth stocks get more expensive relative to value stocks, the mere process of value becoming cheaper relative to growth means that value underperforms growth. Indeed, revaluation accounts for about two-thirds of the variability in factor returns over the past 13½ years and well over 100% of the cumulative shortfall. This is not particularly surprising given that six stocks, which we describe as the FANMAG stocks,4 have collectively appreciated more than tenfold since 2007. These six stocks compose about 20% of US stock market capitalization and 32% of the Fama–French large-cap growth portfolio as of June 30, 2020. Without the FANMAGs, the performance of the S&P 500 Index over the same period would have cumulatively been over 3,000 basis points lower. None of these stocks is a value stock.

The two other performance components are also important. Migration occurs when value stocks appreciate (leading to a lower B/P) and no longer qualify for the value portfolio, and when growth stocks falter (leading to a higher B/P) and no longer qualify for the growth portfolio. Because value strategies underweight or short growth stocks, an underperforming growth stock enhances these strategies’ returns. Migration markedly boosts the performance of value versus growth. Migration also boosts the book value of the value portfolio and lowers the book value of the growth portfolio every time these portfolios are rebalanced. This is because a no-longer-cheap value stock is kicked out of the value index and is replaced with a newly cheap stock, trading at a higher B/P ratio. Likewise a growth stock that has fallen out of favor is replaced with a new highflier, which sports a much lower B/P ratio.5

Profitability is the third driver of relative performance, because most growth stocks are more profitable and exhibit faster growth in sales and profits than most value stocks. Profitability benefits growth relative to value and offsets much, but typically not all, of the benefits from migration. We consider migration and profitability structural drivers of the value premium. When we compare pre-2007 data with post-2007 data, we find little evidence of any meaningful change in the performance attributable to migration or profitability.

We then seek to measure the structural premium of the value strategy by purging the revaluation component from the value-minus-growth return. Specifically, in 2007, the valuation spread (value minus growth) was narrow, in the top quartile (25th percentile). By June 2020, the spread had widened to an unprecedented extent, with the value portfolio at its all-time cheapest, since 1963, level (100th percentile) relative to growth. When value becomes cheaper relative to growth, value stocks underperform growth stocks. The residual return, which we term the structural return, is a combination of the profitability difference favoring growth and migration favoring value.

Our analysis subsumes a number of potential explanations for value’s underperformance. For example, some have said the value trade has become crowded, distorting stock prices so that the factor generates a very small or negative expected return. Crowding should cause the factor to become more richly priced. An increase in the valuation spread between growth and value, from the 25th to the 100th percentile, however, is not consonant with crowding into the value factor. Thus, this narrative is easy to dismiss.6

Likewise, little evidence exists to suggest that the value strategy’s long-run structural return has turned negative or even diminished from the pre-2007 level. The main difference between now and then is the rise in valuations, both for growth relative to value and for US stocks in general. Unless we choose to assume that the valuation spread between value and growth stocks will continue to widen indefinitely, our analysis suggests value is highly likely to outperform growth in the years ahead.

Our results relate, in particular, to Lev and Srivastava (2020), who suggest that value investing has been unusually unprofitable not only during the current drawdown, but for as long as 30 years. They conclude, similarly to us, that one of the reasons for the underperformance lies with the accounting treatment (or, rather, lack thereof) of investments in intangible assets.

Value's Recent Travails

The value strategy as a systematic approach to equity investing dates back at least to the 1930s. Graham and Dodd, in their 1934 classic book Security Analysis, laid down the main principles of value investing. By comparing the intrinsic value (capturing the future discounted stream of a company’s cash flows) and the market’s value of a company, investors can identify good buying and selling opportunities, which is the core of the value investing process. Basu (1977) was one of the first to empirically document a value premium by demonstrating that value stocks, defined as having a high earnings-to-price (E/P) ratio, outperform growth stocks, defined as having a low E/P ratio. In the following decades, multiple research papers showed that almost any definition of value that uses a fundamentals-to-price ratio produces a comparable return difference between value and growth stocks.7 Following the studies by Fama and French (1992, 1993), the academic consensus settled on the B/P ratio as the leading definition of value.

The source of the value premium is controversial. One camp led by Fama and French (1992, 1993) views the premium as a compensation for bearing risk, while the other led by Lakonishok, Shleifer, and Vishny (1994) argues that mispricing drives the premium. Although disagreement surrounds the source of the premium, most agree the premium exists and is not an artifact of a data-mining exercise. Indeed, the value effect is present in most asset classes (Asness, Moskowitz, and Pedersen, 2013), it is robust to perturbations in definition, and it does not require high transaction costs to execute (Beck et al., 2016).

Table 1 shows the performance characteristics of the value factor, compared with a handful of other popular factors. We define this factor using the Fama–French (1992) method, which equally weights large- and small-cap stocks.8 We construct two portfolios, consisting of the highest 30% and the lowest 30% of the market chosen by B/P ratio (hence, the factor name HML for high-minus-low B/P) and weighting each portfolio by market capitalization. Then we take the difference in the performance of the two portfolios. We compare this “factor performance” with the performance of other leading factors, many of which are constructed along similar lines, but use measures other than B/P to differentiate the favored stocks from the less favored. Over the 1963–2020 period of our analysis, even inclusive of the 13½-year drawdown, value remains one of the most impressive factors in terms of risk–return characteristics. Only momentum has better performance over the full span, and that is before taking trading costs into account (momentum has immense turnover).

Since the beginning of 2007, the value factor appears to have reversed its previous course of strong performance. A portfolio of value companies (based on the Fama–French high B/P ratio criterion) held from July 1963 through December 2006, and rebalanced annually to maintain a focus on value stocks, would have grown to 9.5 times the value of a portfolio of low B/P growth companies held over the same period, before it contracted 55% by the end of June 2020.9 Although the value investor’s wealth tumbled by 55% relative to the growth investor’s wealth in the 13½ years since the start of 2007, the value investor is still 4.3 times as wealthy as the growth investor over the period from July 1963 through June 2020.

Table 2 describes the three deepest and three longest value drawdowns in our 57-year sample. The current drawdown, which is still unfolding, unlike other episodes, is the deepest at -54.8%, eclipsing the tech bubble, which at its bottom had a drawdown of -40.6%.10 The current drawdown span of 13½ years is (by a wide margin) the longest-lasting period of value underperformance. The second longest-lasting period of value underperformance was the biotech bubble in the early 1990s, which lasted for a much shorter period of 3 years and 7 months from peak to trough to new high. That said, if we narrow our focus to large-cap stocks, for which the value effect is generally weaker, we find two back-to-back drawdowns—the biotech bubble and the tech bubble—interrupted by a scant one-month new high. Combine these two, and this earlier drawdown lasted 11 years and 10 months and left large-cap value investors more than 39.4% poorer than growth investors. This immense shortfall was recovered (requiring over 65% outperformance) in just 13 months.

Is the current value drawdown an “unlucky” outcome in line with previous drawdowns or is this time truly different? Specifically, if we use the pre-2007 characteristics of value for guidance, should we be shocked to see a drawdown of -54.8% at some stage during a 57-year span?

