June 2015
Abnormal returns to a financial statement analysis investment strategy
Master’s Thesis Accountancy & Finance University of Groningen
Faculty of Economics and Business JEL-classification: M41, G11, G14
Keywords: Accounting, Financial statement analysis, capital markets research, market efficiency, investment decisions
Student No: s1870548 Name: Rutger Roeling1
Study Program: MSc Accountancy Other programs: MSc Finance
1st Supervisor: Dr. H. Gonenc (RUG)
2nd Supervisor: Mr. Dr. W. Kaufmann (RUG) Supervisor PwC2: Klaas Sportel
Submission date: 24-06-2015
1 E-mail: r.r.g.roeling@student.rug.nl
Abnormal returns to a financial statement analysis investment strategy
Abstract:The goal of this paper is to investigate whether a simple investment strategy, based on financial statement analysis, can earn abnormal returns. I find evidence that the Piotroski (2000) F-Score was able to separate ex-ante high Book-to-Market firms with positive and negative abnormal returns during 1976 – 1996. Returns to the same investment strategy in the period 1997 - 2014 can be explained by the Fama and French (1993) three- and Carhart (1997) four-factor models.
1. Research topic and introduction
The objective of every investment manager is to create a portfolio which earns high returns relative to the riskiness of these returns. Several researchers have shown that, on average, mutual funds do not outperform the market (e.g. Jensen, 1968; Malkiel, 1995) and the general belief is that it is very difficult to outperform the market and nearly impossible to do this consistently. On the other hand, investment strategies based on accounting information have been proposed who seem to yield high positive returns. Since Ou and Penman (1989) first showed that historical accounting information can be used to implement a successful investment strategy, many other strategies followed (e.g. Abarbanell and Bushee, 1998; Piotroski, 2000; Mohanram, 2005). One of these methods is the Piotroski (2000) F-Score, which was able to discriminate ex-ante between subsequently outperforming and underperforming high Book-to-Market stocks.
Accounting fundamental analysis examines detailed accounting data (reported in financial statements) to improve our understanding of how efficiently and effectively a firm generates earnings over time, as well as its potential to grow and convert these earnings into free cash flows (Richardson, Tuna, and Wysock, 2010). A vast body of literature has tried to determine
ratios and accounting variables which can be used to estimate a firm’s future earnings. Kothari (2001) suggests that fundamental analysis research should be used to identify mispriced securities for investment purposes. Financial statement analysis can be considered part of fundamental analysis which, according to Ou and Penman (1989), identifies aspects of financial statements that are relevant for investment decisions. Information is relevant for investment decisions if it relates to the risk or return of possible investment opportunities and when information from financial statements is not correctly incorporated into stock prices, this leaves an opportunity for investors to earn excess returns based on this information. The Efficient Market Theory states that it should not be possible to earn excess returns based on publicly known information, as this information should already be incorporated into the stock price. In an efficient market, stock prices follow ‘a random walk’ and prices ‘fully reflect’ all available information (Fama, 1970). Although it is generally assumed that markets are semi-strong efficient, which means that all publicly available information is incorporated into the stock price, there is considerable debate concerning the Efficient Markets Theory. Several anomalies have been documented and there is mounting evidence that capital markets might not be efficient (Kothari, 2001). Ball and Brown (1968) were the first to establish an abnormal relationship between public available accounting information (or financial statement information) and future abnormal returns. By documenting the ability of corporate earnings to predict future abnormal returns they show the existence of the post-earnings announcement drift, which is the tendency of subsequent stock returns to follow the sign of the announcement return. After the finding of the post-earnings announcement drift, many more anomalies have been found. For example, Sloan (1996) discovers the existence of the accrual anomaly, You and Zhang (2009) find that investors underreact to companies 10-K disclosures and Fama and French (1992)discover the value premium. Ou and Penman (1989) argue that financial statements contain information regarding firms’ fundamental values and that stock prices can deviate from (and subsequently gravitate back to) these fundamental values, which makes financial statement analysis relevant to investors. They were among the first to propose a trading strategy which produced ‘abnormal returns’.
Many others followed, but Piotroski (2000) was one of the first researchers to develop a relatively simple, straightforward method to identify mispriced securities. By developing a fundamental score (F-Score), measuring the financial strength of a company, he was able to differentiate ‘expected winners’ from ‘expected losers’ in the high Book-to-Market stock segment. This score consists of nine binary signals related to profitability, capital structure & liquidity and to operational efficiency. A signal receives the score of one if it is a positive signal related to the firm’s financial or operational performance (positive ROA/Cash Flow from Operations, positive change in ROA/liquidity/margin/turnover, negative accruals, negative change in leverage or no issuance of equity in the previous fiscal year) and zero otherwise. The aggregate score is considered a measure of financial and operational strength and indicates whether a stock is expected to subsequently out- or underperform other high Book-to-Market stocks.3 Using this score, Piotroski (2000) shows that a value investor, an investor who invests in the top quintile of high Book-to-Market stocks, could have increased his performance by 7.5% annually and could have earned a hedge return of 23% annually.
