Piotroski F-Score Investing

Introduction

Value investing has been a popular strategy for centuries. An efficient way to do this is by summarizing financial ratios into a qualitative score. Financial ratios are more comparable than absolute numbers, time-invariant, and sector-invariant to some extent, making them perfect candidates to analyze the change in financial health and potential of a company or compare companies with their competitors. 

Developed by Stanford accounting professor Joseph Piotroski, the Piotroski F-score is a popular tool to measure the strength of a firm's financial position. The score comprises three categories and nine sub-categories, each worth one point. Higher F-scores represent the best-value stocks. The original author suggested that a company score of eight or nine is considered a good value, and a score between zero and two points is likely a poor value. Researchers found that thresholds from 5-8 also worked, beating their corresponding benchmarks.

Method

We hypothesized that financial robustness and growth would translate to higher stock returns and provide resilience to poor markets. Our independent variable is the F-Score universe filtering, compared to buy and hold of the SPY benchmark over the last three years (7/1/2020 to 7/1/2023). We adjusted portfolio construction and execution models to mimic the market and reduce risk and friction. We study the annual compound return, Sharpe Ratio, Information Ratio, maximum drawdown, and annual standard deviation to examine the strategy's risk-adjusted profitability, robustness, and consistency. 

Let's examine how we can implement an F-score strategy with QuantConnect and the MorningStar US Fundamental dataset.

Universe Selection

We excluded financially "unhealthy" to avoid penny stocks as they are more susceptible to manipulation, making the F-Score or other fundamental-data metrics inaccurate. We selected stocks with a Piotroski F-Score greater than 7 as it balanced financial strength and portfolio diversification. Extreme thresholds filter out most stocks. We did this in the fundamental universe selection model.

def SelectCoarse(self, coarse):
    # We only want stocks with fundamental data and price > $1
    filtered = [x.Symbol for x in coarse if x.Price > 1]
    return filtered

def SelectFine(self, fine):
    # We use a dictionary to hold the F-Score of each stock
    f_scores = {}

    for f in fine:
        # Calculate the Piotroski F-Score of the given stock
        f_scores[f.Symbol] = self.GetPiotroskiFScore(f)

    # Select the stocks with F-Score higher than the threshold
    selected = [symbol for symbol, fscore in f_scores.items() if fscore >= self.fscore_threshold]
    return selected

To obtain the Piotroski F-Score, we create the GetPiotroskiFScore method to calculate the Piotroski F-Score of each stock, with its Fine Fundamental object as input argument. It accesses the 9 sub-categories to check if the company meets the following criteria:

1. A positive income
2. A positive operating cash flow
3. Showing increased profitability
4. Income realized as cash flow
5. Low long-term debt
6. Able to repay debts within 1 year.
7. Is fundraising
8. Is profitable
9. Efficiency improvements

from f_score import *

def GetPiotroskiFScore(self, fine):
    # initial F-Score as 0
    fscore = 0
    # Add up the sub-scores in different aspects
    fscore += GetROAScore(fine)
    fscore += GetOperatingCashFlowScore(fine)
    fscore += GetROAChangeScore(fine)
    fscore += GetAccrualsScore(fine)
    fscore += GetLeverageScore(fine)
    fscore += GetLiquidityScore(fine)
    fscore += GetShareIssuedScore(fine)
    fscore += GetGrossMarginScore(fine)
    fscore += GetAssetTurnoverScore(fine)
    return fscore

where all the sub-scores are calculated by helper methods stored in f_score.py.