We use a block bootstrap simulation following Arnott et al. (2019) to answer this question. In the simulation, we resample the value factor returns, drawing random six-month blocks of actual long–short HML factor returns from the live historical sample from July 1963 through December 2006. We use the six-month blocks to preserve some of the autocorrelation structure of the return-generating process. Note that we end the historical sample in the last month before the current drawdown began, thereby excluding the recent drawdown. We are asking whether prior data might have led us to believe that the protracted 55% drawdown since 2007 was a plausible outcome.

Each simulated sample is 57 years long to match the length of the history from July 1963 through June 2020. We repeat this exercise 1,000,000 times. In so doing, we generate 1,000,000 alternative histories based on random draws from HML value-versus-growth relative returns. We then measure the size of the largest drawdown in each simulated sample, seeking to know how many of the 1,000,000 simulated histories have a drawdown comparable to the 54.8% decline from January 2007 through June 2020.

The bootstrap simulation shows that the median outcome was a 32.7% drawdown and a drawdown larger than the latest—a 54.8% drawdown—occurs in 2.3% of our simulations. While this meets standard definitions of statistical significance, the analysis is deliberately biased toward a low probability: we specifically excluded the recent drawdown from the data we used in the bootstrap simulations and run this test specifically because of the drawdown.

Is This Time Different?

The recent value underperformance raises a reasonable question: Is this time different? Put another way, is this a new normal for value investors, with the value premium gone or even negative? Many narratives are being offered to suggest that value investing no longer has merit. They generally fall into one of the following categories. Our first two are the simplest, and the easiest to dismiss. The next five are structural changes in the economy, which ostensibly make the value factor newly irrelevant. None fare particularly well in empirical testing.

The final three are the most important and are demonstrably accurate. Intangibles are not captured by book value, so the B/P-based HML is a poor way to distinguish between growth and value. A widening valuation spread between growth and value simultaneously pushes down the past performance for B/P HML and, with value now at the cheapest relative valuation in history, pushes up the likely future performance. And we have a left-tail extreme outlier, in both current relative valuation and recent relative performance. We return to these narratives after briefly reviewing the narratives that have less merit. We propose a return decomposition that suggests that intangibles, revaluation, and a left-tail outlier are all important elements of value’s travails. The evidence for the other narratives is weak. It is beyond the scope of this paper to test all of the narratives, but our approach addresses the most important empirical predictions for all of them.

Was value merely lucky in the past or is it now arbitraged away by its own popularity?

Overfit factor. A particular strategy may have been a product of data mining discovered by multiple testing and working only in the backtest due to overfitting.11 Given the amount of evidence, the economic theory, and the long investment management practice behind value investing, this is a doubtful explanation, further contradicted by the still-positive structural return for the HML value factor, net of revaluation.

Crowded trade. Value is a popular factor, widely accepted as a legitimate factor throughout the academic and factor-investing communities. Smart beta, and its cousin factor investing, have been among the fastest growing strategies in the past decade, attracting, by some measures, US$1 trillion or more (per Morningstar). These flows have ostensibly led to crowding, so that the value factor has been “arbitraged away.” If the crowding narrative were correct, then the value premium would be structurally impaired for as long as crowding persists. Value investors’ trades, however, should boost the prices (and valuation multiples) of value companies, relative to those of growth companies, to a point where the profitability and migration effects exactly cancel. The opposite has happened: value has become cheaper relative to growth, to an unprecedented extent.

Have structural changes in the economy made the value factor newly irrelevant?

Technological revolution, hence better growth stocks. This narrative suggests that today’s growth stocks are growing faster and earning more profit than the growth stocks of the past. In the last decade, we have witnessed the emergence of a vast digital sector, leveraging technological prowess to take over large parts of the macroeconomy. The recent success stories of the FANMAG stocks are captivating. These enterprises have driven many established companies out of business. These US-based tech companies are collectively vastly profitable. The combined capitalization of the FANMAG stocks was US$6.15 trillion in mid-2020, exceeding the stock market capitalization of every country in the world except for the United States and China. These six stocks are worth more than the entire publicly traded economy of economic powerhouses such as Japan, the United Kingdom, or Germany. This narrative suggests that the disruptive new technological leaders can drive outsized monopolistic profits, while the old brick-and-mortar value companies are choked into irrelevance.

If this narrative is correct, then we should expect that value investing may be structurally impaired for a prolonged period of time. Empirically, we should expect that growth companies would have already become even more profitable and faster growing relative to value companies than they were historically. The evidence contradicts this thesis.

Less migration. We hear several reasons that migration may be slowing. For instance, the more-monopolistic structure of many industries compared to a few decades ago makes it harder for new companies to gain market share. Also, as the valuation of growth and value diverge, it becomes more difficult for companies to migrate from growth to value, and vice versa. A related argument suggests that both the markets and the economy have evolved to a point where value stocks stay cheap and growth stocks stay richly priced, slowing the migration that drives the value-stock advantage. The more-stable valuations could also, in part, be driven by market participants’ increased sophistication, allowing them to more often “get it right” on the relative valuations of most companies.

If any of these narratives is correct, then we should observe a lower portion of value’s return attributed to the change in style (i.e., value stocks migrating toward growth, and growth stocks migrating toward value). Empirically, we find that migration is essentially unchanged from the past.

Low interest rates. In the last decade, we witnessed a long period of zero or near-zero interest rates—with no historical precedent—with US$11.6 trillion of government bonds worldwide trading at negative yields at the end of June 2020.12 In the standard Gordon formulation, low interest rates should have a disproportionate valuation impact on longer-duration and lower-yielding assets, unless the low interest rates are driven by a similar-magnitude drop in growth expectations. Liu, Mian, and Sufi (2019) suggest that industry leaders can disproportionately benefit from low interest rates to generate outsized monopolistic profits.

Although the economic mechanism is different, the implications and empirical predictions of this narrative are very similar to those suggested by the technological revolution narrative. Arnott et al. (2020) show, however, over the 1926–2020 period, that there is no meaningful relation between interest rate levels, or changes in rates, and the value premium. In addition, they document that value companies benefit more from low interest rates given they often carry more debt than growth companies.

Stranded assets. The market value of an enterprise reflects the value of the future use of assets owned by a company. As the economy and regulations evolve, certain types of assets can significantly depreciate in value or can become associated with material future liability. Particularly, as environmental, social, and governance (ESG) issues rise to the top of the public’s and regulators’ concerns, the old business models of energy, tobacco, gambling, and many other types of companies—overwhelmingly value stocks—may take a strong hit. Although the ESG conversation is as important and influential as it has ever been, it is merely another form of creative destruction that has been with us since the dawn of civilization, and which almost always afflicts value stocks relative to growth.

The growth of private markets. The number of listed stocks has more than halved in just 23 years, from over 7,500 in 1997 to barely 3,600 today.13 There are many reasons for the decline (not least being the regulatory environment for publicly traded companies), but one narrative suggests that part of the decline may be due to the growth of private equity investors who buy potentially undervalued stocks and take them out of public markets. Such activity leaves fewer value opportunities and potentially lowers the expected return on value.

