Reviewing Piotroski's F-Score: Method, Results, And 10 Stock Ideas

by: Ricardo Espinosa

For all investors reading this, there is a very useful financial metric that is (at least in my view) underused, and that's why I'm writing an homage to Piotroski's F-Score.

In 2002, the University of Chicago Graduate School of Business published a paper called "Value Investing: The Use of Historical Financial Statements to Separate Winners from Losers," written by Joseph D. Piotroski. (Click here for a link to the complete paper.)

In the abstract, Piotroski stated:

I show that the mean return earned by a high book-to-market investor can be increased by at least 7.5% annually through the selection of financially strong high BM firms while the entire distribution of realized returns is shifted to the right. In addition, an investment strategy that buys expected winners and shorts expected losers generates a 23% annual return between 1976 and 1996, and the strategy appears to be robust across time and to controls for alternative investment strategies.

Nine Components

Piotroski chose nine fundamental signals to measure three areas of the firm's financial condition: profitability, financial leverage/liquidity, and operating efficiency.

Piotroski went on to explain his method:

In this paper, I classify each firm's signal realization as either 'good' or 'bad,' depending on the signal's implication for future prices and profitability. An indicator variable for the signal is equal to one (zero) if the signal's realization is good (bad). I define the aggregate signal measure, F-Score, as the sum of the nine binary signals. The aggregate signal is designed to measure the overall quality, or strength, of the firm's financial position, and the decision to purchase is ultimately based on the strength of the aggregate signal.


There are four variables used by Piotroski to measure these performance-related factors:

1. ROA: Net income before extraordinary items, one point awarded if positive, zero otherwise. If the firm's ROA is positive, the indicator variable is equal to one, zero otherwise. This is the binary method of scoring for all nine areas.

2. CFO: Cash Flow from Operations, one point awarded if positive, zero otherwise.

3. ΔROA: Current year's ROA less the prior year's ROA. One point awarded if positive, zero otherwise.

4. ACCRUAL: Current year's net income before extraordinary items less cash flow from operations. The indicator variable F-ACCRUAL equals one if CFO > ROA, zero otherwise. This is used because in 1996, Sloan showed that earnings driven by positive accrual adjustments (i.e., profits are greater than cash flow from operations) is a bad signal about future profitability and returns.

Financial Performance Signals: Leverage, Liquidity, and Source of Funds

According to Piotroski, "three of the nine financial signals are designed to measure changes in capital structure and the firm's ability to meet future debt service obligations."

5. ΔLEVER This variable captures the changes in the company's long-term debt levels.

It's the historical change in the ratio of total long-term debt to average total assets, and views an increase (decrease) in financial leverage as negative (positive) signal.

By raising external capital, a financially distressed firm is signaling its inability to generate sufficient internal funds, aside from placing additional constraints on the firm's financial flexibility.

Piotroski gives one point to this variable if the company's leverage ratio fell relative to the previous year, and zero if it rose.

6. ΔLIQUID: This variable measures the historical change in the firm's current ratio between the current and prior year. Improvement in liquidity adds one point to the score, because it is a good sign of the company's ability to service current debt obligations, zero points if the current ratio decreased.

7. EQ-OFFER: This indicator will equal one if the firm did not issue common equity in the year preceding current year, zero otherwise.

Companies that raise external capital could be signaling their inability to generate sufficient internal funds to service future obligations. This indicator variable will equal one if the company did not issue common equity the previous year, zero if it did.

Financial Performance Signals: Operating Efficiency

The two remaining signals measure changes in the efficiency of the company's operations, and reflect two key constructs underlying a decomposition of return on assets.

8. ΔMARGIN: The firm's current gross margin ratio. An improvement in margins signifies a potential improvement in factor costs, a reduction of inventory costs, or a rise in the price of the firm's product. F-ΔMargin will equal one if ΔMARGIN is positive, zero otherwise.

9. ΔTURN: The firm's current year asset turnover ratio (sales/beginning of the year assets) less the prior year's asset turnover ratio. An improvement in asset turnover signifies greater productivity from the asset base. This can come from more efficient operations (fewer assets generate the same amount of sales) or an increase in sales, which could also signify improved market conditions for the company's products.

F-ΔTURN will equal one if ΔTURN is positive, zero otherwise.

As mentioned earlier, F-SCORE is the sum of the individual binary signals:



Given the nine underlying signals, F-SCORE can range from 0 to 9.

He then performed an empirical study with 14,043 firms, and while I suggest reading the full paper to get the full statistical method he employed for his calculations, here are some of the tables I found most relevant:

Click to enlarge images.

Piotroski also noted that most of the companies scored between 3 and 7 in his F-Score, giving conflicting signals. But returns were consistent when the F-Score was on the extreme side if the companies scored a high F-Score (8 or 9), with 1,448 observations, or low (0 or 1), with 396 observations.

Next are the results:

As you can see in the next table, the returns for Piotroski's study are almost halved as the company gets bigger, but 15.2% outperformance between high-scoring companies and their weaker counterparts is nothing to scoff at.

He also noted that "the concentration of the greatest benefits among smaller, thinly traded and underfollowed stocks suggests that information-processing limitations could be a significant factor leading to the predictability of future stock returns."

This effect can be seen in the next table:

This seems to be the most important factor for outperforming stock indices.

While most of the stocks I will be valuating will have a lot of analysts following them, I am open to suggestions on valuating small firms, where you can get the highest returns, according to Piotroski's study. Hopefully, you can now do it too.

Next we have a table that shows us the yearly returns one would have earned by being long the strongest companies (greater to or equal to 5 F-Score) and short the weakest ones (F-Score less than 5):

Quick Ideas

Doing a quick screening, I came up with 10 stocks that scored a perfect 9 on their F-Scores. Remember that low BM value and small size are riskier, but can offer greater returns:

Company Market Cap. P/Book
Honda Motor Company (NYSE:HMC) 58.3B 1.04
Big Lots Inc. (NYSE:BIG) 2.41B 2.93
Assisted Living Concepts INC (NYSE:ALC) 297M 0.96
Coventry Healthcare Inc (CVH) 4.7B 0.99
Nike Inc (NYSE:NKE) 46.6B 4.51
General Steel Holdings (NYSE:GSI) 43.3M 0.47
Dynatronics Corporation (NASDAQ:DYNT) 6.3M 0.99
Grupo Aeropuertuario del Sureste (NYSE:ASR) 2.05B 1.80
La-Z-Boy Incorporated (NYSE:LZB) 677.1M 1.56
Cobra Electronics (NASDAQ:COBR) 29.6M 0.78

Do your own homework before you buy any of these, but they look healthy from a financial perspective.

Still Don't Like the Method?

Consider this, taken from Forbes:

The Piotroski approach to stock picking got a special boost after the American Association of Individual Investors revealed that it was the only stock screening strategy out of 56 screening methodologies that had positive results in 2008.

Believe it or not, the five stocks that AAII bought using Piotroski's strategy in 2008 gained 32.6% on average through the end of the year. The median performance for all of the AAII strategies last year? -41.7%.

Readers should note that I provided a link to Piotroski's complete paper at the beginning of this article, and all the tables and studies are his work -- this is just an homage to his method, which I find very interesting given the empirical results.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.