Woodley, Jones, and Reburn (2011) study the Piotroski score in the US in a more recent time period and find that stocks with a high score do no longer earn higher returns than stocks with a low score. They also find that stocks with a high F-Score have significantly lower systematic market risk between 1997 and 2008. This can potentially explain the higher returns of low F-Score stocks but Woodley et al. (2011) do not formally test whether systematic market risk can indeed explain the difference in returns. Despite the findings of Woodley et al. (2011), the Piotroski (2000) F-Score is still a measure which is often used in investment screens for value investors. As an investor should care both about the risks and returns of a strategy, the continued use of the F-Score as an investment screen can potentially be explained by the (lower) risk of high F-Score stocks.
The high returns to the F-Score investment strategy documented by Piotroski (2000) lead to criticism from Guay (2000) who states that the magnitude of abnormal returns generated by
3 High Market stocks with a high (low) score are expected to outperform (underperform) other high
this simple trading heuristic is very high compared to realized returns of more sophisticated investing strategies employed by hedge and mutual funds. Piotroski (2000) and Woodley et al. (2011) determine the market-adjusted returns as the buy and hold return on the portfolio less the value-weighted market return over the same period. Guay (2000) argues that this methodology might not be appropriate for controlling for expected returns and suggests to use the Fama and French (1993) framework instead. Moreover, Duong, Pescetto and Santamaria (2014) emphasize that using referencing portfolios, such as the value weighted market portfolio, can lead to misspecification of test statistics and distortion of the results. I follow the suggestion of Guay (2000) and examine the returns on high and low F-Score portfolios in a Fama and French (1993) three- and Carhart (1997) four-factor asset pricing model. This allows me to test whether the difference in returns can be explained by several risk factors which were previously not included in the calculation of market adjusted returns. Sharpe ratios are calculated to further measure the performance of the F-Score portfolios.
By investigating whether accounting information can be used for portfolio formation and investment decisions, contributions to several academic and practical fields are made. First of all, a decision usefulness approach underlies the IASB/FASB framework which means that investors should be supplied with information that is useful for decision-making (Scott, 2012). Investigating the usability of financial statement information for investors is thus of significance to policymakers, as well as to the investment community. Research in fundamental analysis also contributes to our understanding of what determines value (Kothari, 2001) and, studies such as this thesis in particular, what information is (not) incorporated into the valuation of stocks. Moreover, Ball (1992) states that the conclusion that markets are inefficient should follow from the rejection of a specific market-inefficiency hypothesis. Although it is difficult to state whether findings of abnormal returns are the result of market inefficiency or biased asset pricing models, investigating abnormal returns to an investment strategy based on publicly known accounting information adds to the growing body of market efficiency and anomaly related literature.
While consistent with Piotroski (2000) s’ and Woodley et al. (2011) s’ findings, I find lower differences in average returns between stocks with a high and stocks with a low F-Score. By examining the returns in contemporary asset pricing models, I show that a portfolio consisting of high F-Score stocks earns an average risk-adjusted positive return (alpha) in the period studied (May 1976 – April 1997) by Piotroski (2000) but that returns in the second period (May 1997 – April 2014) can be explained by the Fama and French (1993) three- and Carhart (1997) four-factor models. Moreover, I find that the difference in factors loadings between the high and low F-Score stock portfolios substantially changed between the period studied by Piotroski (2000) and the period after his study and that the findings of Woodley et al. (2011) can be explained by an asset pricing model as stocks with a low F-Score are riskier and thus require higher expected returns. Overall, I show that it was possible to separate good from bad value stocks using accounting information between 1976 and 1997 but that the ability of the F-Score to separate good from bad value stocks disappeared in a more recent time period.
The next section provides the theoretical background and hypothesis development, while section 3 presents the methodology and section 4 the results. Finally, in section 5, the conclusion and discussion will be presented.