This narrative suffers from two logical inconsistencies. First, most private equity investors are seeking growth not value. Second, given the growth of private equity, the buying pressure should increase the prices of deep-value stocks when they become, and are, private equity targets. So, on the one hand, some stocks that would fall into the value portfolio may disappear, but on the other hand, the activities of private equity investors should elevate the prices of certain value stocks before they disappear.

Let’s turn our attention to the narratives that demonstrably have merit.

The Trouble with Intangibles

The B/P ratio is one of many ways to define value. Intrinsic value is another definition, introduced by Graham and Dodd (1934). Indeed, they specifically cautioned against the use of B/P as a substitute for intrinsic value.14 In today’s economy this warning is ever more relevant, as companies’ intangible assets—intellectual property, brand, patents, brands, software, human capital, reputation capital, customer relationships, and so forth—are often at the core of their ability to generate and maintain profit margins, yet are almost totally ignored by the book value. Book value only captures the traditional tangible capital locked in bricks and mortar and in financial assets such as cash and other securities.

From an accounting viewpoint, book value can only capture the value of intangibles through contributed capital, or goodwill, in a corporate acquisition.15 This makes the B/P ratio vulnerable to misclassifying intangibles-heavy companies as expensive because book value understates the firms’ assets, and to misclassifying intangibles-light companies as cheap. Is there a better, more-objective measure of a company’s assets, including its intangibles?

Let’s presume that companies invest in research and development (R&D) and selling, general, and administrative (SG&A) expenditures because they expect to earn their money back within a reasonable span. Accordingly, following Peters and Taylor (2017), we capitalize all R&D expenditures as knowledge capital and apply a 30% share of SG&A expenditures as capital related to human capital, brand, and a company’s distribution network.16 Suppose these sums are added to book value, rather than expensed, much as if the expenditures were used to buy a building, then amortized away over a suitable span. After all, no one will buy a building or invest in R&D unless they expect this investment to be profitable within a reasonable span. After we capitalize both R&D and 30% of SG&A expenses, we then amortize those expenses, much as a building is depreciated, with the perpetual inventory method used by Peters and Taylor.17

Figure 1 plots the ratio of capitalized intangible capital to the book value of equity for all publicly traded companies in the United States. We show the equally weighted average for the growth and value portfolios (selected on the basis of B/P, not intangibles-adjusted B/P), as well as the market average, from 1963 to 2020.

In 1963, if we capitalize R&D and 30% of SG&A (then amortize both away), the book value for the US stock market goes up by just over 30%. A lot has changed since then. In the last three years, capitalized intangibles have tripled to nearly 100% of tangible book value. As of 2020, even for value stocks, intangible capital exceeds 50% of tangible book value, and for the average growth stock, intangibles are nearly twice as large as book value and have exceeded book value for nearly 20 years. It is very clear that book value is a tired, outdated metric for distinguishing between value and growth stocks.

What if we redefine the HML value factor based on a measure of company capital that includes both tangible and intangible capital? To answer this question, we construct an iHML factor following the same rules we previously used to construct the regular B/P-based HML factor, with only one change.18 Instead of using the book-to-market ratio to define value, we use the ratio of our intangibles-adjusted book value to market value (iBook to Market) to define our value factor. [Data for our iHML factor can be downloaded here.]

Figure 2 plots the cumulative performance, defined as the performance difference between the newly constructed value portfolio relative to the performance of the newly constructed growth portfolio, for the B/P-based HML and iHML factors.

In the full sample, iHML, the factor based on intangibles-adjusted B/P, outperforms the traditional value factor by 1% per year. We observe a reasonably uniform return advantage averaging to about 50 basis points per year prior to 2007. After 2007 the performance gap between the B/P-based HML and iHML becomes far more pronounced, at 2.7% per year, chopping the 13½-year loss in half.

Many low B/P growth stocks of companies that are investing heavily in intangibles are not nearly as expensive after we make this change. Reciprocally, some value stocks of companies that are disinvesting in their future look surprisingly expensive on this intangibles-adjusted metric, and some even move into the growth portfolio. Once we incorporate intangibles in our book value measure, the drawdown for value shrinks by nearly three-fourths in duration, from 13½ years to 3½, and by one-fourth in depth, from −54.8% to a still-daunting -41.4%, with the last new high for value relative to growth occurring in early 2017 instead of early 2007.

The iHML strategy subsumes B/P-based HML, but not vice versa. Once we control for B/P-based HML and other traditional factors, including momentum, the outperformance of the iHML factor, relative to B/P-based HML, is marginally statistically significant (at the 5% significance level). Appendix B reports these results.

It is important to emphasize that iHML, like traditional HML, would have performed poorly over the past 3½ years, as illustrated in Figure 2. Including intangibles does little to insulate against the peril of revaluations: iHML, like its traditional counterpart, suffered from a similar drawdown. Going forward, incorporating intangibles in the definition of a B/P-based value factor should help protect the structural value return, because a measure that includes intangibles runs a lower risk of misclassifying value stocks as growth stocks, and vice versa.19

Profitability, Migration, and Revaluation

Although the popular narratives propose very different mechanisms for why value has underperformed growth, the implications of the narratives can be described by disaggregating value factor returns (the performance difference between the value portfolio and the growth portfolio) into three constituent parts: 1) migration, 2) profitability, and 3) changes in value-versus-growth relative valuation, or revaluation.20 If these elements vary over time—for example, if a structural break permanently alters them—then the returns on value investing will vary as well. Using an accounting identity (the decomposition and derivation are detailed in Appendix C), we can attribute the value factor’s return to these three elements, as follows:

The three elements in the decomposition have the following interpretations:

Migration (stock-level mean reversion in valuation multiples). This term captures the return associated with changes in the composition of the growth and value portfolios. Fama and French (2007) introduced the concept and coined the term “migration” in their study of attribution for the performance of value portfolios relative to growth. They examined stocks’ migration between the six portfolios (small-cap value, neutral, and growth, and large-cap value, neutral, and growth) that underlie their HML value factor. They attributed most of the value factor’s performance to the mean reversion in the stocks’ style. For example, each year some value stocks migrate up into the neutral or growth portfolios, while some growth stocks migrate down into the neutral or value portfolios. Both contribute positive performance to value relative to growth, the former by helping the performance of value portfolios, and the latter by hurting the performance of growth.

Profitability. This term captures the difference in profitability between the value and growth portfolios. Growth stocks are typically far more profitable than value stocks, while growing faster, and is the reason they deservedly command premium multiples. The term combines dividend yield (a term common in many return attributions) and retained earnings. Cohen, Polk, and Vuolteenaho (2003) show that about half of the information contained in the B/P differences between value and growth stocks is attributable to the differences in their future profitability. They find that persistence in growth stocks’ valuations reflects their future expected (15-year) profitability, which tends to support their trading more expensively than value stocks.

Similarly, Arnott, Li, and Sherrerd (2009) demonstrate a roughly 50% cross-sectional correlation between the historical “fair-value” multiples of individual stocks, using a discounted-cash-flow model based on subsequent actual performance of a business, which Bill Sharpe termed “clairvoyant value,” and the then-prevailing actual multiples. The market appears to be adept in identifying future growth and appears to pay more for that growth than it’s worth.

