Value (Book-to-Market) Anomaly

The Book-to-Market effect is probably one of the oldest effects which has been investigated in financial markets. It compares book value of company to price of the stock - inverse of P/B ratio. The bigger the book-to-market ratio is, the more fundamentally cheap is the investigated company. Book-to-Market wasn‘t even considered as a market anomaly at the beginning of the century when Ben Graham famously popularized its use. The ratio lost some of it popularity when the Efficient Market Theory and CAPM became main Wall Street theories, but it gained back its position after several studies have shown the rationality of using it. This anomaly is well-described in the classical Fama and French research paper (1993). Additional details are calculated from data which are presented in Kenneth French data library (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). Pure value effect portfolios are created as long stocks with the highest Book-to-Market ratio and short stocks with the lowest Book-to-Market ratio. However, this pure value effect has substantial drawdowns with more than 50% drawdown in the 1930s. Value factor is still a strong performance contributor in long only portfolios (formed as long stocks with highest Book-to-Market ratio without shorting stocks with low Book-to-Market ratios).

Fundamental reason

One explanation is that investors overreact to growth aspects for growth stocks, and value stocks are therefore undervalued. According to some academics, the ratio of market value to book value itself is a risk measure, and therefore the larger returns generated by low MV/BV stocks are simply a compensation for risk. Low MV/BV stocks are often those in some financial distress.

Markets traded
equities
Confidence in anomaly's validity
Strong
Notes to Confidence in anomaly's validity
Period of rebalancing
Yearly
Notes to Period of rebalancing
Number of traded instruments
1000
Notes to Number of traded instruments
Complexity evaluation
Complex strategy
Notes to Complexity evaluation
Strategy complexity depends on number of stocks investor wishes to include into his/her portfolio, as strategy could be much simpler for execution if investor picks less stocks.
Financial instruments
stocks
Backtest period from source paper
1927-2010
Indicative performance
11.34%
Notes to Indicative performance
per annum, benchmark performance 9,79%
Estimated volatility
26.62%
Notes to Estimated volatility
benchmark volatility 20,10%
Maximum drawdown
-81.98%
Notes to Maximum drawdown
benchmark drawdown -85,67%
Sharpe Ratio
0.28

Keywords:

value, stock picking, financial statements effect

Simple trading strategy

The investment universe contains the top 20% biggest companies (based on market capitalization) on NYSE, AMEX, and NASDAQ. Quintile portfolios are then formed based on the Book-to-Market ratio and the highest quintile is held for one year (portfolio is weighted based on market cap.) after which the portfolio is rebalanced.

Source Paper

Fama, French: The Cross-Section of Expected Stock Returns
http://www.bengrahaminvesting.ca/Research/Papers/French/The_Cross-Section_of_Expected_Stock_Returns.pdf
Abstract:
Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market beta, size, leverage, book-to-market equity and earnings price ratios. Moreover, when the tests allow for variation in beta that is unrelated to size, the relation between market beta and average return is flat, even when beta is the only explanatory variable.

Other Papers

Gray: The Quantitative Value Investing Philosophy - Buy the Cheapest, Highest Quality Value Stocks
http://blog.alphaarchitect.com/2014/10/07/the-quantitative-value-investing-philosophy
Abstract:
Benjamin Graham, who first established the idea of purchasing stocks at a discount to their intrinsic value more than 80 years ago, is known today as the father of value investing. Since Graham’s time, academic research has shown that low price to fundamentals stocks have historically outperformed the market. In the investing world, Graham’s most famous student, Warren Buffett, has inspired legions of investors to adopt the value philosophy. Despite the widespread knowledge that value investing generates higher returns over the long-haul, value-based strategies continue to outperform the market. How is this possible? The answer relates to a fundamental truth: human beings behave irrationally. We are influenced by an evolutionary history that preserved traits fitted for keeping us alive in the jungle, not for optimizing our portfolio decision-making ability. While we will never eliminate our subconscious biases, we can minimize their effects by employing quantitative tools.

