The Piotroski F_Score

(Zen Buddha Silence by Marilyn Barbone)

(Image:  Zen Buddha Silence by Marilyn Barbone.)

December 18, 2016

There are several ways to measure cheapness, including low EV/EBIT, low P/E, and low P/B.  Historically, these metrics have effectively identified groups of cheap stocks that outperform the market over time.  Many academic studies of value investing have focused on low P/B stocks (equivalently, high book-to-market stocks).

If you look at the cheapest group of low P/B stocks (quintile or decile), you find that, during most historical periods, this group has outperformed the market and has done so with less risk.  Here “risk” is defined—following Lakonishok, Shleifer, and Vishny—in terms of performance in bear markets, recessions, or other “bad states” of the world, and in terms of more traditional betas and standard deviations.  Link to the 1994 paper by Lakonishok, Schleifer, and Vishny:

And yet each individual low P/B stock is more likely than the average stock to underperform the market and is, in that sense, riskier.

Joseph Piotroski, a professor of accounting at the University of Chicago (currently at Stanford), noticed this disparity.  Even though low P/B stocks as a group have beaten the market during most historical time periods, Piotroski found that 57% of the low P/B stocks underperformed the market.  The outperformance of the low P/B group has been driven by only 43% of the stocks in the group, while it has been held back by the other 57%.

Given that low P/B stocks are often distressed, Piotroski wondered whether you could distinguish between “cheap and strong” companies and “cheap but weak” companies.  Piotroski invented a measure called the F_Score for this purpose.  Applying the F_Score to the group of low P/B stocks (the cheapest quintile) improved performance by 7.5% per year between 1976 and 1996.  The biggest improvements in performance were concentrated in cheap micro caps with no analyst coverage.



Piotroski invented his F_Score by thinking about what measures you would expect to distinguish between “cheap and strong” companies and “cheap but weak” companies.  He focused on recent changes in fundamentals that could be detected in a company’s financial statements.  Piotroski identified three areas to look for improving fundamentals:

  • Profitability and Cash Flow
  • Leverage and Liquidity
  • Operating Efficiency

Piotroski thought of four measures for profitability and cash flow, three for leverage and liquidity, and two for operating efficiency.  Each measure is binary, “1” for good and “0” for bad.  Thus for a given cheap company, a total score of “9”—a “1” on each of the nine measures—would indicate the maximum possible financial strength, whereas a “0” would indicate the minimum.  Because the F_Score is applied to cheap—often distressed—stocks, it’s reasonable to expect it to help in general.  And it does.

Link to Piotroski’s paper, “Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers” (2002, University of Chicago Graduate School of Business):



As Piotroski notes, current profitability and cash flow are indicative of a firm’s ability to generate cash internally.  A distressed company showing a positive trend in earnings and cash flows is more likely to do well.

Piotroski has four measures for profitability and cash flow:

  • ROA measures current net income before extraordinary items.
  • CFO measures current cash flow from operations.
  • ΔROA measures this year’s ROA minus last year’s ROA.
  • ACCRUAL measures cash flow from operations versus net income before extraordinary items.

If ROA > 0—if net income before extraordinary items is positive—then the indicator variable F_ROA = 1, otherwise F_ROA = 0.

If CFO > 0—if cash flow from operations is positive—then the indicator variable F_CFO = 1, otherwise F_CFO = 0.

If ΔROA > 0—if net income before extraordinary items has increased from the prior year—then the indicator variable F_ΔROA = 1, otherwise F_ΔROA = 0.

If CFO > ROA—if cash flow from operations is greater than net income before extraordinary items—then F_ACCRUAL = 1, otherwise F_ACCRUAL = 0.

The logic is straightforward.  If the firm in question—which is cheap and likely to be distressed—is showing positive net income and cash flow, the firm is generating cash internally.  Similarly, an improvement in net income is a positive signal.  Finally, cash flow from operations being larger than net income before extraordinary items is positive:  distressed firms have an incentive to distort or “manage” earnings (to prevent covenant violations), but it is much harder to distort cash.



Because many cheap firms are distressed, an increase in debt, a decrease in liquidity, or the use of external financing is a bad signal.  Thus, Piotroski invented the following three simple measures:

  • ΔLEVER captures change in the firm’s long-term debt level.
  • ΔLIQUID measures change in the firm’s current ratio.
  • EQ_OFFER indicates whether the firm has issued common equity.

If ΔLEVER < 0—if the long-term debt level fell—then the indicator variable F_ΔLEVER = 1, otherwise F_ΔLEVER = 0.

If ΔLIQUID > 0—if the current ratio (current assets divided by current liabilities) improved—then the indicator variable F_ΔLIQUID = 1, otherwise F_ΔLIQUID = 0.

If the firm did not issue common equity, then the indicator variable EQ_OFFER = 1, otherwise EQ_OFFER = 0.

If a distressed firm does not have to raise external capital via an increase in long-term debt, that is a positive signal about its ability to generate sufficient cash internally.  Also, an improvement in liquidity bodes well for the firm’s ability to service current debt obligations.  If a distressed firm has to issue new equity to raise cash, that’s not a good signal, especially if the new equity is cheaply priced.



Piotroski looked at two key constructs in a decomposition of return on assets: gross margin ratio and asset turnover.  Both are signals of the efficiency of the firm’s operations.

  • ΔMARGIN measures the firm’s current gross margin ratio relative to the previous year.
  • ΔTURN measures the firm’s current asset turnover relative to the previous year.

If ΔMARGIN > 0—if the gross margin ratio has improved—then the indicator variable F_ΔMARGIN = 1, otherwise F_ΔMARGIN = 0.

If ΔTURN > 0—if asset turnover increased—then the indicator variable F_ΔTURN = 1, otherwise F_ΔTURN = 0.

An improvement in margins means a reduction in costs or an increase in the price of the firm’s product.  An increase in asset turnover—greater productivity of the asset base—can result from more efficient operations (greater sales/assets) or an increase in sales.  Increased sales may signify improved market conditions for the firm’s product.



The overall F_SCORE is the sum of the nine individual binary signals:



From the low P/B quintile, Piotroski isolated all the companies that had F_SCORES of 8 or 9.  This low P/B, high F_SCORE portfolio outperformed the low P/B quintile by 7.5% per year between 1976 and 1996.  The biggest improvements in performance were concentrated in cheap micro caps with no analyst coverage.



An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time.  See the historical chart here:

This outperformance increases significantly by focusing on cheap micro caps.  Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals.  We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio.  The size of each position is determined by its rank.  Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost).  Positions are held for 3 to 5 years unless a stock approaches intrinsic value sooner or an error has been discovered.

The goal of the Boole Microcap Fund is to outperform the Russell Microcap Index over time, net of fees.  The Boole Fund has low fees. 


If you are interested in finding out more, please e-mail me or leave a comment.

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Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed. No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.