Revaluation. This term captures the return coming from changes in relative valuations, between the growth and value portfolios. Over long periods, unless we allow for a permanent trend in relative valuations (which implies that prices can stray to limitless deviations from fundamentals), these changes in valuations should not contribute significantly to a factor’s performance.21

We show later that revaluation explains two-thirds of the annual variance in the HML factor’s performance. Fama and French (2002) and Arnott and Bernstein (2002) show that the equity risk premium can significantly benefit or lose from changes in valuations, even when the premiums are measured over many decades. They argue that the returns induced by the changes in the valuations should be purged from the estimates of the risk premium because no a priori reason exists to explain why any trend in valuation should persist. Following Arnott et al. (2016), we extend this argument to the value factor premium.

The migration and profitability components are at the core of the value premium—combined they form what we call the structural component of the value premium. It is not unreasonable to expect profitability and migration to persist, with the former always benefitting growth and the latter always benefiting value, with revaluation to follow something of a perhaps mean-reverting random walk. Accordingly, we describe the first two as structural sources of return. Because the changes in aggregate valuations cannot trend indefinitely—equivalent to saying that no bubble can last forever—the revaluation component should average roughly zero over a sufficiently long period. That said, relative valuations of value and growth stocks could drift to a “new normal,” and the value factor would as a result earn an abnormal (good or bad) return during this transition period.

Table 3 displays the results of the value factor’s return decomposition in the pre- and post-2007 samples. (We also provide details of the attribution for the six HML portfolios in Appendix D.) Because our value strategy (HML) is rebalanced annually at the end of June, and because our decomposition uses the observations between rebalancing points, our analysis focus on the periods between rebalancing points. Specifically, for the pre-2007 period, we examine the period from July 1963 through June 2007, and for the post-2007 period, we examine the period from July 2007 through June 2020.

On average, because growth stocks are more profitable and faster-growing than value stocks, the profitability difference contributed -13.2% per year to the value-minus-growth return in the pre-2007 period. Over the same period, the migration component, at 19.2% a year, more than offsets the difference in profitability. Combining the profitability and migration components, we observe a structural value return of 5.9% per year, which is very near the average HML premium return of 6.1%. Revaluation played very little role in this 44-year span.

In the post-2007 sample, the profitability and migration components are close to their values in the pre-2007 sample. The profitability differential widens from -13.2% to -15.9%. It would seem that today’s growth stocks are in some ways better businesses than the growth stocks of the past, though not by much. Meanwhile, the migration effect narrows from 19.2% to 17.0%.22 It would seem that migration has slowed, as valuation spreads have widened, though again not by much. Their sum—the structural return—is distinctly smaller than before 2007, at 1.1% versus 5.9%, but it remains positive and economically meaningful. The value effect appears to be alive and well, albeit weaker than in the past.

Revaluation contributed -7.2% annually to the return, down from an average upward revaluation of 0.2% before 2007. As a result, the total value return flips from 6.1% in the first 44 years to an annualized shortfall averaging -6.1% in the last 13 years. It took value cheapening relative to growth by 7.2% per year to create a performance shortfall of 6.1% per year. Since 2007, well over 100% (116%) of the shortfall of value relative to growth is a consequence of value becoming cheaper relative to growth. In the most recent 13-year period, the revaluation component appears to be the key to understanding why growth stocks outperformed value stocks.

Figure 3 illustrates the evolution of the cumulative value return (solid line, left axis), which is the same as in Figure 2, and the value–growth relative valuation (dashed line, right axis).23

The relative valuation is the ratio of B/P for the growth portfolio to B/P for the value portfolio. If the B/P ratio of the growth portfolio is 0.4 and the B/P ratio of the value portfolio is 2, then the relative valuation is 0.20. The median relative valuation is 0.21, which means that growth stocks are, on average, about 4.8 times more expensive than value stocks, when measured by B/P.24 As Figure 3 shows, however, the valuations of value stocks, measured relative to growth, fluctuate widely over time, and correlate strongly with the concurrent performance of the value factor.

When we put the performance and the revaluation charts together, the short-term movements of the two appear to be joined at the hip. In the short run, the revaluation component (changes in the B/P of value relative to growth) is the dominant driver of the value portfolio’s performance relative to growth. Over the long run, however, the two lines diverge. This wedge of divergence suggests that the value premium is driven by structural return and is not a lucky discovery due to a temporary revaluation. Indeed, the factor has delivered impressive long-term profits, despite a substantial downtrend in relative valuation. The regression reported in Figure 3 shows that log-changes in valuations explain two-thirds of the variation in log-HML’s returns.

We observe what seems to be a pronounced trend, which may reflect the waning relevance of classically defined book value as a valuation metric. That said, even a very substantial trend over the last 57 years amounts to only a 0.8% negative annualized slope25—and the valuation spreads may be abnormally high at the start of the series and/or abnormally low at the end.

The relative valuation in 1963 is at the time-series median of 0.21. The relative valuation varies from 0.30, five years after the Nifty Fifty bubble burst, to 0.10, at the peak of the dot-com bubble, to 0.085 at end-June 2020. In every episode when value substantially underperforms growth, a key driver is value stocks’ becoming cheaper relative to growth stocks.

During the drawdown from 2007 to 2020, the value factor lost a cumulative 54.8% in performance, or -6.2% per year. From July 2007 to June 2020, the relative valuation moved from 0.23, which is relatively expensive at the 25th percentile of the distribution, to 0.085, at the cheapest relative valuation percentile ever. One way to view this comparison is that it took a 64% drop in relative valuation, for value relative to growth, in order to create a 55% drawdown.26

At the current valuation level, growth stocks trade nearly 12 times the P/B valuation ratios of value stocks. The relative valuation has been close to this level only twice over the 57-year history of our analysis: the peak of the dot-com bubble and the nadir of the global financial crisis. Our decomposition indicates that the change in relative valuation since mid-2007 contributed -7.2% per year and turned the 1.1% structural return into the −6.1% per year realized value return.

Alternative Definitions of Value

The B/P HML has performed the worst, over a longer span, than any of the other definitions we use. Every measure of value that we considered, however, has underperformed, and the bulk of that underperformance has been associated with a large drop in relative valuations. This behavior is not limited to the B/P-based HML. Table 4 displays the performance characteristics for five segments of the B/P-based HML value metric and four alternative value strategies. Unlike our other tables, we use arithmetic returns instead of log returns in our analysis.

The four alternative value strategies include iHML (which was introduced in the previous section) and earnings-to-price (E/P) ratio and sales-to-price (S/P) ratio, each constructed using the same Fama–French methodology for constructing the growth, neutral, and value portfolios.27 We also show results for a composite that equally weights the relative B/P, E/P, S/P, and D/P (dividend yield, limited to the stocks that pay dividends) in measuring a stock’s valuation relative to the market.28

Using all four value definitions, value underperformed growth in the post-2007 period. Also, for all definitions, value’s underperformance was associated with value’s having neutral to expensive relative valuations in June 2007 and having bottom-decile relative valuations in June 2020. Interestingly, the large-cap half of the HML factor experienced the largest underperformance, -6.2% per year, in the post-2007 period, accompanied by a huge move in relative valuations from the 15th percentile to the cheapest percentile.