2 Theoretical background and hypothesis development
2.1 On value stocks
Value stocks are stocks that have a relatively high Book-to-Market, earnings to price or cash flow to price ratio (Fama and French 1998). In this study, value stocks are defined as stocks that have a high Book-to-Market ratio following Fama and French (1992;1995;1998), Piotroski (2000) and Woodley et al. (2011). Although it is generally agreed that value investing strategies, on average, outperform growth investment strategies, the reasons underlying this outperformance are not clear (Chan and Lakonishok, 2004). Several explanations have been proposed, Fama and French (1992) for example attribute the value premium to risk whereas Lakonishok, Shleifer and Vishny (1994) state that the difference in returns between value and growth stocks arises from expectational errors such as the naïve extrapolation of growth.
Piotroski (2000) argues that financial statement analysis is particular suitable for value stocks. First of all, the outperformance of a value investing strategy over a growth investment strategy typically depends on the strong performance of a few value stocks, as most value stocks earn negative market-adjusted returns (Piotroski, 2000). Differentiating ex ante between the strong performers or eliminating the weak performers could be very useful for investors. Moreover, where the valuation of growth firms is often based on non-fundamental aspects of operations and on information which is not found in financial statements (Mohanram, 2005), the valuation of a value firm is based on recent changes in firm fundamentals such as financial leverage, liquidity, profitability and cash flow adequacy which can easily be obtained from financial statements (Piotroski, 2000). As value firms have low valuations relative to fundamentals and do not require the valuation of growth options to the extent that growth firms do, traditional fundamental valuation techniques are well suited for value firms (Sloan, 2001). Lastly, financial statements are the most reliable and accessible information dissemination channels for value stocks as voluntary disclosure might not be viewed as reliable given the poor recent performance (Piotroski, 2000).
2.2 Financial statement analysis investment strategies
Graham and Dodd (1934) inspired the investment community to use security analysis to find undervalued stocks. Since then, several academics have suggested that market prices can deviate from their fundamental value in the short-term but will revert back to their fundamental value in the long-term. This is the basis of most accounting investment strategies, to identify under or overpriced stocks which will revert back to their fundamental values due to long-term market efficiency, allowing for a profit in the process. Financial signals are identified and the existence of abnormal returns depends on the market’s inability to fully process the implications of these financial signals (Piotroski, 2000). In general, most financial statement analysis investment strategies identify a measure to signal a change in performance and subsequently study whether the cross section of returns on portfolios which are periodically formed based on this measure are consistent with a model of expected earnings (Kothari, 2001).
As mentioned in the introduction, Ou and Penman (1989) started this line of research, after an extensive analysis of financial statement items they create a summary measure of predicted earnings change. They use this measure to form long/short portfolios and find that this investment approach yields positive hedge returns. Lev and Thiagarajan (1993) argue that the statistical approach of Ou and Penman (1989) identified some hard to justify variables and implement a guided search for relevant fundaments. By searching in appropriate publications and newsletters they identify twelve variables which are relevant for fundamental analysis and are typically used by financial analysts. They find that an aggregate score of these signals is related to the earnings response coefficient and subsequent earnings growth.
Abarbanell and Bushee (1998) use these signals to propose an investment strategy based on nine of these signals. They find that based on a selection of signals related to changes in inventories, accounts receivables, gross margin, selling expenses, capital expenditures, effective tax rates, inventory methods, audit qualifications and labor productivity it is possible to form a portfolio earning an average yearly abnormal return of 13.2%. Piotroski (2000)
adopts this methodology and succeeds in establishing a simplistic method to construct portfolios based on a limited set of intuitively appealing accounting variables. Using nine binary accounting signals which accumulate to a summary measure (F-Score)4 he succeeds in separating winners from losers in the high Book-to-Market segment. Mohanram (2005) builds further on the F-Score by developing an adjusted F-Score, which he calls the G-Score to separate winners from losers in the low Book-to-Market (growth) stock segment. Recently, Penman and Zhang (2006) developed a measure (S-Score) for the sustainability of earnings which Dickinson and Sommers (2012) use to base their ‘competitive S-Score’ on, a measure which predicts the change in (industry and risk-adjusted) operating profitability one year ahead.
2.3 The Piotroski (2000) study
Piotroski (2000) notices that, although value stocks as a group outperform the market, the actual majority of individual stocks within this group underperforms the market. The positive results therefore stem from the ability of a relatively small group of stocks to perform very good. This triggers the question whether it is possible to use fundamental analysis to differentiate between eventual outperformers and underperformers. The central question is whether it is possible to use financial statement analysis to eliminate firms with poor prospects and skew the distribution of returns to a more favourable distribution. Piotroski (2000) shows that a high Book-to-Market investor can increase his annual returns by 7.5% by following a simple selection process. He performs several tests to identify the source of the premium to his investment strategy and shows that the F-Score’s ability to predict future returns is robust to variables that capture momentum, accrual reversal and equity issuance but that the highest returns are found in "slow information-dissemination environments", which are small and medium sized companies with low share turnover and firms with no analyst’s following. It is likely that information from these kind of companies is incorporated into stock prices (more)
slowly and it seems that the F-Score depends on the markets’ inability to incorporate information from financial statements in a timely manner.