Chaves, Hsu, Kalesnik, Shim: Cheaper than Value
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1940504
Abstract:
Value strategies appear to provide an extra source of return. Academic literature provides two competing theories on what drives the value premium: exposure to risk factors or mispricing of the securities. Existing empirical studies have not conclusively rejected one in support of the other. Using Fama and MacBeth (1973) regressions and extensions of the portfolio tests based on Daniel and Titman (1997), we provide evidence that the book-to-market characteristic largely subsumes the loading on the value factor (HML) as a variable that explains the cross-section of stock returns. We improve the power of these tests by using daily data for estimating factor loadings and by using data from 23 developed countries going back more than 30 years. Given these results, we conclude mispricing is likely a more significant portion of the value premium. There appears to be a free lunch after all.

Damodaran: Value Investing: Investing for Grown Ups?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2042657
Abstract:
Value investors generally characterize themselves as the grown ups in the investment world, unswayed by perceptions or momentum, and driven by fundamentals. While this may be true, at least in the abstract, there are at least three distinct strands of value investing. The first, passive value investing, is built around screening for stocks that meet specific characteristics - low multiples of earnings or book value, high returns on projects and low risk - and can be traced back to Ben Graham’s books on security analysis. The second, contrarian investing, requires investing in companies that are down on their luck and in the market. The third, activist value investing, involves taking large positions in poorly managed and low valued companies and making money from turning them around. While value investing looks impressive on paper, the performance of value investors, as a whole, is no better than that of less “sensible” investors who chose other investment philosophies and strategies. We examine explanations for why "active" value investing may not provide the promised payoffs.

Asness, Frazzini: The Devil in HML's Details
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2054749
Abstract:
This paper challenges the standard method for measuring “value” used in academic work on factor pricing and behavioral finance. The standard method calculates book-to-price (B/P) at portfolio formation using lagged book data, aligns price data using the same lag (ignoring recent price movements), and hold these values constant until the next rebalance. We propose two simple alternatives that use timely price data while retaining the necessary lag for measuring book. We construct portfolios based on the different measures for a US sample (1950-2011) and an International sample (1983-2011). We show that B/P ratios based on timely prices better forecast true (unobservable) B/P ratios at fiscal yearend. Value portfolios based on the most timely measures earn statistically significant alphas ranging between 305 and 378 basis point per year against a 5-factor model itself containing the standard measure of value, as well as market, size, momentum and a short term reversal factor.

Israel, Moskowitz: The Role of Shorting, Firm Size, and Time on Market Anomalies
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2089466
Abstract:
We examine the role of shorting, firm size, and time on the profitability of size, value, and momentum strategies. We find that long positions comprise almost all of size, 60% of value, and half of momentum profits. Shorting becomes less important for momentum and more important for value as firm size decreases. The value premium decreases with firm size and is weak among the largest stocks. Momentum profits, however, exhibit no reliable relation with size. These effects are robust over 86 years of U.S. equity data and almost 40 years of data across four international equity markets and five asset classes. Variation over time and across markets of these effects is consistent with random chance. We find little evidence that size, value, and momentum returns are significantly affected by changes in trading costs or institutional and hedge fund ownership over time.

Frazzini, Israel, Moskowitz: Trading Costs of Asset Pricing Anomalies
http://www.gsb.stanford.edu/sites/default/files/documents/fin_12_12_moskowitz.pdf
Abstract:
Using nearly a trillion dollars of live trading data from a large institutional money manager across 19 developed equity markets over the period 1998 to 2011, we measure the real-world transactions costs and price impact function facing an arbitrageur and apply them to size, value, momentum, and short-term reversal strategies. We find that actual trading costs are less than a tenth as large as, and therefore the potential scale of these strategies is more than an order of magnitude larger than, previous studies suggest. Furthermore, strategies designed to reduce transactions costs can increase net returns and capacity substantially, without incurring significant style drift. Results vary across styles, with value and momentum being more scalable than size, and short-term reversals being the most constrained by trading costs. We conclude that the main anomalies to standard asset pricing models are robust, implementable, and sizeable.

Liang: Performance of Value Investing Strategies in Japan’s Stock Market
http://vpcenter.ust.hk/public/files/Performance%20of%20Value%20Investing%20Strategies%20JP_2013-07-05.pdf
Abstract:
This white paper examines the performance of several value investing strategies based on various quantitative value measures of stocks in the Japanese stock market. These strategies significantly outperformed the aggregate stock market in the period from January 1975 to December 2011. In addition, they generated promising profits in the long-term bear market in the 1990-2011 period when the stock market dropped 62.21%.