The value-to-neutral and neutral-to-growth factors have similar underperformance (and combined match the HML underperformance), so there is symmetry in the results. The value-to-neutral factor is long the 30% of stocks with the highest B/P ratios and short the 40% of stocks in the middle of the B/P distribution. The neutral-to-growth factor is long the neutral stocks and short the 30% of stocks with the lowest B/P ratios. The valuation change for the neutral-to-growth definition very nearly matches the move for large-cap HML from the 15th percentile, well into the top quintile, to the cheapest percentile. The ending percentile implies that the growth portfolio trades today at unprecedented valuations relative to neutral, not just relative to value.

The traditional B/P-based HML strategy suffered the worst drawdown, underperforming by -5.4% per year,29 whereas the five alternative strategies reported in the bottom half of Table 4 fared much better. iHML cuts that shortfall in half, but even the adjustment of book value to include intangibles does not fare as well as the E/P or S/P value factor models since 2007. The underperformance from January 2007 through June 2020 ranges from -1.0% per year for the S/P-based value factor to -3.6% per year for the composite, which was clearly hurt by including traditional HML in its process.

We would emphasize that the B/P-based HML model is the worst model in this comparison, since 2007. Losses from the other value metrics range from modest for S/P to moderate for iHML and the composite. Not shown in this table, every metric other than HML has seen a drawdown ranging from 3½ years to 6½ years, since the last peak, not the grinding 13½ year dry spell for HML.

What to Expect from Value?

In the aftermath of the tech bubble in 2000, the relative valuation of B/P-based HML rose from a then-record low of 0.10 in June 2000 to a borderline top-quartile valuation of 0.25 in June 2005, delivering 110% return for value relative to growth in just five years. Then value stalled. Over the last 13½ years, the relative valuation of HML (value versus growth) moved from the top quartile (specifically, the 25th percentile) to a new record low in relative valuation and a newly reset 100th (lowest) percentile.30 We display the historical distribution of relative valuations in Figure 4. This downward revaluation since 2007 explains more than 100% of value’s underperformance and two-thirds of its annual variability. Today, the relative valuation of the HML value factor is in its most attractive valuation percentile in history, considerably cheaper than the relative valuation of value stocks at the peak of the tech bubble in 2000.

Given the historical relationship between value’s starting valuation levels and value’s subsequent return, what return can we reasonably anticipate from the expected value premium in the years ahead? Should we expect a sharp rebound in value as we observed after the tech bubble of 1999–2000, the global financial crisis, and the Nifty Fifty of 1972–1973? We can gauge the forward-looking expected return estimates of the value premium by using the revaluation-migration-profitability decomposition we reviewed in Table 3.

We cannot, of course, simply assume a revaluation return to the historical median and keep the other components at their historical average. As discussed in Appendix C, the three terms in the decomposition correlate significantly. Over the 1963–2020 sample, the correlation between the profitability and revaluation terms is -0.32, between the profitability and migration terms is -0.43, and between the revaluation and migration terms is -0.04.31 These negative correlations mean that when the HML factor benefits from a tailwind of upward revaluation, the lower profitability and migration terms typically offset some of the revaluation profits.

The question we want to answer is: What is the expected return on HML conditional on any given magnitude of revaluation? Conveniently, if we use historical data as a guide and model the conditional expected returns, we can use our linear regression to provide some answers.

What HML return can we expect in a year when a specific scenario is realized? Table 5 displays the estimated results.32 The central assumption of our analysis is that revaluations will not exhibit a permanent trend (otherwise prices would be indefinitely unmoored from fundamentals). Even if the relative valuations were to stay at the current level, value investors should still expect to collect the structural return of 4.5%, estimated over the full 57-year sample (see Figure 3). Because of the presence of structural return, a further decline over the next year from the current bottom-percentile valuation to yet another new low, at a relative valuation of 0.081 or lower, is required in order for value to have a zero or negative return.

Historically, relative HML and iHML valuations have shown a tendency to mean revert. A regression of the B/P-relative HML valuation against the year-earlier valuation has an intercept of -0.41 (t-stat = -2.55) and a slope of 0.73 (t-stat = 6.84). The slope roughly corresponds to a rapid 2.2-year half-life mean-reversion rate.33 These are average historical tendencies, which never play out exactly.

Full reversion to the median, if it happened in a single year, would require value to beat growth by 77% (on a log scale, meaning that value more than doubles relative to growth). If this were to happen over several years instead of a single year, the structural return of the value factor would add to this every year, generating an even larger gain (although a lower annualized gain). Even a move to the historical 75th percentile, halfway between cheapest-ever and the median valuation for value relative to growth, should deliver 65% relative performance for value over growth. Arguably the most surprising result in Table 5 is that a modest improvement from the current 100th percentile to the 95th percentile—the midpoint of the cheapest decile in history—would result in a return of about 37%. Finally, even if valuations were to stay at current levels, the model suggests a positive 4.5% return, driven solely by the average structural return of the past 57 years.

No one knows with certainty whether we will return to the lofty structural return earned through 2006, whether mean reversion in relative valuation will happen, how long the mean reversion will take, or if the mean has itself shifted to a new normal, perhaps due to the increasing importance of intangibles. From the peak of the tech bubble in early 2000, to the peak for value stocks in early 2007, HML appreciated from the then-cheapest percentile ever to the 25th percentile—marginally top quartile—in just seven years. Recoveries following the Nifty Fifty bubble and the global financial crisis both happened more rapidly. The present and future rarely play out in the same way as the past. We have our expectations, but others can and will set their own.


Many narratives purport to explain why “this time is different,” why value may be structurally impaired. These narratives include the new-normal interest rate environment, growth of private markets, crowding, less migration, stranded assets, and technological change, among others. We examine many of these explanations and find insufficient evidence to declare a structural break.

We address the important issue of mismeasurement of value, due to a core failing of book value as a valuation metric. This classic measure of value was designed at a time when the economy was much less reliant on intellectual property and other intangibles. In today’s economy, intangible investments play a crucial role, especially in growth stocks and even in value stocks, yet book value ignores most internally sourced (intangible) investments. We capitalize intangibles and show that this measure of value outperforms the traditional measure, notably beating B/P-based HML by nearly a twofold margin after 1990. Nonetheless, this improved measure of value has also recently suffered a large drawdown, and post-2007 is still not as good as S/P or E/P. Perhaps intangibles-adjusted B/P is still missing something important.

We also offer a simple model that decomposes the returns of value relative to growth. The framework attributes the relative performance to three components: migration, profitability, and change in relative valuation. Our evidence suggests that migration (e.g., individual value stocks becoming growth stocks) and profitability are not materially different in the pre- and post-2007 periods. Migration benefits value stocks and profitability benefits growth stocks, with migration reliably dominating profitability, leading to the value premium. We refer to the combination of the two as the structural return.