def GetROAScore(fine):
    '''Get the Profitability - Return of Asset sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Profitability - Return of Asset sub-score'''
    # Nearest ROA as current year data
    roa = fine.OperationRatios.ROA.ThreeMonths
    # 1 score if ROA datum exists and positive, else 0
    score = 1 if roa and roa > 0 else 0
    return score

def GetOperatingCashFlowScore(fine):
    '''Get the Profitability - Operating Cash Flow sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Profitability - Operating Cash Flow sub-score'''
    # Nearest Operating Cash Flow as current year data
    operating_cashflow = fine.FinancialStatements.CashFlowStatement.CashFlowFromContinuingOperatingActivities.ThreeMonths
    # 1 score if operating cash flow datum exists and positive, else 0
    score = 1 if operating_cashflow and operating_cashflow > 0 else 0
    return score

def GetROAChangeScore(fine):
    '''Get the Profitability - Change in Return of Assets sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Profitability - Change in Return of Assets sub-score'''
    # if current or previous year's ROA data does not exist, return 0 score
    roa = fine.OperationRatios.ROA
    if not roa.ThreeMonths or not roa.OneYear:
        return 0

    # 1 score if change in ROA positive, else 0 score
    score = 1 if roa.ThreeMonths > roa.OneYear else 0
    return score

def GetAccrualsScore(fine):
    '''Get the Profitability - Accruals sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Profitability - Accruals sub-score'''
    # Nearest Operating Cash Flow, Total Assets, ROA as current year data
    operating_cashflow = fine.FinancialStatements.CashFlowStatement.CashFlowFromContinuingOperatingActivities.ThreeMonths
    total_assets = fine.FinancialStatements.BalanceSheet.TotalAssets.ThreeMonths
    roa = fine.OperationRatios.ROA.ThreeMonths
    # 1 score if operating cash flow, total assets and ROA exists, and operating cash flow / total assets > ROA, else 0
    score = 1 if operating_cashflow and total_assets and roa and operating_cashflow / total_assets > roa else 0
    return score

def GetLeverageScore(fine):
    '''Get the Leverage, Liquidity and Source of Funds - Change in Leverage sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Leverage, Liquidity and Source of Funds - Change in Leverage sub-score'''
    # if current or previous year's long term debt to equity ratio data does not exist, return 0 score
    long_term_debt_ratio = fine.OperationRatios.LongTermDebtEquityRatio
    if not long_term_debt_ratio.ThreeMonths or not long_term_debt_ratio.OneYear:
        return 0

    # 1 score if long term debt ratio is lower in the current year, else 0 score
    score = 1 if long_term_debt_ratio.ThreeMonths < long_term_debt_ratio.OneYear else 0
    return score

def GetLiquidityScore(fine):
    '''Get the Leverage, Liquidity and Source of Funds - Change in Liquidity sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Leverage, Liquidity and Source of Funds - Change in Liquidity sub-score'''
    # if current or previous year's current ratio data does not exist, return 0 score
    current_ratio = fine.OperationRatios.CurrentRatio
    if not current_ratio.ThreeMonths or not current_ratio.OneYear:
        return 0

    # 1 score if current ratio is higher in the current year, else 0 score
    score = 1 if current_ratio.ThreeMonths > current_ratio.OneYear else 0
    return score

def GetShareIssuedScore(fine):
    '''Get the Leverage, Liquidity and Source of Funds - Change in Number of Shares sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Leverage, Liquidity and Source of Funds - Change in Number of Shares sub-score'''
    # if current or previous year's issued shares data does not exist, return 0 score
    shares_issued = fine.FinancialStatements.BalanceSheet.ShareIssued
    if not shares_issued.ThreeMonths or not shares_issued.TwelveMonths:
        return 0

    # 1 score if shares issued did not increase in the current year, else 0 score
    score = 1 if shares_issued.ThreeMonths <= shares_issued.TwelveMonths else 0
    return score

def GetGrossMarginScore(fine):
    '''Get the Operating Efficiency - Change in Gross Margin sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Operating Efficiency - Change in Gross Margin sub-score'''
    # if current or previous year's gross margin data does not exist, return 0 score
    gross_margin = fine.OperationRatios.GrossMargin
    if not gross_margin.ThreeMonths or not gross_margin.OneYear:
        return 0