Lakonishok, Schleifer, Vishny: Contrarian Investment Extrapolation and Risk
https://www.nber.org/papers/w4360
http://www.lsvasset.com/pdf/Contrarian-Investment-Extrapolation-and-Risk.pdf
Abstract:
For many years, scholars and investment proffesionals have argued that value strategies outperform the market. These value strategies call for buying stocks that have low prices relative to earnings, dividends, book assets, or other measures of fundamental value. While there is some agreement that value strategies produce higher returns, the interpretation of why they do so is more controversial. This article provides evidence that value strategies yield higher returns because these strategies exploit the suboptimal behavior of the typical investor and not because these strategies are fundamentally riskier.

Cakici, Tan: Size, Value, and Momentum in Developed Country Equity Returns: Macroeconomic and Liquidity Exposures
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362521
Abstract:
The paper investigates value and momentum factors in 23 developed international stock markets. We find that typically value and momentum premia are smaller and more negatively correlated for large market capitalization stocks relative to small. Momentum factors are more highly correlated internationally relative to value. We provide international evidence on three sets of risk exposures of value and momentum returns: macroeconomic risk, funding liquidity risk, and stock market liquidity risk. We find that value returns are typically lower prior to a recession while momentum returns often exhibit little sensitivity. Value returns are typically lower in times of poor funding liquidity, whereas, with notable exceptions, momentum returns are typically unaffected. Lastly, for almost all countries, value returns are high in poor stock market liquidity conditions. The same result appears to be true for momentum in Asia Pacific, North America, and largely in Europe.

Jensen-Gaard: Equity Investment Styles - Recent evidence on the existence and cyclicality of investment styles
http://studenttheses.cbs.dk/xmlui/bitstream/handle/10417/4053/christian_jensen-gaard.pdf?sequence=1
Abstract:
Over the past two decades, financial academics and investment professionals have documented several anomalies on the global financial markets. A subset of these anomalies, known as equity style strategies, has been shown to yield substantial excess returns, which cannot be explained by traditional finance theory. However, in the light of the financial turmoil during the 2000s, several studies have shown considerable changes in the magnitude of the style-based strategy premiums. The purpose of this thesis is to investigate whether recent data support the continued existence of these premiums and evaluate how these premiums fluctuate in relation to the economic cycle. Furthermore, this thesis provides practical advice on how investors can apply the findings.

Hsu: Value Investing: Smart Beta vs. Style Indices
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2477293
Abstract:
The active shares of traditional value style indices are dominated by industry bets. They also capture less than the entire value premium because, weighting constituents on the basis of capitalization, they tend to hold large positions in overpriced stocks and small positions in underpriced (i.e., value) stocks. Smart beta strategies, in comparison, are better diversified, and they systematically buy low and sell high by periodically rebalancing to non-price related target weights. In addition to exploiting mean reversion in prices, smart beta strategies profit from mean reversion in the value premium by effectively implementing a dollar cost averaging program.

Hsu, Myers, Whitby: Timing Poorly: A Guide to Generating Poor Returns While Investing in Successful Strategies
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2560434
Abstract:
Value investing is viewed as a historically successful investment strategy. The literature generally agrees on the robustness of the strategy but disagrees on the explanations for the success. While the empirical research focuses exclusively on the time-series returns — or the buy-and-hold return — of a value portfolio, the investor experience is, of course, driven by the internal rate of return (IRR) — or the dollar-weighted average return. Although the buy-and-hold average portfolio return may be the proper way to document the anomaly, the dollar-weighted average return can shed light on some interesting questions which cannot be addressed by analyzing the buy-and-hold returns. In particular, examining the dollar-weighted returns allows us to ask whether investors have actually generated superior IRR consistent with the reported buy-and-hold outperformance of value strategies.

Leshem, Goldberg, Cummings: Optimizing Value
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2603308
Abstract:
We investigate how the choice of accounting metric and implementation affect the performance of a value strategy. We find that:
- Strategies based on book-to-price (B/P) and earnings-to-price (E/P) ratios delivered a positive premium over the 60-year horizon from 1951 to 2013.
- E/P had higher return and lower risk than B/P over the full horizon.
- However, B/P outperformed E/P between 1963 and 1990, and that was the basis of the landmark study establishing B/P as the academic standard.
- Strategies based on a blend of B/P and E/P outperformed both single-metric strategies during most 10-year periods between 1973 and 2013.
- Over the same horizon, optimized value strategies had lower tracking error, lower turnover, and a higher information ratio than “rank-and-chop” strategies, which weight high-percentile value stocks by capitalization.
- Sector constraints raised both the Sharpe ratio and the information ratio of an optimized blended-value strategy.