The reason B/P HML has suffered a -55% drawdown has nothing to do with failings in the structural return and is entirely due to the collapse of relative valuations. Over the drawdown period, relative valuations have moved from the 25th to the 100th percentile, with value becoming cheaper relative to the market while growth stocks have soared. Oversampling a period of negative residuals may also contribute modestly to the drawdown. Our initial bootstrap analysis, which does not account for changes in valuations, suggests the current drawdown would have been thought to be 2.3% probable. This is true even when based on past returns that exclude the drawdown period, using historical data from 1963 through mid-2007, a span in which value beat growth by 6% per year. We believe this outcome is improbable, but it is not an extreme outlier.

As of mid-2020, relative valuations for value relative to growth are in the extreme left tail of the historical distribution. If, as history suggests, there is any tendency for mean reversion, the expected future returns for value, by almost any definition, should be above historical norms. Indeed, we show that even if the relative valuation remains in the current bottom percentile, the structural components (migration and profitability) should offer a positive overall return.

That said, we would like to emphasize two important caveats. First, the percentiles are backward looking; it is possible to cross, yet again, into unexplored territory. Second, returns are very noisy. While expected returns of value relative to growth are high, the role of luck (both good and bad) creates a wide distribution of outcomes over shorter spans, even over the next five years. Although value strategies seem as attractive as they have ever been, an elevated expected return is not a guarantee that value must outperform growth in the years ahead.

Appendix A. Histogram of Largest Drawdowns

We display in this appendix the distribution of the largest drawdowns in the simulations. Each bar in the histogram shows how common it is to have a worst drawdown of the indicated magnitude.

Appendix B. iHML vs. HML Spanning Tests

With conventional B/P, the coefficients for market (beta) and size are negative, suggesting that value has a low-beta and large-cap bias on average over time. With iHML, incorporating intangibles, the signs flip and the coefficients become slightly more neutral, suggesting that iHML value has a mild high-beta and small-cap bias.

When iHML is included, the alpha is not significantly different from zero, implying that iHML subsumes HML. In columns (4)–(6), iHML is the dependent variable and is regressed on the market, size, and momentum factors, as well as on the traditional HML factor. In this case, the alpha for iHML is significant at the 5% level under the assumption of a single hypothesis test. This is consistent with iHML subsuming HML, but not the opposite.

Appendix C. Return Decomposition Details

In the section “Profitability, Migration, and Revaluation,” we decompose a portfolio’s return into three parts: the revaluation, profitability, and migration components. In this appendix we derive this decomposition by starting from the definition of log returns. We then show the decomposition results for the value and growth portfolios’ log returns as well as for log HML. The decomposition we derive holds as an identity for the portfolios’ log returns. In Table 3 in which we decompose the HML factor’s return (not the log return), it holds as an approximation.


rt+ = return from time t − 1 to time t on the portfolio formed at time t − 1;

Dt– = dividend distributions from time t − 1 to time t from the portfolio formed at time t − 1;

Pt–1 = portfolio-weighted market capitalization at time t − 1 of the portfolio formed at time t − 1;

Bt–1 = portfolio-weighted book value of equity at time t − 1 of the portfolio formed at time t − 1;

Bt– = portfolio-weighted book value of equity at time t of the portfolio formed at time t − 1;

Pt– = portfolio-weighted market capitalization at time t of the portfolio formed at time t − 1;

Pt+ = portfolio-weighted market capitalization at time t of the portfolio formed at time t;

Bt+ = portfolio-weighted book value of equity at time t of the portfolio formed at time t;


With this notation, a return on a portfolio can be represented as

This decomposition holds as an identity for a portfolio’s log returns.

Appendix D. Detailed Attribution

In this appendix, we display the results of the value factor’s return decomposition in the pre- and post-2007 samples.

Appendix E. Estimating a Revaluation Model and the Left-Tail Hypothesis

The accounting identity decomposition in Appendix C fully attributes the impact of changes in relative valuations of the rebalanced portfolio on the portfolio returns, between the start and endpoint of the portfolio observations. The full attribution would be more intuitive if the strategy had little turnover; that is, the stocks the portfolios hold next year are the same as they hold today. In the presence of turnover, however, the stocks held in the six strategy portfolios (growth, neutral, and value in both large-cap and small-cap stocks) do not fully benefit (or suffer) from the revaluations of the value and growth stocks.

To illustrate, suppose we track the valuation of a group of small value stocks from year t to year t + 1. Let’s assume that on average the small value portfolio earns a structural return of 5%. Let’s assume also that a year after rebalancing the average valuation of these stocks has increased by 10%. The change in the valuation ratio alone does not mean that we will earn the 10% return on top of the structural return; the elements of structural return—migration and profitability—may be correlated with changes in relative valuations. Further, turnover can introduce additional noise. Suppose, for example, that the group of small value stocks that we bought last year earned just 8% on top of the structural alpha. The 2% gap between the 10% valuation change and the 8% return we experienced is due to the correlation of revaluation with structural return and the turnover effect.

We take this turnover effect and the correlation with the structural return into account by estimating the average relationship between the revaluation component and the value (HML) factor’s return. Specifically, we define the independent variable as the revaluation term from the preceding decomposition as


Note: Following the notation, detailed in Appendix C,

t+ denotes the moment right after the rebalancing.

and use the full sample to run a regression with rolling 12-month HML returns as the dependent variable:


We account for serial correlation in the data by computing Newey–West standard errors with one annual lag. This regression helps answer a simple question: If the valuations of value stocks relative to those of growth stocks change, what is the average return of HML? Table E1 presents the estimates from this linear regression (estimated using annual data from July 1963 through June 2020).

The regression resolves this ambiguity by measuring the average relationship between valuation changes and price changes.34 Specifically, the regression slope of 0.80 means that when the valuations of value stocks increase by 10% relative to those of growth stocks, HML on average returns 8.0% more than its regression-based structural alpha.35 The regression also shows that revaluations have a significant link to the returns of HML. The R2 of 66.5% over the full span means that changes in the relative valuations of value and growth stocks explain two-thirds of the variance in the HML factor’s returns.36

Table E1 also shows the regression estimates separately for the pre- and post-2007 samples as well as for the full sample. The association between the return of HML and revaluation is quite similar around the 2007 breakpoint: the estimated slope is 0.76 before mid-2007 and 0.74 thereafter. In the pre-2007 sample, this intercept is 6.0%; in the post-2007 sample, it is -0.8%.

It is tempting to interpret the intercepts from these regressions as estimates of the conditional returns on value, if valuations had remained unchanged. Although the post-2007 sample has only 13 data points and the near-zero intercept is not significant, does the estimate imply that value would have earned nothing even in the absence of the 7.2% downward revaluation each year? If this interpretation is correct, should we expect zero structural premium going forward?

This interpretation is overly simplistic. When we explicitly analyze drawdowns, we introduce a selection bias by picking the sample to analyze based on the values of the dependent variable. In this case, we are studying the most recent 13½-year period precisely because of the poor performance of value, which is likely in part due to negative residuals.37 As an analogy, suppose that we were to analyze the performance of Tiger Woods from 1999 through 2004 (when he was the top-ranked player in the world for 264 consecutive weeks) but, instead of looking at his total record, we only include the tournaments in which he played the worst. The resulting selection bias would lead us to struggle to explain why Tiger’s performance was not commensurate with his skill (alpha). Similarly, if we try to explain any factor’s performance, but only study a sample in which the factor performs poorly, we cannot hope to recover the factor’s true unconditional alpha; oversampling of negative residuals hopelessly contaminates the sample.