Piotroski (2000) argues that there is no risk based explanation for the results as the signals indicate ex ante lower levels of financial and operational risk. Moreover, he simply implies that the returns are too big to be explained by risk but he concludes his paper with the following statement: “Whether the market behavior documented in this paper equates to inefficiency, or is the result of a rational pricing strategy that only appears to be anomalous, is subject for future research.” Since its publication, the F-Score has been adopted by financial analysts and equity investors and has been integrated into many popular stock screeners. Moreover, the F-Score and adjusted F-Scores have been studied in several markets and within different stock segments, such as within the growth stock segment (Mohanram, 2005). Recently, the F-Score has successfully been tested in the UK (Duong, Pescetto, and Santamaria, 2014), Australia (Aspris, Finch, Foley, and Meyer, 2013), Japan (Noma, 2010) and India (Aggarwal and Gupta, 2009). Hyde (2014) examines the applicability of the F-Score in several emerging markets and finds that stocks with a high F-Score earn significant higher returns than stocks with a low F-Score. Alberto, Dorantes and Dosamantes (2013) find that an adjusted F-Score has value relevance in the Mexican stock market and that high score stocks earn higher returns than low score stocks. Aggarwal and Gupta (2009) apply the F-Score framework to the Indian market and find evidence that portfolios with high score stocks performed significantly better than the overall market and low score portfolios.
Woodley et al. (2011) study the ability of the F-Score to differentiate winners from losers in the U.S in two different time periods. The first period is 1976 – 1996, which is the period under investigation in the original Piotroski (2000) study and the second period is from 1997 till 2008. Although several papers have documented positive returns in other markets for high F-Score stocks in this period, Woodley et al. (2011) find that the F-Score is no longer able to differentiate future winners from future losers among high Book-to-Market stocks in the U.S. stock market. They confirm the findings of Piotroski (2000) for the 1976 - 1996 period, but find
reversed results for the next 12 years when low Score stocks actually outperform high F-Score stocks. As Woodley et al. (2011) explain: a question which is not asked by Piotroski (2000) is whether differences in the average beta can explain the excess market-adjusted returns. Therefore, they investigate the beta’s of high and low F-Score portfolios. The average betas of high F-Score stocks are only marginally lower during the first period. During the next 12 years, however, Woodley et al. (2011) document relatively large differences in the average and median betas between high and low F-Score firms. They argue that these differences are economically significant, which could explain the lower returns of high F-Score firms during the 1997 – 2008 period. Moreover, idiosyncratic risk is substantially lower for high F-Score stocks relative to other value stocks in the period between 1997 and 2008 and as Fu (2009) shows, there is a positive relation between idiosyncratic volatility and expected return. It thus seems that high F-Score stocks were substantially less risky than low F-Score stocks in the period 1997 – 2008. This is supported by the notion of Guay (2000) that the expected returns for value firms with strong signals regarding future financial performance (with a high F-Score) should be lower than the expected returns for weak firms (with a low F-F-Score) because the risks for the latter firms are higher.
2.4 The disappearance of the abnormal returns of High F-Score stocks
The disappearance of the positive market-adjusted returns to the F-Score strategy documented by Woodley et al. (2011) has several potential explanations. First of all, from the notion of the risk-return tradeoff and the finding that high Score stocks are less risky compared to low F-Score stocks (during 1997 – 2008) it follows that high F-F-Score stocks should have lower expected returns than low F-Score stocks. Moreover, since its publication, the F-Score has become a widely available stocks selection screen for value investors. It is often argued that any opportunity to earn abnormal returns will be exploited by arbitrageurs, which in turn will eliminate the opportunity. When arbitrage opportunities are published, investors will try to take advantage of this new knowledge, eliminating or diminishing the opportunity. Mclean and Pontiff (2015) show that abnormal returns on anomaly trading decreases by about 32%
after publication of the anomalies and that abnormal returns to more popular strategies such as the post earnings announcement drift and the accrual anomaly have decreased even more. This is supported by the finding that the accrual anomaly has not yielded positive abnormal returns since 2001 (Green, Hand, and Soliman, 2011), and that transaction costs can explain the returns to the accrual and post earnings announcement drift anomalies (Richardson et al., 2010). Milian (2015) even shows that the earnings announcement abnormal returns have reversed for easy to arbitrage firms and suggests that investors have learned about the post-earnings announcement drift and are overcompensating. This all supports the notion of McLean and Pontiff (2015) that investors learn about mispricing from academic publications.
