Relation Between Book-to-Market Ratio and Returns (1992–2000)

The ratio of book equity to market equity has been an interesting player in explaining the factors behind stock returns. As Fama and French (1992) shows us, BE/ME (book-to-market equity ratio) present a strong connection to the cross-section of average stock returns, and Fama and French (1995) further shows its relevance to expected future earnings/profitability of firms. Especially when it comes to value investing, high BE/ME firms could be appealing investments, as Piotroski (2000) uncovers, as long as further fundamental analysis could distinguish financially healthy high BE/ME firms.

This article seeks to look at the aforementioned papers one at a time and draw connections to see what they tell us about the market.

The Cross Section of Expected Stock Returns (Eugene F. Fama and Kenneth R. French)

Background / Assumptions

  • SLB model (asset-pricing model of Sharpe, Lintner, and Black) shows that “market βs suffice to describe the cross-section of expected returns”
  • But over the years, there is piling evidence that size, BE/ME, E/P, and leverage also explain the cross-section of expected returns, in some cases more so than β

Key Findings

  • Relation between average stock returns and β as an individual factor existed in pre-1969 period, but it disappears during 1963–1990 period
  • Size and BE/ME suffice to cover to roles of other variables (E/P and leverage): they “provide a simple and strong characterization of the cross-section of average stock returns for the 1963–1990 period”.

Key Takeaways

  • Relevant factors change over time! As market β ceased to be relevant factor during the 1963–1990 period, same could apply for other factors. This means persistence is also of importance.
  • What do we know about the market through BE/ME? In the rational-market point-of-view, size and BE/ME must reflect the risk factors, such that it captures the cross-section of average returns. In fact, BE/ME “should be a direct indicator of the relative prospects of firms”. If high BE/ME firms and low BE/ME firms could be characterized separately on various economic fundamentals — especially earnings — then this argument gains persuasiveness, as we would see in Fama and French (1995).
  • In the irrational-market point-of-view, the results of the study could be summarized as the market overreacting/underreacting. But in this case, the persistence of the study is more suspect, as the market could react more accordingly with the results of the study.

Size and Book-to-Market Factors in Earnings and Returns (Eugene F. Fama and Kenneth R. French)

Background / Assumptions

  • Rational stock price reflects current earnings + expected future earnings
  • If size and BE/ME proxy for risk, then they must also proxy for unexpected changes in earnings

Key Findings

  • “BE/ME is a stronger indicator of profitability than size”
  • High BE/ME firms are persistently financially distressed. Low expectation of earnings leads to low market equity.
  • There does exist size and BE/ME factors in earnings, as they do in returns. But while market&size factors in earnings explain the same factors in returns, the same cannot be said for BE/ME (due to suspected noise)

Key Takeaways

  • Again, factors change over time. Relation between size and profitability weakens after 1980.
  • It seems that the cross-section of average returns could be explained through BE/ME because of efficient-asset-pricing theory, as BE/ME is a strong indicator of profitability, and therefore provides a sufficient guideline for expected stock pricing and entailed risk
  • But we still lack evidence to determinedly set the economic interpretation of this behavior.

Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers (Joseph D. Piotroski)

Background / Assumptions

  • The success of high BE/ME investment strategy relies on a few strong performers. In fact, “less than 44% of all high BM firms earn positive market-adjusted returns in the two years following portfolio formation”.
  • Value stocks (high BE/ME stocks) are usually neglected by investors and analysts alike.
  • Financial statements are the most credential source to analyze value stock firms
  • High BE/ME firms are financially distressed (remember this was established by Fama and French (1995)). Thus valuation focuses on fundamentals.