Although this mechanism is intuitive, an important question remains: Is the intercept of -0.8% in the post-2007 period evidence of exceptionally improbable bad luck or just ordinary bad luck that we might expect to encounter when we examine any drawdown? We examine this question in Figure E1 with a bootstrap scheme in which we introduce a comparable selection bias.

In this analysis, our goal is to create a set of simulated drawdowns that resemble the post-2007 drawdown, but to do so by resampling the pre-2007 data. Specifically, we first take the annual July 1963–June 2007 data with the HML returns and revaluation terms and create 1,000,000 simulated samples. Each sample length is 57 years. Within each sample, we identify all drawdowns that last longer than 10 years. If there are no such drawdowns, we discard the sample, and if there is more than one such drawdown, we retain the one that comes the closest to matching the magnitude of the actual post-2007 drawdown.

Within each drawdown, we then focus on the period from peak to trough. The purpose of this step is to mimic the actual data of value’s fall from its peak in 2007 to its trough in 2020. Finally, we regress these peak-to-trough returns against the revaluation terms and retain the intercepts. Figure E1 shows the distribution of these intercepts.

We can see that when we use random draws from a 44-year span with a true intercept of 6.0%, and then focus on decade-long bear markets in value relative to growth, the regression intercept is above 6.0% in only 5.2% of the random samples. The median measured intercept is 0.5%, meaning that the selection of a particularly bad period for value leads this regression to understate the true structural premium by 5.5%! Indeed, the measured intercept is quite often negative. The actual intercept of -0.8% shown in Table C1 lies at the 28th percentile of the regression results, when we draw from a distribution with a true intercept of 6.0%. This analysis tells us that if we take the pre-2007 value-versus-growth returns, with an average structural premium of 6%, and find drawdowns that approximately resemble the actual post-2007 drawdown, value’s performance net of the revaluation effects would often be even more underwhelming than it was in the actual data.

Whether the observed structural premium of the past 13½ years has been +1.1% or -0.8%, skeptics who suggest that the efficacy of the value strategy has swung sharply negative are only partly right, because they are overlooking the massively important impact of downward revaluation of value relative to growth. In realized returns, value has fallen seriously off the rails, but only because it has become cheaper by 7.2% per year compounded. Neither result is at odds with the 6.0% structural premium that was measured from 1963 through the end of 2006.

Taken together, Table E1 and Figure E1 attribute value’s poor performance in the post-2007 period to two sources. The first is the systematic underperformance from soaring valuations of growth stocks relative to value. These increasing valuations created a headwind that accounted for essentially all of value’s losses over the past 13½ years. The second source of value’s poor performance is that we, in effect, oversample bad luck over this recent span, because we are not attempting to explain value’s performance over a randomly chosen period. We are attempting to explain precisely the recent span in which value’s performance stands out as particularly weak. Our bootstrap analysis indicates that when we account for this selection bias the post-2007 period does not stand out. Had we experienced a similar drawdown in the pre-2007 data, then value’s theoretical poor performance in that period would have required almost the same amount of bad luck as in the post-2007 period.