2.5 F-Score signals
The basis for the variable selection is the expectation that the average high Book-to-Market firm is financially distressed to some degree (Piotroski, 2000). This notion is based on findings of Chen and Zhang (1998) who find that value stocks in the United States are on average “in distress, have high financial leverage, and face substantial earnings uncertainty in the future” and Fama and French (1995) who state that that a “high Book-to-Market ratio is typical for firms that are relatively distressed”.
Distress risk is associated with declining and/or low margins, cash flows, liquidity and high levels of financial leverage (Piotroski, 2000). This is supported by research of, for example, Altman (1968) and Campbell, Hilscher, and Szilagyi (2011) who use several measures to forecast corporate bankruptcy and ‘failure’5 of companies. These forecast measures include measures of profitability, leverage, liquidity, operating efficiency and the Book-to-Market ratio. Moreover, Campbell et al. (2011) find that firms that experience a ‘failure’ have experienced losses, high leverage, low and volatile stock returns and have low levels of cash holdings. Piotroski (2000) therefore concludes that an improvement in these characteristics should be useful for indicating performance improvement for high Book-to-Market stocks.
There are four signals related to the profitability of the firm which signal the firm’s ability to generate funds internally. Piotroski (2000) assumes that any value firm which currently generates positive cash flows or profits is demonstrating the ability to generate funds through operating activities. Fama and French (1995) show that high Book-to-Market stocks have poor past earnings performance and are also expected to have poor future earnings performance, therefore a signal indicating the (increase in the) ability of a firm to generate funds is considered a positive signal.
The first measure of profitability is the return on assets (ROA). The return on assets is often used as a measure of firm performance and is calculated as net income before extraordinary items divided by total assets, it indicates the effectivity of the company’s assets in producing profits. It should however be noted that value is created by the operating activities of a firm and not by the non-operating (f.e. financing) activities of a firm (Koller, Goedhart, and Wessels, 2010). Because the ROA includes the (return on) non-operating activities and ignores the benefits of operating liabilities6, Koller et al. (2010) suggest to use the Return on Invested Capital and Dickinson and Sommers (2012) state that the Return on Net Operating Assets is a better measure for forecasting future profitability.
The second measure of profitability is the cash flow from operations scaled by total assets. Measures of earnings performance, such as the return on assets, can relatively easy be distorted by managerial decisions in contrast to the cash flow from operations measure (Sloan, 1996). Moreover, current earnings performance attributable to accruals is less likely to continue in the future compared to the earnings performance that can be attributed to the cash flow component of earnings (Sloan, 1996). Therefore, the cash flow from operations is a profitability measure that is likely to contain additional information beyond the return on assets. It should be noted that the same reasoning applies as for the return on assets as the cash flow from operations is affected by non-operating items and the capital structure of a firm.
Piotroski (2000) suggests that firms with positive earnings trends show that their ability to generate positive future cash flows improves. He therefore includes a measure, the change in return on assets, to indicate whether there is a positive earnings trend. The trend in a firm’s earnings is a common measure of performance (Koonce and Lipe, 2010) and as the average high Book-to-Market firm has poor earnings performance and is expected to have poor earnings performance in the future (Fama and French 1995), any increase in the earnings performance of the firm can therefore be considered as a good signal. However, it should be noted that the consistency of the earnings trend is especially important for the value of a firm (Koonce and Lipe, 2010) and that this is not captured by the signal.
The last profitability signal is a measure for the quality of earnings. It relates to the accrual effect which was documented by Sloan (1996) who shows that stock prices do not fully reflect information contained in accruals. Accruals can be used by managers to manipulate earnings and can be considered as a measure of earnings quality (Chan, Chan, Jegadeesh, and Lakonishok, 2006; Perotti and Wagenhofer, 2014). Firms in financial distress are more likely to use discretionary accruals to manage earnings (Sweeney, 1994) and the accrual measure might therefore be of additional importance to high Book-to-Market stocks. Chan, Chan, Jegadeesh, and Lakonishok (2006) classify accruals as the difference between accounting earnings and cash flowand state that high accruals indicate that the quality of earnings is low.
The next three signals measure changes in the capital structure and the firm’s ability to meet future debt obligations. These signals, in particular, are based on the specific characteristics of value stocks and a decrease in leverage, an improvement of liquidity and no issuance of equity are considered to be good signals (Piotroski, 2000).