    # 1 score if gross margin is higher in the current year, else 0 score
    score = 1 if gross_margin.ThreeMonths > gross_margin.OneYear else 0
    return score

def GetAssetTurnoverScore(fine):
    '''Get the Operating Efficiency - Change in Asset Turnover Ratio sub-score of Piotroski F-Score
    Arg:
        fine: Fine fundamental object of a stock
    Return:
        Operating Efficiency - Change in Asset Turnover Ratio sub-score'''
    # if current or previous year's asset turnover data does not exist, return 0 score
    asset_turnover = fine.OperationRatios.AssetsTurnover
    if not asset_turnover.ThreeMonths or not asset_turnover.OneYear:
        return 0

    # 1 score if asset turnover is higher in the current year, else 0 score
    score = 1 if asset_turnover.ThreeMonths > asset_turnover.OneYear else 0
    return score

Portfolio Construction and Execution

We will invest in all the filtered stocks, but we carefully choose the positional sizing and order execution models to reduce risks and transaction costs. We invested the same size in every sector using the  SectorWeightingPortfolioConstructionModel. We also used a SpreadExecutionModel to reduce friction costs due to large bid-ask spread in illiquid stocks.

self.SetPortfolioConstruction(SectorWeightingPortfolioConstructionModel())
self.SetExecution(SpreadExecutionModel(0.01))       # maximum 1% spread allowed

Reality Modeling

We are unsure about the liquidity of the invested stocks, so we adapt the VolumeShareSlippageModel model with price impact on volume invested via a custom security initializer. This could allow the backtest to capture more realistic filling behavior to reflect performance closer to the actual situation.

# in Initialize
self.SetSecurityInitializer(CustomSecurityInitializer(self))

class CustomSecurityInitializer(BrokerageModelSecurityInitializer):

    def __init__(self, algorithm: QCAlgorithm) -> None:
        security_seeder = FuncSecuritySeeder(
            lambda symbol: algorithm.History[TradeBar](symbol, 3, Resolution.Daily))
        super().__init__(algorithm.BrokerageModel, security_seeder)

    def Initialize(self, security):
        super().Initialize(security)
        
        # We want a slippage model with price impact by order size for reality modeling
        security.SetSlippageModel(VolumeShareSlippageModel())

Results

Result metrics over the three years are as shown below:

Discussion

We can observe that the Sharpe Ratio and Information Ratio of the F-Score strategy are much better than that of the SPY benchmark, implying that each active selection is earning a higher risk-adjusted return. We can also observe that the poor market situation in 2022 had much less impact on the F-score portfolio, which fluctuated less and had a positive trend. This provides qualitative proof of the consistency and robustness of the strategy.

However, the 95% confidence interval of the compounded annual return of the F-Score strategy is (9.197%, 76.637%), while that of the SPY benchmark is (-3.063%, 31.807%). The overlapping 95%CI of the two portfolios showed no significant difference between their annual return. The sample size is too small to draw a high-confidence conclusion that the F-Score strategy earns better than the SPY benchmark. Higher sampling frequency and more extended sampling (backtest) window shall be adapted to draw further conclusions.

The out-performance of the proposed portfolio suggested that the Piotroski F-Score is a great tool to spot under-valued stocks that provide excess returns. The investment strategies using fundamental factor analysis and value investment are consistently working factors while quantifiable to carry out a quantitative analysis. 
Nonetheless, it is certainly not a silver bullet for various market regimes. It has no prediction, valuation value, or rationale for defending a poor market. Mohr (2012) used F-score and momentum to produce a stable, positive return over the 2008 global financial crisis. Hyde (2018) created a market-neutral strategy by buying high F-score and selling low F-score stocks with equal- and beta-weighting to eliminate systemic risk. 

Conclusion

This research has weakly proven the profitability, robustness, and consistency of the Piotroski F-Score filtering.

References

1. Stockopedia. https://www.businessinsider.com/the-piotroski-f-score-reviewing-joseph-piotroskis-accounting-based-value-investing-screen-2011-4. Business Insider.
2. Piotroski, Joseph D. (January 2002). http://www.chicagobooth.edu/~/media/FE874EE65F624AAEBD0166B1974FD74D.pdf (PDF). The University of Chicago Graduate School of Business.
3. Eremenko, E. (2017). Quantitative Fundamentals. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3262154. (April 9, 2017).