Executive SummaryIn this article, we identify how we can improve the performance of the F-Score and enhance a generic value investing approach. In a 2000 study, “Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers” (Journal of Accounting Research, 2000), Joseph Piotroski examined whether an investor could improve his or her investment returns by using simple accounting-based fundamental analysis. The F-Score is designed to identify fundamentally strong stocks within the cheapest stocks in the universe. For Piotroski, a cheap stock, or “value stock,” is defined as a stock with a high book value relative to its market price (in other words, a low price-to-book ratio). Professor Piotroski was inspired to find a better way to invest in value stocks, as a majority of value stocks (approximately 57%) underperform the market over one- and two-year stretches. Piotroski found that by identifying financially strong value stocks according to his F-Score, he could improve the return of a low price-to-book portfolio by at least 7.5% per year. In addition, he found that an investment strategy that bought expected winners and sold short expected losers generated a 23% annual return between 1976 and 1996. Assuming that the “average [value stock] is financially distressed,” Piotroski chose nine fundamental signals to measure three areas of the stock’s financial health: profitability, financial leverage/liquidity, and operating efficiency. He sought to classify each fundamental signal into mutually exclusive states, as either “good” or “bad,” depending on the signal’s implication for a stock’s future prices and profitability. Each fundamental signal analyzed is expressed as a binary outcome. In other words, if the fundamental signal analyzed is good, it is marked as a one, and if the fundamental signal analyzed is bad, it is marked as a zero. The aggregate of the signals is the F-Score, which represents the sum of the nine binary signals. The aggregate signal is designed to measure the overall quality, or strength, of the stock’s financial health, and the decision to include the stock in a portfolio is ultimately based on the strength of the aggregate signal.
Analyzing the F-ScorePiotroski’s nine fundamental signals measure three areas of financial health: profitability; leverage, liquidity and source of funds; and operating efficiency.
ProfitabilityPiotroski uses four variables to measure a stock’s current profitability and cash flow realizations to glean information about the stock’s ability to generate funds internally. These performance-related variables are return on assets (ROA), cash flow from operations (CFO), the change in return on assets (ΔROA), and accruals (ACCRUAL). (Note that the Δ symbol refers to delta and means change in or difference, so ΔROA means change in ROA). ROA and CFO are net income before extraordinary items and cash flow from operations, respectively, divided by beginning of the year total assets. If the stock’s ROA or CFO is positive, Piotroski defines the variable F_ROA or F_CFO as one, and zero if otherwise. He defines ΔROA as the current year’s ROA less the prior year’s ROA. We are measuring not the static change in this profitability metric, but instead are scaling dynamically, using the firm’s asset base, which changes over time. If ΔROA is greater than 0, the variable F_ΔROA is marked one, and zero otherwise. Piotroski defines the variable ACCRUAL as the stock’s current year’s net income before extraordinary items less cash flow from operations, scaled by beginning of the year total assets. The use of non-cash accruals is a signal that can contain information about the composition and quality of a firm’s earnings. The variable F_ ACCRUAL is marked one if CFO is greater than ROA, and zero if otherwise.