A healthy firm might benefit from increased levels of leverage due to an increasing tax shield (Graham, 2000) or a reduction of agency costs (Jensen, 1986). An increase in leverage for a firm in financial distress however indicates that a firm is unable to generate enough funds internally and decreases a firms financial flexibility (Piotroski, 2000). Moreover, agency costs can also rise if the leverage is (too) high as firms may forgo positive NPV projects (Myers,
1977) and bankruptcy costs increase (Jensen, 1986). As the average leverage ratio of value stocks is relatively high (Chen and Zhang, 1998), it is plausible that the positive consequences of a decrease in leverage outweigh the negative consequences for the average value firm.
The same reasoning applies to the liquidity of a firm, high liquidity can increase agency costs but also make it easier for firms to raise external capital (Myers and Rajan, 1998) and thus improve financial flexibility. Moreover, liquid firms have lower ex-ante borrowing costs (Graham, 2000) and liquidity measures the firm’s ability to meet current debt obligations (Piotroski, 2000). An increasing liquidity does not necessarily mean that the value of a firm decreases but for the average high Book-to-Market firm it is plausible that the positive consequences outweigh the negative consequences.
The last signal regarding the capital structure of the firm is whether the firm issued equity in the preceding year. As investors correctly assume that the management is better informed about the true value of the firm and only issues equity if this is in the interest of the management or current shareholders, the issuance of equity gives a negative signal regarding the value of the firm (Leland and Pyle, 1977; Myers and Majluf, 1984). This is supported by findings of, among others, Masulis and Korwar (1986) who show that stock prices react negatively to the issuance of equity. Moreover, the ‘pecking order theory’ (Myers and Majluf, 1984) suggests that firms prefer to use internal sources of funds, and if external financing is needed prefer the issuance of debt over the issuance of equity. The issuance of equity can therefore be considered as ‘a last resort’ and will only be used if a firm has no other options of raising capital. The issuance of equity of high Book-to-Market firms, who tend to have relatively low stock prices7, indicates even more the lack of alternatives and poor financial conditions such companies are facing (Piotroski, 2000).
The efficiency of the operating activities is the last group of signals, it comprises of the change in margin and change in turnover which directly relate to measures of profitability (Fairfield and Yohn, 2001) and are key determinants for the value creation of a company. Fairfield and
Yohn (2001) state that changes in the asset turnover and profit margin should be useful for predicting future profitability as they relate to productivity and profitability, respectively. They find that changes in both variables are indeed useful for forecasting the change in return on assets one year ahead. Just as in the Abarbanell and Bushee (1998) study, the gross margin relative to sales is considered as a measure of operating profitability. The change in asset turnover can be considered as a measure of operating efficiency.
To determine whether a signal is positive or negative, a benchmarks has to be chosen. The benchmark for return on assets and cash flow from operations are zero profits and zero cash flow from operations. This can be supported by Fama and French (1995) who state that value stocks, on average, have had poor earnings performance in the past and are expected to have poor earnings performance in the future and Piotroski (2000) who concludes that positive earnings are meaningful events for high Book-to-Market stocks. Some researchers suggest to use the industry average (Mohanram, 2005) or forecasts of financial analysts as benchmarks but Piotroski (2000) finds that using industry-adjusted factors does not substantially alter the results.8 The other signals indicate an improvement in fundamentals or indicate whether there was an issuance of equity. The same reasoning applies for these signals as some kind of forecast could have been chose. However, as the average recent performance of high Book-to-Market stocks is relatively poor, any improvement in these variables can be considered as a good signal.
An important notion of Piotroski (2000) is that every signal is not always necessary positive for the future performance of a particular high Book-to-Market stock, but it is expected that the signals, on average, indicate positive improvements.
2.6 Hypothesis development
Success of investment strategies based on fundamental analysis is only possible if prices do not accurately reflect the incremental value of a firm and if the drift from this incremental
8 Using analyst’ forecast would not be practicable as most high Book-to-Market stocks are not followed by analysts
value is temporarily. If this is the case, investors can benefit from revisions of biased expectations and related price corrections (Piotroski and So, 2012). Piotroski (2000) proposes a way to use fundamental analysis to select stocks which he calls ‘expected winners’ (the stocks with the highest F-Score) which will outperform the ‘expected losers’ (the stocks with the lowest F-Score). Woodley et al. (2011) confirm the findings of Piotroski for the 1976 – 1996 period but find reversed results for the 1997 – 2008 period.
