web analytics

Reclaiming Value & Restoring its Place in Active Management

Exploiting the Valuation/Cheapness Gap

By: Derek Bergen, CFA and John Holt, CFA

Applied Finance has recently unveiled the Valuation vs. cheapness investing concept.  The primary focus of this quarter’s write-up expounds on this broader theme that Applied Finance will continue to champion as long as there is widespread embrace that price multiples are reasonable proxies for intrinsic value. We will further elaborate on this theme over the course of this year, but for our first study, we wanted to simply emphasize single-factor observations on Applied Finance’s Percent to Target metric vs. Book to Price.

The insights delivered by this study are truly fascinating.  On one hand, the evidence that price multiples are incomplete in forming a definition of value is obvious, and this should align with intuition.  If broader market participants heed this advice, this study will have been a noble effort to improve the flow of accounting information and analyst forecasts into market prices.  On the other hand, there has never been obvious justification for measures of cheapness to define value in the first place.  Many investors simply use these factors out of convenience or tradition, while many others invest in products built upon them with little understanding of the classification error they introduce.  If that behavior likely continues, this study will provide succinct evidence to articulate the merits of Applied Finance’s investment approach.

Charting our research goals over the course of this year, we also plan on exploring quality factors and asset pricing models utilizing our database.  We plan to use this to fully articulate the dominance of economically-derived factors over commonly-used alternatives rooted in tradition and accounting convention.

Exploiting the Valuation/Cheapness Gap:
Reclaiming Value & Restoring its Place in Active Management

Market participants have unrealistic expectations for price multiples.  A simple ratio of a firm’s common stock as a percentage of market cap is expected to simultaneously provide insight into leverage ratios, style classification, asset pricing models, and intrinsic value.  It is also increasingly accepted that, despite this one-dimensional worldview being trumpeted by a significant number of academics and practitioners, markets are supposedly efficient to a degree that investors should not even attempt to outperform.

Despite this widespread application of book to price ratios in equity research and index construction, little thought is expended on the actual performance of the book to price factor and the leverage, style or valuation misclassification that becomes rampant as firms repurchase shares, causing book equity to become an even less economically reliable proxy for the intrinsic value of a firm’s equity base.  The assumption that this simple ratio can be the basis of a comprehensive thesis for competing applications in the investment landscape should appear absurd; that this has become dominant thought across the industry can only be a function of limited curiosity on the subject.

It has become standard industry practice to blur the lines between value and valuation despite all of the shortcomings of commonly-used price multiples.  Many research shops with a self-proclaimed value focus proxy multiples for a more robust estimate of intrinsic value due to their own data limitations; their seasons of underperformance cast doubt on the merits of an authentic value-based investing approach.  Research shops focused on alternative factors use the low performance hurdle provided by book to price to claim these alternatives are more robust than value in stock selection.  The largest institutions echo these observations to infer that it is reasonable to accept the cap-weighted constraints of significant AUM levels (while also referring to this approach as “value-weighted”). Everyone wants to claim or discredit value, but very few have the research capacity to study a robust version of valuation!

Applied Finance intends to reclaim intrinsic value from its obfuscated position in current practice.  To help differentiate our intrinsic value data from industry convention, we will simply refer to “price-to-something”-based market multiples as measures of cheapness. It should not be controversial to claim that a comprehensive estimate of firm value unbiased by accounting convention will dominate a simple multiple.  Applied Finance has been delivering live intrinsic value databases on a weekly basis since the mid-1990s.  We can use this point-in-time dataset to differentiate the merits of an approach that defies commonly-accepted industry convention.

The evidence is compelling.  A comprehensive estimate of intrinsic value does, in fact, dominate measures of cheapness. This theme is observable in broad markets over the last 21 years, as well as in large and small cap investable universes.  The opportunity to exploit classification error will likely persist as long as passive strategies are prevalent, index providers use measures of cheapness to form style methodologies, and academics champion these same measures of cheapness to accommodate research horizons back to the 1960s.

Executive Summary:

  • Cheapness measures are commonly used as proxies for valuation in both academic research and practice.
  • Performance comparison for portfolios formed on a valuation preference or cheapness preference when classification error exists can be used to determine which classification system best aligns with future stock performance.
  • A sizable performance gap is evident between a portfolio formed on a valuation preference from both a return and risk-adjusted return basis. Investors benefit from defying multiple-based industry convention with a more robust measure of intrinsic value.
  • The valuation vs. cheapness theme can form the basis of a unique large cap US equity strategy. Additional modifications to enhance precision of misclassification claims lead to improved diversification and reduced turnover.