Key Findings

  • Differentiating between healthy value stocks and struggling ones through financial statements alone is possible. In fact, buying and shorting at the same time generates a 23% annual return in the 1976–1996 period.
  • Piotroski (2000) does not provide the most optimal model to predict the performance of value firms, yet it does prove that fundamental analysis through financial statements could be a useful strategy
  • Financial statement analysis is most effective when applied to small, medium-sized, or neglected firms, and is not dependent on size (ME).
  • “One-sixth of the annual return difference… is earned over the four three-day periods surrounding these earnings announcements”

Key Takeaways

  • First, while Fama and French (1992) argue that value stocks work because of their financial stress and the risk associated with it, Piotroski (2000) shows conversely that healthy firms among high BE/ME firms generate strongest returns.
  • The last two Key Findings suggest that market sluggishness/underreaction is the reason for this strategy to work
  • If this strategy’s effectiveness is indeed due to market inefficiency, then the persistence of the strategy’s performance could come under scrutiny
  • The most optimal way for high BE/ME firm valuation has not been stated… The study only lights a view that such model could exist


Efficient market? Inefficient market?

Fama and French (1992) and Fama and French (1995) put a lot of effort in trying to explain the economic background behind the evident relation between BE/ME and average stock return, but the results are inconclusive. While we gain a lot of insight into the relation between various factors, and earnings and returns, it is hard to tout either market efficiency or inefficiency as the force at work. What it seems to show, rather, especially when considering Piotroski (2000), is that the market is “efficiently inefficient”, a term I will borrow from Pedersen (2015).

Fundamental Analysis & Where ML Fits In

Piotroski (2000) presents a strategy based on fundamental analysis of financial statements that shows promising returns. That this strategy works on a few (exactly 12) fundamental signals that are not too hard to derive suggest an interesting ground for research. As, well, the current year is 2020, which is 20 years well past the publication of Piotroski (2000), I am most definitely certain that there will already be abundant related studies that cover that ground of interest. Still, I cannot help but notice that the field of using a series of features to predict a certain value is what machine learning excels at. Especially when we do not know which factors contribute the most to superior prediction, using machine learning algorithms such as random forest regression, neural network, linear regression, etc can all come in handy. Even when keeping in mind that the persistency of Piotroski (2000) could be suspect, this does tell me in what ways ML could fit in the area of fundamental analysis.

Relevant Factors Change

It’s also worth noticing how relevant factors keep changing over time. As market conditions, industry rules, etc change, so do the relevant factors. Although this sounds obvious, it wasn’t so obvious to me when I started studying. Some factors might be universally relevant, winning against the tide of time, but the degree of that relevance will change…

Pitfalls to Avoid When Handling Data

The most dangerous thing to do when analyzing data is to take a biased database and derive a biased result. The steps that Fama takes to avoid these pitfalls is worth noting. For example, Fama takes extra care to avoid look-ahead bias and survival bias while using CRSP-COMPUSTAT data. As a beginner in, well, anything related to finance, I would find these tips very useful when drafting my own data project based on a relevant subject.

  1. Fama, Eugene F. and French, Kenneth R., 1992, The cross-section of expected stock returns, Journal of Finance 47, 427–465
  2. Fama, Eugene F. and French, Kenneth R., 1995, Size and book-to-market factors in earnings and returns, Journal of Finance 50, 131–155
  3. Piotroski, Joseph D., 2000, Value investing: the use of historical financial statement information to separate winners from losers, Journal of Accounting Research 38




Columbia University student, CS. Former iOS developer, presently pursuing career in data science.

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Yes to capitalism, au contraire, mon frère?

Occupy Starfish

The Wake-Up Call | How Can Entrepreneurs Fix Government

Why Idaho Needs $15 An Hour

Socialists and Systems-Thinkers Can Co-create a Better World.

Big Short Project Proposal

Schneider Electric Infrastructure Limited (SCHNEIDER.NS) Moves 1.19%

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Seouk Jun Kim

Seouk Jun Kim

Columbia University student, CS. Former iOS developer, presently pursuing career in data science.

More from Medium

1: Engineering Serendipity: Leveraging Network Analysis to cultivate vibrant Startup Ecosystems.

3 Ways That Machine Learning Applications Can Reduce Home Care Workforce Attrition

Tipping the Circle of Life — Spark Perception

7 reasons why a Data Scientist must play poker — Bright