H1: A portfolio of high F-Score stocks earns higher return than a portfolio consisting of low F-Score
stocks during the first period (May 1976 – April 1997)
H1b: A portfolio of high F-Score stocks does not earn higher returns than a portfolio consisting of low
F-Score stocks during the second period (May 1997 – April 2014)
The expectation is thus that high F-Score stocks earn higher returns relative to low F-Score stocks in the first period but not anymore in the period after 1997. The disappearance of the relatively high (low) returns on high (low) F-Score stocks can be explained by several theories. After the Piotroski (2000) paper was published, the F-Score became known to the investment community and is now a known investment metric and ‘stock screen’ for value investors. As Xue and Zhang (2011) show, institutional investors trade on fundamental signals which could mean that the abnormal returns have been arbitraged away since the publication. The surprising finding that low F-Score firms outperform high F-Score firms indicates that the arbitrage opportunity has reversed which can happen if market participants trade on the documented anomaly too much and overcompensate (Milian, 2015). Another possibility is that the seemingly anomalous returns documented by Piotroski (2000) were not truly anomalous, but an effect of data fitting. This seems unlikely as several researchers have replicated the results in other markets (e.g. Duong et al., 2014, Aspris et al., 2013, Noma, 2010 and Aggarwal and Gupta, 2009) which lets Richardson et al. (2010) to conclude that the F-Score has been able to mitigate this criticism. Another explanation, suggested by Guay (2000), is that the method of determining excess returns is not appropriate. Woodley et al. (2011) document that high F-Score stocks have significantly lower (systematic) risk which could
potentially explain lower returns on high F-Score stocks compared to low F-Score stocks but do not test whether this is the case. By using the Fama and French (1993) three-factor model it is possible to investigate whether the returns of F-Score stock portfolios can be explained by a contemporary asset pricing model. Based on the findings of Piotroski (2000) and Woodley et al. (2011) I expect that a high (low) F-Score stock portfolio earns a positive (negative) alpha in the first period and that the returns can be explained by the Fama and French (1993) three-factor model in the second period.
H2: The high (low) F-Score portfolio earns abnormal positive (negative) returns in the Fama and French (1993) three-factor model during the first period (May 1976 – April 1997)
H2b: The high and low F-Score portfolio returns can be explained by the Fama and French (1993) three-factor model in the second period (May 1997 – April 2014)
3. Methodology
The calculation of the signals and the scores are shown in table 1.
3.1 Selection of the variables
Table 1. Construction of F-Score signals
Profitability signals Score of signal (1)
Return on Assets (ROA)
Net income before extraordinary items scaled by beginning of the year total assets
if positive
∆ Return on Assets (∆ROA)
Current year’s ROA less prior year’s ROA if positive
Cash flow from operations (CFO)
Cash flow from operations scaled by beginning of the year total assets
if positive
(Low) Accruals CFO less ROA if positive
Leverage, liquidity and source of funds
∆ Leverage The historical change in the ratio of long-term debt to average total assets
if negative
∆ Liquidity The historical change in the firm’s current ratio between the current and prior year
if positive
Equity offer Issuance of common equity in the year preceding portfolio formation
if no issuance
Operating efficiency
∆Margin Firm’s current gross margin ratio less the prior year’s gross margin ratio
if positive
∆Turnover Firm’s current year asset turnover ratio less the prior year’s asset turnover ratio
if positive
Following Piotroski (2000) and Woodley et al. (2011) I classify stocks with an aggregate score of eight or nine as high Score companies and stocks with a score of zero or one as low F-Score companies. As there is a limited amount of stocks with a score below two, I also consider an adjusted low F-Score portfolio, consisting of companies with a score of zero, one and two. This choice is supported by Duong et al. (2014) who classify low F-Score companies as companies with a score from zero to three as they also find few observations with a score of below two.
3.2 Data
The necessary accounting data for calculating the F-Score is obtained from the Center for Research in Security Prices (CRSP)/Compustat Merged database and stock return data is obtained from the CRSP monthly stock file. The independent factors [Market risk, Small Minus Big (SMB), High Minus Low (HML), Momentum (MOM)] are obtained from the Ken French website9 and the risk-free rate is obtained from CRSP10.
3.3 Sample Selection
Every year, between 1972 and 2013, all stocks with sufficient available information are selected from Compustat. Only stocks with a normal share code11 and non-missing values for book value of equity12, (beginning of the year) total assets, number of shares outstanding and fiscal-years end prices on Compustat are included in the sample. The remaining firms-fiscal-years are sorted based on the calendar year in which the fiscal year-end month falls. Based on this sample I calculate the yearly Book-to-Market quintile cut-off values. Stocks in the highest Book-to-Market quintile are considered value stocks. For these value stocks I calculate the F-Score signals and subsequently the aggregate score based on fiscal year-end financial statement information. After exclusion of the companies for which not all F-Score signals can be calculated, 24.702 firm-years remain.