Fan, Opsal, Yu: Equity Anomalies and Idiosyncratic Risk Around the World
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2611047
Abstract:
In this study, we examine how idiosyncratic risk is correlated with a wide array of anomalies, including asset growth, book-to-market, investment-to-assets, momentum, net stock issues, size, and total accruals, in international equity markets. We use zero-cost trading strategy and multifactor models to show that these anomalies produce significant abnormal returns. The abnormal returns vary dramatically among different countries and between developed and emerging countries. We provide strong evidence to support the limits of arbitrage theory across countries by documenting a positive correlation between idiosyncratic risk and abnormal return. It suggests that the existence of these well-known anomalies is due to idiosyncratic risk. In addition, we find that idiosyncratic risk has less impact on abnormal return in developed countries than emerging countries. Our results support the mispricing explanation of the existence of various anomalies across global markets.

Moskowitz: Asset Pricing and Sports Betting
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2635517
Abstract:
I use sports betting markets as a laboratory to test behavioral theories of cross-sectional asset pricing anomalies. Two unique features of these markets provide a distinguishing test of behavioral theories: 1) the bets are completely idiosyncratic and therefore not confounded by rational theories; 2) the contracts have a known and short termination date where uncertainty is resolved that allows any mispricing to be detected. Analyzing more than a hundred thousand contracts spanning two decades across four major professional sports (NBA, NFL, MLB, and NHL), I find momentum and value effects that move betting prices from the open to the close of betting, that are then completely reversed by the game outcome. These findings are consistent with delayed overreaction theories of asset pricing. In addition, a novel implication of overreaction uncovered in sports betting markets is shown to also predict momentum and value returns in financial markets. Finally, momentum and value effects in betting markets appear smaller than in financial markets and are not large enough to overcome trading costs, limiting the ability to arbitrage them away.

Lambert, Fays, Hubner: Size and Value Matter, But Not the Way You Thought
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2647298
Abstract:
Fama and French factors do not reliably estimate the size and book-to-market effects. We demonstrate inconsistent pricing of those factors in the US stock market. We replace Fama and French’s independent rankings with the conditional ones introduced by Lambert and Hübner (2013). Controlling ex-ante for noise in the estimation procedure, we have been able to highlight a much stronger book-to-market and size effects than have conventionally been documented similar to Asness et al. (2015). As a significant related outcome, the alternative risk factors have been found to deliver less specification errors when used to price investment portfolios.

Qiao: Conditional Market Exposures of the Value Premium
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2687528
Abstract:
Value strategies exhibit a large positive beta if contemporaneous market excess returns are positive, and a small beta if contemporaneous market excess returns are negative. Value also has a large positive beta after bear markets, but a small beta after bull markets. These facts hold for equity-value strategies in 21 countries, and to a lesser extent for three non-equity-value strategies. Betas conditional on contemporaneous market returns are able to capture expected return variation associated with the book-to-market ratio. These betas partially explain the value premium, and are related to a larger cash-flow risk of value strategies.

Lambert, Hubner: Size Matters, Book Value Does Not! The Fama-French Empirical CAPM Revisited
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2506690
Abstract:
The Fama and French (F&F) factors do not reliably estimate the size and book-to-market effects. Our paper shows that the former has been underestimated in the US market while the latter overestimated. We do so by replacing F&F's independent rankings by the conditional ones introduced by Lambert and Hubner (2013), over which we improve the sorting procedure. This new specification better reflects the properties of the individual risk premiums. We emphasize a much stronger size effect than conventionally documented. As a major related outcome, the alternative risk factors deliver less specification errors when used to price passive investment indices.

Golubov, Konstantinidi: A Closer Look at the Value Premium: Evidence from a Multiples-Based Decomposition
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2702822
Abstract:
We use industry multiples-based market-to-book decomposition of Rhodes-Kropf, Robinson and Viswanathan (2005) to study the value premium. The market-to-value component drives all of the value strategy return, while the value-to-book component exhibits no return predictability in both portfolio sorts and firm-level return regressions controlling for other stock characteristics. Prior results in the literature linking value/glamor to expectational errors and limits to arbitrage hold due to the market-to-value component, whereas the results linking market-to-book to cashflow risk, exposure to investment-specific technology shocks, and analyst’s risk ratings hold only for the unpriced value-to-book. Overall, our evidence points towards the mispricing explanation for the value premium.