Leverage, Liquidity and Source of FundsPiotroski’s F-Score assumes that an increase in leverage, deterioration in liquidity, or the use of external financing is an unfavorable signal about financial health. Three of the nine financial signals are therefore designed to measure changes in capital structure and the stock’s ability to meet future debt service obligations: ΔLEVER, ΔLIQUID, and EQ_OFFER. ΔLEVER seeks to capture changes in the stock’s long-term debt levels. Piotroski measures ΔLEVER as the historical change in the ratio of total long-term debt to average total assets; he views an increase in financial leverage as a negative signal, and vice versa. By raising external capital, a financially distressed stock is signaling its inability to generate sufficient internal funds. In addition, an increase in long-term debt, relative to assets, is likely to place additional constraints on the stock’s financial flexibility. Piotroski marks the variable F_ΔLEVER as one if the stock’s leverage ratio fell in the preceding year, and zero if otherwise. ΔLIQUID seeks to measure the historical change in the stock’s current ratio between the prior and current year, where Piotroski defines the current ratio as the ratio of current assets to current liabilities at fiscal year-end. Thus, has the firm’s current ratio increased or decreased, versus a year ago? He assumes that an improvement in liquidity is a good signal about the stock’s ability to service current debt obligations. The variable F_ΔLIQUID is marked one if the stock’s liquidity improved (increase in current ratio), and zero if otherwise. F_EQISS measures whether a firm issued equity in the preceding year. The fact that these stocks are willing to issue equity when their stock prices are depressed highlights their poor financial health. F_EQISS captures whether a stock has issued equity in the year preceding portfolio formation. The variable F_EQISS is set to one if the stock did not issue common equity in the preceding year, and zero if otherwise.
Operating EfficiencyPiotroski’s two remaining signals—ΔMARGIN and ΔTURN—seek to measure changes in the efficiency of the stock’s operations and use of its assets. Piotroski believes these ratios are important because they reflect two key parts of the return on assets. Piotroski defines ΔMARGIN as the stock’s current gross margin ratio (gross margin divided by total sales) less the prior year’s gross margin ratio. Piotroski believes that an improvement in margins signifies a potential improvement in costs, a reduction in inventory costs, or a rise in the price of the stock’s product, all of which are positive for the stock. The indicator variable F_ΔMARGIN equals one if ΔMARGIN is positive, and zero if otherwise. Piotroski defines ΔTURN as the stock’s current year asset turnover ratio (total sales scaled by beginning of the year total assets) less the prior year’s asset turnover ratio. He says that an improvement in asset turnover signifies greater productivity from the asset base. Such an improvement can arise from more efficient operations (fewer assets generating the same levels of sales) or an increase in sales (which could also signify improved market conditions for the stock’s products). The indicator variable F_ΔTURN equals one if ΔTURN is positive, and zero if otherwise. Now that we’ve defined all of the signals in the F-Score, let’s see how Piotroski combined them to find the F-Score, and then learn how to interpret the output.
F-Score Formula and InterpretationPiotroski calculates his F-Score by summing the individual binary signals, or, more formally:
- F-Score = F_ROA + F_ΔROA + F_CFO + F_ ACCRUAL + F_ΔMARGIN + F_ΔTURN + F_ΔLEVER + F_ΔLIQUID + F_EQISS
Creating a Better F-ScorePiotroski’s F-score approach to identifying winners and losers is a good first step, but the F-score measure is, in the words of the author, ad hoc. Nobody wants their investment process to be ad hoc, but we do like the simplicity associated with the F-Score. In this section we do not intend to reinvent the wheel. Instead, we look to make intelligent changes to the F-Score that improve performance. Using the F-Score as a foundation, we have created a new financial strength score (FS-Score), which we divide into the same three categories as the F-Score:
- Current profitability,
- Stability, and
- Recent operational improvements.
Current ProfitabilityWe use three variables to measure a stock’s current profitability and cash flow realization: ROA and FCFTA are net income before extraordinary items and free cash flow, respectively, divided by most recent total assets. If the stock’s ROA or FCFTA is positive, we define the respective variable FS_ROA or FS_FCFTA as one, and zero if otherwise. ACCRUAL is the stock’s current year’s net income before extraordinary items less cash flow from operations, scaled by beginning of the year total assets. The variable FS_ACCRUAL is marked one if FCFTA is greater than ROA, and zero if otherwise. Our current profitability variables are similar to Piotroski’s profitability variables, except that we replace the CFO variable with free cash flow divided by total assets ( . We make this change to take into account the impact of capital expenditures on the stock’s cash flows. We also exclude the variable ΔROA from this category and put it and ΔFCFTA in our “recent operational improvements” category because we believe it is a more intuitive category for these variables.