Defining the Measures of Valuation and Cheapness

To develop claims of misclassification for the purposes of performance comparison, we first must define our measures of cheapness and valuation.  It is commonly assumed (and even clearly stated in the index methodology of Russell) that book to price is the basis of “value” definitions, so we will use this metric as our definition of cheapness.  Applied Finance can leverage our point-in-time client database to form monthly book to price portfolios.

Applied Finance will leverage the Percent to Target – Current metric that reflects our primary intrinsic value thesis to represent valuation.  As a reminder, this factor assumes the immediate decay of current calendar year economic profitability over a firm-specific competitive advantage period, while incorporating diminishing rates of organic growth and firm-specific discount rates to create a systematic approach to discounted cash flow models.

Active managers are not subject to minimal modifications of cap-weighted constraints that minimize active share.  Studying portfolios formed on an equal-weight in sector basis against cap-weighted benchmarks can help managers determine if robust returns of a factor are possible on a risk-adjusted basis in a portfolio construct more consistent with active management.  Portfolio returns in this study reflect total returns of an equal-weight in sector approach, while risk-adjusted returns are based on tracking error and covariance to passive benchmarks.(1)

Russell 3000 Index ®: Book to Price and Percent to Target, 9/30/98 to 12/31/19

AFG Research Database: Russell 3000 Book to Price LFY & Percent to Target – Current
Sector-Ranked Quintiles from 9/30/98 to 12/31/19 (Equal-Weight in Sector Returns) | All Sectors
Jump to Definitions 

Book to Price as a stand-alone factor offers underwhelming performance, especially on a risk-adjusted basis.  While the top three quintiles of cheap stocks have mildly outperformed the bottom two quintiles of expensive stocks over the last 21 years, the top quintile is associated with a significantly higher beta coefficient to deliver negative alpha.  Most other measures of risk-adjusted returns for the top quintile appear less attractive than the overall benchmark, implying higher returns are more than offset by increased volatility and beta.  Most glaringly, the top quintile of book to price has lagged the overall Russell 3000 index by more than 143% on a cumulative basis over the last decade!  Despite mild outperformance over long-term time horizons, the high beta, high tracking error and low risk-adjusted returns of the top quintile of book to price serve as a logical rationale against the “deep value” investment style when value is inappropriately defined with an inadequate measure of cheapness.

Recasting this table based on Applied Finance’s measure of intrinsic value, or Percent to Target – Current, delivers much more robust returns between the top and bottom quintiles.  While top quintile stocks with this metric are also associated with inflated betas and increased tracking error, the top half and top quintile perspectives deliver attractive returns per unit of risk in excess of benchmark levels.  This factor also drastically outperforms corresponding quintiles under a book to price convention.

It should not be provocative to claim that Applied Finance’s approach will lead to a more reliable estimate of firm value compared to the book equity delivered by accounting convention.  Applied Finance posits that exploiting this information gap created by cheapness misclassification can deliver outperformance without assuming commensurate levels of volatility, beta, and tracking error.  We we will explore this theory in more detail on the next page.

(1)Note that cap-weighted portfolios tend to lag equal-weighted portfolios over long horizons.  This is generally attributable to the small cap premium.

Exploiting the Valuation/Cheapness Gap

Overlaying measures of valuation and cheapness into a 5×5 grid of independently ranked variables on a quintile basis clearly highlights the dominance of measures of intrinsic value compared to simple measures of cheapness.

To articulate this claim, we can first display the annualized return spreads from all 25 portfolios formed on screens based on quintile classification provided by Percent to Target – Current and Book to Price LFY relative to the annualized total returns delivered by the Russell 3000 index over our study time horizon.  For this exercise, we will ignore the stocks where the valuation and cheapness factors agree.  Instead, we will focus on classification error between each approach and form two portfolios: the first on stocks that are preferred by intrinsic value and the second on stocks that are preferred by measures of cheapness.  We will refer to these portfolios as “Valuation Preference” and “Cheap Preference” for the remainder of this research article.

In the first study, we will include all stocks with any level of quintile classification error between valuation and cheapness.  In the table to the upper right, the 5×5 baskets included in the Valuation Preference portfolio are highlighted in light green, while the 5×5 baskets included in the Cheap Preference are highlighted in light red to further clarify how the Valuation/ Cheapness gap is defined at various quintile delta levels.