  1. Appendix A provides a histogram of the worst drawdowns from June 1963 through June 2020.
  2. For our purposes, except as otherwise noted, we define relative valuation as the ratio of the book-to-price ratio (B/P) for the growth portfolio, measured relative to B/P for the value portfolio. In the case of the standard B/P-based value factor, we measure the B/P of the growth portfolio relative to the B/P of the value portfolio.
  3. Arnott, Kalesnik, and Wu (2017) and Patton and Weller (2020) complement the analysis in Lettau et al. (2019). They find that those funds with value exposure earn only a fraction of the value premium after accounting for the implementation costs.
  4. The FANMAG stocks combine the so-called FANG stocks (Facebook, Amazon, Netflix, and Google) with the largest survivors from the tech bubble of 20 years ago, Apple and Microsoft. Apart from Saudi Aramco, which has less than 2% of its shares held by the public, the five most valuable companies in the world are on this list as of midyear 2020, three with a market value over US$1 trillion.
  5. In the standard B/P HML value factor, this rebalancing happens annually at midyear. This rebalancing effect, value becoming cheaper and growth more expensive with each rebalance, means that the relative valuation of the value portfolio relative to growth becomes materially cheaper every time the portfolios are rebalanced, then moves the other way over the next 11 months. To adjust for this, we rebalance HML monthly rather than annually and then remove any remaining seasonalities (which emanate from most firms’ fiscal years ending in December) by computing seasonally adjusted revaluation metrics.
  6. Indeed, most multi-factor strategies now trade at premium valuation multiples relative to the market, so even those who claim to embrace value as a key part of their strategy are now allowing growth to swamp value in their portfolios.
  7. For example, Barbee et al. (1996) document the value effect for the price-to-sales ratio; Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) document the value effect for the B/P ratio; and Naranjo, Nimalendran, and Ryngaert (1998) show the value effect for the dividend yield. Jacobs and Levy (1988) demonstrate that many different definitions of value are related and that they produce correlated returns.
  8. The equal weighting of small- and large-cap stocks introduces a weighting peculiarity in which the largest-cap stocks in small value and small growth portfolios receive a weighting more than 10 times that of the smallest-cap names in the large value and large growth portfolios.
  9. Unless otherwise noted, our return measures are log returns when we are looking at longer-term compound rates of return and are simple returns when looking at individual samples or, as in this case, a cumulative return.
  10. Davis, Fama, and French (2000) extend HML performance to 1926. The worst pre-1963 drawdown was −43.5%; this bottom was reached at the end of March 1935.
  11. Harvey, Liu, and Zhu (2016) study the overfitting issue and declare the HML version of value “significant” after controlling for test multiplicity.
  12. According to the BNYDMVU Index.
  13. As of June 30, 2020, 3,622 firms were publicly traded on the NYSE, AMEX, and Nasdaq.
  14. Specifically Graham and Dodd wrote (emphasis added): “In general terms [intrinsic value] is understood to be that value which is justified by the facts, e.g., the assets, earnings, dividends, definite prospects, as distinct, let us say, from market quotations established by manipulation or distorted by psychological excesses. But it is a great mistake to imagine that intrinsic value is as definite and as determinable as is the market price. Some time ago intrinsic value (in the case of common stock) was thought to be the same as ‘book value,’ i.e., it was equal to the net assets of the business, fairly priced. This view of intrinsic value was quite definite, but it proved almost worthless as a practical matter because neither the average earnings nor the average market price evinced any tendency to be governed by book value.”
  15. The two main components of the book value of equity are contributed capital and retained earnings (Ball et al., 2019). Contributed capital represents the net contribution of capital from the company’s shareholders through initial or seasoned public offerings in excess of share repurchases, and retained earnings are the earnings accumulated since the company’s inception less accumulated dividends. Beneish et al. (2020) study how intangible capital is incorporated into book value in mergers and acquisitions.
  16. Following Peters and Taylor (2017) we capitalize R&D expenses by applying the perpetual inventory method to a company’s past R&D: Git = (1 – δ)Git–1 + R&Di,t, where Gi,t is the end-of-period stock of knowledge capital for company i, δ is the industry-specific discount rate, and  is the real company R&D expenditures during the year. We apply the Bureau of Economic Analysis (BEA)–estimated discount rates for R&D for different industries. Examples of R&D expenses include patents, software, and internal knowledge development costs. The R&D capitalized measure could be interpreted as the replacement cost of the knowledge capital. Similarly, we capitalize a fraction of SG&A. Just like with R&D, the capitalized SG&A expense could be interpreted as the replacement cost for recreating brand awareness, training costs to build human capital, and so forth.  The perpetual inventory method requires assumptions about the initial stocks of knowledge (R&D) and organization (SG&A) capital at the time of the IPO. We follow Peters and Taylor (2017, Appendix B.2) and construct these initial stocks by using average pre-IPO growth rates.
  17. It is arbitrary to capitalize 100% of R&D and 30% of SG&A expenditures, and no less arbitrary to choose any particular amortization rules. It will be an interesting topic for future research to gauge which metrics perform best in producing a better HML value factor or in predicting future corporate profits, and whether optimal settings for these metrics vary by industry, sector, or country. We find it a striking result that our first crude effort to introduce intangibles into book value leads to a 50% improvement in the efficacy of HML over the past 40 years and a near-doubling of efficacy over the past 30 years.\
  18. Park (2020) also constructs an iHML factor that incorporates intangibles. Also, see Lev and Srivastava (2020).
  19. When we incorporate intangibles into book value, the labels “growth” and “value” become even more inappropriate than they already are. A “cash cow” company, spending nothing on intangibles, may pop into the growth portfolio merely because its book to price is newly lower relative to other companies, which does not mean the company is pursuing growth, only that it is expensive.
  20. The idea of decomposing the return of equity factors into structural and revaluation components was first introduced by Arnott et al. (2016).
  21. We assume that valuations do not exhibit endless bubbles, a more relaxed assumption than the one by Cohen et al. (2003) or Asness et al. (2000) that relative valuations revert to the mean. The mean-reversion assumption would further strengthen the argument.
  22. This narrowing is consistent with the finding of Lev and Srivastava (2020) that migration has slowed. Our decomposition puts a number on how much this slowdown has lowered the returns on value investing—2.2% per year.
  23. We compute the relative valuations each month by constructing a monthly rebalanced version of HML. The signal is the book value of equity from a fiscal year that ended at least six months earlier divided by the market value of equity lagged by six months. This signal matches the signal of the annually rebalanced HML: when HML rebalances at the end of June in year t, the book value of equity is from the fiscal year that ended in year t – 1, and the market value is from the December of year t – 1. Our monthly version of HML matches the standard HML’s valuations at the rebalancing points, while still tracing out valuations at a monthly frequency. Moreover, because most US firms have December fiscal-year ends, value factor (HML) gets predictably cheaper at the June rebalancing date. This rebalancing effect then dissipates over the following year. We remove the resulting seasonalities from valuations by subtracting the calendar-month-specific (e.g., February) mean valuation and adding back the unconditional mean valuation. An alternative method for constructing a timely measure of value (and valuations) is the “HML devil,” which divides the lagged book value of equity with the current price (Asness and Frazzini, 2013).
  24. We report relative-valuation summary statistics, such as median or values at specific percentiles, using the monthly observations of relative valuations.
  25. We obtain the slope by regressing the log valuation ratio on the annualized time trend. We interpret the slope to mean, on average, that the valuation has been declining by about 0.8% per year over the 57-year sample.
  26. If a stock falls 55% and its P/B falls by 64%, we can choose to react emotionally (“Get me out of here!”) or in a contrarian fashion (“I can’t believe how cheap this is!”) or somewhere in between. We lean toward the latter reaction, but we could of course be wrong!
  27. Again, in keeping with the Fama–French methodology, we do this exercise for both large- and small-cap stocks and then equally weight the resulting large and small growth, value, and neutral portfolios.
  28. We do not separately show results for a D/P model because most of the “action” in growth stocks—for over a quarter-century—has been in companies that pay no dividends. Excluding those stocks makes no sense.
  29. This differs from the −6.1% in Table 3 because these results reflect arithmetic returns rather than log returns and a slightly different time span, beginning in January 2007, instead of July 2007.
  30. The relative valuation of iHML moved from the 40th percentile to the 98th percentile over the same 13½-year period. The similarity in the movements in the relative valuations of HML and iHML suggests that the omission of intangible capital from the classical definition of value does not explain why value has become exceedingly cheap relative to growth over the last 13½ years.
  31. Based on unreported results that are available on request.
  32. In the scenario analysis shown in Table 5, we consider movements in an estimated theoretical distribution of relative valuations. We provide additional details in Appendix E.
  33. A slope less than 1.0 would be associated with mean reversion, a slope greater than 1.0 would be associated with momentum, and a slope not significantly different from 1.0 would imply no autocorrelation.
  34. The expected return on HML, applying the accounting identity conditional on a particular draw of revaluation, is

    E[HMLt | Revaluationt] = E[Revaluationt + Profitabilityt + Migrationt | Revaluationt],

    If we use the conditional expectation, it further simplifies to

    E[HMLt | Revaluationt] = Revaluationt + E[Profitabilityt | Revaluationt] + E[Migrationt | Revaluationt],

    that is, in order to estimate the HML return given a particular realization of revaluation, we need to have an expectation of how the profitability and migration terms perform conditional on this revaluation.\
  35. The regression constant term can be viewed as another way of computing the structural alpha. It should resemble the disaggregation in the main body of the article, but there is no reason for it to exactly match.
  36. We also use similar regressions to examine the performance of two alternative value strategies—value relative to neutral and neutral relative to growth—and find that the results are symmetric.
  37. The residuals from the linear regression add to zero by definition. If we condition on the realization of the dependent variable as we do when we select periods based on value’s performance, we bias the estimated intercept. To see why, suppose that the model generating the data is yi = a + b * xi + ei, where ei is an innovation. Suppose further that a = 0 and that the average ei in our sample is zero. If we select observations in which yi < 0, it has to be that either b * xi < 0 or ei < 0. That is, when we condition on the realization of yi, we indirectly condition on the realized value of the innovation, ei. We call this mechanism “oversampling bad luck”: the average ei in the resulting sample is negative. If we take the observations in which yi is negative and estimate a linear regression, the estimated intercept becomes negative; because the linear regression’s residuals add to zero, we push the average negative innovation into the intercept. This problem is akin to the problem that Fama and MacBeth (1973, p. 615) encountered when sorting stocks into portfolios by estimated betas: “Forming portfolios on the basis of ranked 771-reports-of-values-death-beta-hat-i.png thus causes bunching of positive and negative sampling errors within portfolios. The result is that a large portfolio 771-reports-of-values-death-beta-hat-p.png, would tend to overstate the true βp, while a low 771-reports-of-values-death-beta-hat-p.png would tend to be an underestimate.”

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