StabilityLike Piotroski, we assume that an increase in leverage, deterioration in liquidity, or the use of external financing is a bad signal about financial health. Our stability signals measure changes in capital structure and the stock’s ability to meet future debt service obligations:
- ΔLEVER is the historical change in the ratio of total long-term debt to total assets. FS_ΔLEVER is marked one if the stock’s leverage ratio fell in the preceding year, and zero if otherwise.
- ΔLIQUID is defined as the year-over-year change in the ratio of current assets to current liabilities. The variable FS_ΔLIQUID is marked one if the stock’s liquidity improved (higher ratio), and zero if otherwise.
- NEQISS is equity repurchases minus equity issuance, or net equity issuance. FS_NEQISS is set to one if repurchases exceed equity issuance, and zero otherwise.
Recent Operational ImprovementsWe introduce a new section for the FS-Score: recent operational improvements. This category is roughly equivalent to the F-Score’s operating efficiency section, except that the focus in our FS-Score is on improvements. We include in our recent operational improvements category the following:
- ΔROA is the current year’s ROA less the prior year’s ROA. If ΔROA is greater than 0, the variable FS_ΔROA scores a one, and zero otherwise.
- ΔFCFTA is the current year’s FCFTA less the prior year’s FCFTA. If ΔFCFTA is greater than 0, the variable FS_ΔFCFTA is marked one, and zero otherwise.
- ΔMARGIN is the stock’s current gross margin ratio (gross margin divided by total sales) less the prior year’s gross margin ratio. The indicator variable FS_ΔMARGIN equals one if ΔMARGIN is positive, and zero if otherwise.
- ΔTURN is the stock’s current year asset turnover ratio (total sales scaled by beginning of the year total assets) less the prior year’s asset turnover ratio. The indicator variable FS_ΔTURN equals one if ΔTURN is positive, and zero if otherwise.
Does the Improved F-Score Work?Our FS-Score has 10 metrics, versus Piotroski’s nine, across the three categories of profitability, stability, and recent operational improvements. The final score is from zero to 10, where 10 is a perfect score, and zero is the worst score possible. The FS-Score formula is as follows:
- FS-Score = FS_ROA + FS_FCFTA + FS_ACCRUAL + FS_ΔLEVER + FS_ΔLIQUID+FS_NEQISS + FS_ΔROA + FS_ΔFCFTA + FS_ΔMARGIN + FS_ΔTURN
Table 1. F-Score and FS-Score Performance (1974 to 2014)
|Compound annual growth rate (%)||13.3||12.6||11.2|
|Standard deviation (%)||15.2||15.3||15.5|
|Downside deviation (%)||10.7||10.9||11.1|
|Sortino ratio (min. accepted ret. = 5%)||0.82||0.75||0.62|
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.The small tweaks we applied to the F-Score caused the FS-Score to outperform by a small but economically meaningful amount. Additionally, the structure of the FS-Score is more intuitive and grounded in value-investing philosophy than the F-Score. Next, we analyzed the F-Score and the FS-Score in the context of cheap stocks, which is more akin to the original study conducted by Piotroski. We looked at the returns from cheap stocks (defined as being in the 20% cheapest based on book-to-market, which is the inverse ratio of price-to-book) with an F-Score of 6, 7, 8, or 9 and compared those to the performance of cheap stocks with an FS-Score of 7, 8, 9, or 10. We examined the returns to the value portfolios containing the high scorers in each strategy over the period from January 1, 1974, to December 31, 2014, as shown in Table 2 and Figure 2.
Table 2. Value Stocks and F-Score and FS-Score Performance (1974 to 2014)
|Compound annual growth rate (%)||15.9||15.2||11.2|
|Standard deviation (%)||15.4||15.2||15.5|
|Downside deviation (%)||10.2||10.4||11.1|
|Sortino ratio (min. accepted ret. = 5%)||1.08||0.99||0.62|
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.