Kok, Ribando, Sloan: Facts About Formulaic Value Investing
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716542
Abstract:
The term ‘value investing’ is increasingly being adopted by quantitative investment strategies that use ratios of simple fundamental metrics (e.g., book value, earnings) to market price. A hallmark of such strategies is that they do not involve a good faith effort to determine the intrinsic value of the underlying securities. We document two facts about such strategies. First, we see little compelling evidence that such strategies deliver superior investment performance for U.S. equities. Second, instead of identifying undervalued securities, these strategies typically identify firms with temporarily inflated accounting numbers. We argue that these strategies should not be confused with value strategies that are based on a good faith effort to determine the intrinsic value of the underlying securities.

Cakici, Tang, Yan: Do the Size, Value, and Momentum Factors Drive Stock Returns in Emerging Markets?
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2727257
Abstract:
This paper investigates the size, value and momentum effects in 18 emerging stock markets during the period 1990−2013. We find that size and momentum strategies generally fail to generate superior returns in emerging markets. The value effect exists in all markets except Brazil, and it is robust to different periods and market conditions. Value premiums tend to move positively together across different markets, and such inter-market co-movements increase overtime and during the global financial crisis.

de Carvalho, Xiao, Soupe, Dugnolle: Diversify and Purify Factor Premiums in Equity Markets
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2894171
Abstract:
In this paper we consider the question of how to improve the efficacy of strategies designed to capture factor premiums in equity markets and, in particular, from the value, quality, low risk and momentum factors. We consider a number of portfolio construction approaches designed to capture factor premiums with the appropriate levels of risk controls aiming at increasing information ratios. We show that information ratios can be increased by targeting constant volatility over time, hedging market beta and hedging exposures to the size factor, i.e. neutralizing biases in the market capitalization of stocks used in factor strategies. With regards to the neutralization of sector exposures, we find this to be of importance in particular for the value and low risk factors. Finally, we look at the added value of shorting stocks in factor strategies. We find that with few exceptions the contributions to performance from the short leg are inferior to those from the long leg. Thus, long-only strategies can be efficient alternatives to capture these factor premiums. Finally, we find that factor premiums tend to have fatter tails than what could be expected from a Gaussian distribution of returns, but that skewness is not significantly negative in most cases.

Folkinshteyn, Meric, Meric: Value and Growth Stock Price Behavior During Stock Market Declines
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2814956
Abstract:
Using data for five major stock market declines during the 1987-2008 period, this paper provides evidence that value stocks are generally less sensitive to major stock market declines than growth stocks, controlling for beta, firm size, and industry group. Further analysis using several hundred different significant market move events between 1980 and 2015 confirms the observation that value stocks tend to outperform both the market average and growth stocks during market declines. The implication for investment practitioners is that following a value strategy does not lead one to assume greater sensitivity to unfavorable market conditions.

Asness, Frazzini, Israel, Moskowitz: Fact, Fiction, and Value Investing
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2595747
Abstract:
Value investing has been a part of the investment lexicon for at least the better part of a century. In particular the diversified systematic “value factor” or “value effect” has been studied extensively since at least the 1980s. Yet, there are still many areas of confusion about value investing. In this article we aim to clarify many of these matters, focusing in particular on the diversified systematic value strategy, but also exploring how this strategy relates to its more concentrated implementation. We highlight many points about value investing and attempt to prove or disprove each of them, referencing an extensive academic literature and performing simple tests based on easily accessible, industry-standard public data.

Herskovic, Kind, Kung: Size Premium Waves
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3220825
Abstract:
This paper examines the link between microeconomic uncertainty and the size premium across different frequencies in an investment model with heterogeneous firms. We document that the observed time-varying dispersion in firm-specific productivity can account for a large size premium in the 1960's and 1970's, the disappearance in the 1980's and 1990's, and reemergence in the 2000's. Periods with a large (small) size premium coincide with high (low) microeconomic uncertainty. During episodes of high productivity dispersion, small firms increase their exposure to macroeconomic risks. Our model can also explain the strong positive low-frequency co-movement between size and value factors, but a negative relation with the market factor.

Hypothetical future performance

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