Two basic observations are material:  (1) on a returns-only basis, the Valuation Preference portfolio outperforms the Cheap Preference portfolio by 4.0% per year, and (2) more than 67% of the Russell 3000 forecast universe reflect a classification error of at least one quintile when cheapness is used as a proxy for valuation.  In other words, there appears to be a significant structural gap in returns unexplained by traditional price multiple definitions.

We can further refine this claim through the lens of risk-adjusted returns. Valuation Preference offers a significantly higher information ratio and improved risk-adjusted returns compared to the overall index.  Meanwhile, the Cheap Preference portfolio delivers lower returns accompanied by higher betas relative to the Valuation Preference portfolio, which translates to negative alpha and risk-adjusted returns below benchmark levels.

Jump to Definitions 

Widening the Valuation/Cheapness Gap

We can further measure performance with an expanded tolerance of classification error; in the second version of this test we limit portfolios to stocks that have classification error of at least two quintiles between valuation and cheapness measures.  These portfolios still cover 32% of the Russell 3000 forecast universe, but reflect a return spread of nearly 6.2% per year between Valuation Preference and Cheap Preference.  Risk-adjusted returns clearly favor Valuation Preference, as the Cheap Preference now has negative information ratios, significantly higher beta and negative alpha.

Jump to Definitions 

A final version of the single-factor Valuation/Cheapness gap further expands the misclassification tolerance to only include stocks with classification error of at least three quintiles. This extreme definition of classification error still includes roughly 14% of Applied Finance’s forecast universe in the Russell 3000, but the gap in returns between Valuation Preference and Cheap Preference portfolios increases to more than 10% per year!

AFG Research Database: Russell 3000 Book to Price LFY & Percent to Target – Current
Sector-Ranked Quintiles from 9/30/98 to 12/31/19 (Equal-Weight in Sector Returns) | All Sectors
Jump to Definitions 

Valuation Preference outperformance and risk-adjusted returns are fairly consistent across the Quintile Delta >=1, Quintile Delta >=2 and Quintile Delta >= 3 approaches. Beta mildly increases with each widening of the acceptable error tolerance, while information ratios, downside tracking error, and measures of alpha or return per unit of risk are fairly stable.  Cheap Preference, on the other hand, delivers drastic performance deterioration as the error tolerance widens.  Price multiple axioms classify these types of stocks as “value traps”, but this analysis provides evidence that these stocks are better classified as “cheapness traps”, where high book to price ratios are not supported by an intrinsic value thesis.

Valuation/Cheapness Gap in Large & Small Markets

Using the same methodology for the Russell 3000 study, we can recreate the Cheap Preference and Valuation Preference portfolios across varying levels of classification error tolerance in a Russell 1000 and Russell 2000 context.  The themes from a broad market approach are further affirmed in both a large cap and small/mid cap context: classification error is rampant and risk-adjusted outperformance is possible by investing in stocks in the Valuation Preference portfolio.  This performance gap is just shy of 3% in the Russell 1000 when all error is included in the construction of preference portfolios.  The gap expands to 4.1% when classification error is expanded to at least two quintiles.

Jump to Definitions 

In the Russell 2000, the one quintile delta test delivers 4.1% annualized return spreads between valuation and cheapness preferences, and this expands to 7.0% per year when the error tolerance is increased to at least two quintiles.

AFG Research Database: Russell 1000 & Russell 2000 Book to Price LFY & Percent to Target – Current
Sector-Ranked Quintiles from 9/30/98 to 12/31/19 (Equal-Weight in Sector Returns) | All Sectors
Jump to Definitions 

In the context of Russell benchmarks, it is clear that incomplete measures of cheapness can be exploited by a more robust estimate of intrinsic value.  The Valuation Preference portfolio offers attractive risk-adjusted returns, and the Cheap Preference portfolio provides insight towards stocks that managers may want to avoid, short, or decrease allocation relative to benchmark weights depending on unique investment mandates and constraints.

Exploiting the Valuation/Cheapness Gap in the S&P 500

Shifting our focus to the S&P 500, we affirm similar observations noted in the Russell-based analysis.  Book to price on a stand-alone basis offers long-term outperformance from its highest quintile tier that appears to be adequately offset by risk adjustments.  Applied Finance’s measure of intrinsic value, on the other hand, increases the robust nature of factor returns; top quintile performance delivers higher returns, lower beta, reduced tracking error, and increased returns per unit risk compared to a book to price methodology.

S&P 500 Index ®: Book to Price & Percent to Target, 9/30/98 to 12/31/19

Jump to Definitions 

Overlaying these measures of valuation and cheapness into the 5×5 study format highlights the dominance of this theme in an S&P 500 context, as well. When incorporating all quintile error, the Valuation Preference portfolio outperforms the Cheap Preference portfolio by 1.5% per year.  This expands to 3.1% per year in a two-quintile error minimum, and to 8.0% with a three-quintile error minimum.

Valuation/Cheapness Gap: S&P 500 Index ®

Classification error levels are similar to those observed in the Russell 3000. Roughly 71% of S&P 500 forecast stocks have at least one quintile of classification error between valuation and cheapness, which falls to 35% at two quintiles and 16% at three quintiles.  (Classification error was 68% on a one-quintile basis, 32% on a two-quintile basis and 14% on a three-quintile basis in the Russell 3000 study)

The long-only performance of Valuation Preference portfolios provides compelling returns.  The +1 Quintile Delta version, based on roughly a third of benchmark constituents, has outperformed the S&P 500 by 2.6% per year with an information ratio near 0.59 and a beta of 1.01.  The +2 Quintile Delta version has outperformed by 3.0% per year with a beta below 1.0 accompanied by an information ratio of 0.55.  This outperformance expands to 5.2% per year for the +3 Quintile Delta approach with a slightly inflated beta.

This +3 Quintile Delta portfolio warrants additional observation.  This approach delivers a fascinating array of historical returns, but seasons of inadequate diversification increased tracking error, leading to lower information ratios.  Turnover of this Valuation Preference portfolio is also nearly 200% per year, introducing implementation challenges. Applied Finance can introduce modifications that better align with live implementation by ensuring diversification to drastically improve risk-adjusted performance and lower turnover.

AFG Research Database: S&P 500 Book to Price LFY & Percent to Target – Current
Sector-Ranked Quintiles from 9/30/98 to 12/31/19 (Equal-Weight in Sector Returns) | All Sectors


  • Intrinsic Value – The cash flows implied by fading Economic Margins and diminishing capital growth over each firm’s Competitive Advantage Period can then be discounted to a present value estimate of a firm’s enterprise value. Debt and other obligations with superiority to common equity holders can be subtracted to estimate the intrinsic value of a firm’s equity, and this can be divided by current shares outstanding to estimate the firm’s stock price…. more
  • Percent to Target – Current – Compares the intrinsic value estimate to the most recent closing price for each firm.
  • Cumulative: Cumulative return from 9/30/98 to 12/31/19
  • Annualized: Annualized return from 9/30/98 to 12/31/19
  • Return Spread: Relative annualized performance vs. benchmark
  • IR (12M): Information Ratio, based on active return divided by tracking error to benchmark on a rolling twelve-month basis, using calendar month returns
  • Beta: All-time covariance divided by benchmark variance using monthly returns
  • Max Draw Down vs. Bench: maximum drawdown relative to benchmark, or maximum underperformance to benchmark on an absolute basis over all possible study time horizons.
  • Jensen’s Alpha: Portfolio annualized return minus benchmark annualized return multiplied by portfolio beta (assumes risk-free rate=0%).
  • Treynor Ratio: Annualized return divided by beta
  • Avg/StDev: Average monthly portfolio returns divided by standard deviation of monthly portfolio returns.
  • Sortino: Average monthly quintile returns divided by standard deviation of negative returns (using minimum acceptable return=0%)
  • Turnover: Average positional turnover on an annual basis
  • Benchmark Performance reflects total returns of index provider reflective of their cap-weighted or float-adjusted methodology.
  • Portfolio Performance reflects total returns of portfolios based on factor screens formed with an equal-weight within sector weighting scheme.
  • Stock Universe reflects point-in-time benchmark constituents that have data availability for measures of book to price and Percent to Target – Current as of each rebalance at calendar month end.


  • Applied Finance, a thought leader in valuation and portfolio construction, is a true “value” investment management company.  Unlike the majority of firms today that focus on low multiples to define “value”, we define value as identifying companies trading below their intrinsic value.  Our Valuation Driven™ approach forms the foundation of our investment decisions...more


What are the Value Expectations® priced-in to NVIDIA (NVDA) shares?

Download PDF Version The Financial Facts Over the past three years, NVDA shares are up 429% (02/20/2021 – 02/23/2024) Demand for the firm’s high-end semiconductors has rocketed, a result of Artificial Intelligence and the need [...more]

ValuationEdge™ Newsletter

Join to receive updates and exclusive

Valuation Driven® insights!

You have Successfully Subscribed!