3.4 The trading strategy
To ensure that all financial statement information is available when the portfolios are constructed, portfolios for a given calendar year will be formed at the beginning of the fifth month after December 31 (following Piotroski, 2000). This way, there are at least four months between the last possible date of the fiscal year-end13 and the forming of the portfolios, this
9 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html accessed on May 2015 10 The risk-free rate is the one month treasury bill rate
11Share code is retrieved from the CRSP monthly stock file and following the literature, I include only shares with CRSP
share code 10 or 11 (Lee and Swaminathan, 2000., Hong, Lim and Stein, 2000).
12 I also require the book value of equity to be positive 13 December 31
ensures that all information was readily available for investors at the time of formation. Following Piotroski (2000), I classify low F-Score stocks as firms with a score of zero or one and high F-Score stocks as firms with a score of eight or nine. Moreover, I construct another portfolio: the Adjusted Low F-Score portfolio, consisting of stocks with a score of zero, one or two.
Following common finance literature (f.e. Lakonishok, Shleifer, and Vishny, 1994), I equally weight the stocks in the portfolio and use an annual buy and hold strategy to calculate the returns. The portfolio is subsequently rebalanced every year on the first trading day of May. In this regard, my methodology differs from Piotroski s’ (2000) who rebalances the portfolio every month. By applying one formation point per year I follow Duong et al. (2014) who argue that applying multiple rebalances leads to spurious economic and statistical inferences [based on research of Liu and Strong (2008)]. Assuming one formation/rebalancing point per year mitigates these concerns. Moreover, rebalancing a portfolio every month leads to substantial costs, such as taxes and transaction, time and labour costs (Tokat and Wicas, 2007).The downside of annual rebalancing is that relatively stale information is used to calculate the F-Scores if firms have other than December year-ends and that the risk increases over the year as the portfolio drifts to a higher risk – higher returns asset allocation (Tokat and Wicas, 2007).
For the last day of each month, the value of the different portfolios are calculated assuming that one dollar is invested in the portfolio on the first trading day of May. Monthly returns are calculated as the difference in portfolio value between month(t-1) and month(t) divided by the portfolio value at month(t-1). This ensures that the returns reflect the true buy and hold return of an investor who buys the portfolio in May and sells the portfolio on the last trading day in April (one year later). If a firm delists, the delisting return is assumed to be zero (following Piotroski, 2000 and Woodley et al., 2011) and dividends are assumed to be reinvested in the stock disbursing these dividends.
3.5 The aggregate F-Score
After calculation of the different F-Score signals,14 the aggregate F-Score is determined as follows
F-Score = f-roa + f-cfo + f-Δroa + f-accrual + f-Δlever + f-Δliquid + f-issuance + (1) f-Δmargin + f-Δturnover.
3.6 Expected return
The Efficient Market Theory assumes that investors are risk-averse and therefore demand a compensation for risk, which is given in the form of a higher expected return. However, not all risk is compensated because investors have the ability to diversify their portfolio and therefore, only non-diversifiable or ‘systematic’ risk will be compensated by a higher expected return. From the concept of efficient markets and risk averse investors, it follows that it is not possible to achieve above average returns without accepting above average risks (Malkiel, 2005). Whether abnormal returns, returnsdifferent from the expected return, can be achieved is thus a test of market efficiency. Sharpe (1964) and Lintner (1965) develops the Capital Asset Pricing Model which calculates the expected return as a function of a stocks’ systematic risk and the risk free rate. Anomalous findings for value and small stocks lead Fama and French (1993) to develop their multifactor pricing model. Fama and French (1993) suggest that the risk of a stock is related to different factors, such as the Book-to-Market and Size factors. In essence, Fama and French (1993) state that the value and size premiums are compensations for systematic risk which are not captured by beta. Carhart (1997) proposes to add another factor which had proven to be a source of returns, the momentum factor, to explain returns of mutual funds. Combining these factors makes it possible to investigate whether returns can be attributed to market risk, the high Book-to-Market, small company premiums or the momentum factor. Whether or not the value, size and momentum factors are related to
systematic risk is still a matter of debate15, but there is substantial evidence that these factors can better explain stock returns than the CAPM.
It is common practice to measure abnormal returns by using a benchmark portfolio. However, this can potentially lead to distorted results as the risk of the benchmark portfolio should be equal to the risk of the portfolio under investigation. Although Piotroski (2000) performs several robustness tests for known risk factors, he does not implement an asset pricing model as proposed by Fama and French (1993)/Carhart (1997). As high F-Score stocks are per definition high Book-to-Market stocks and Piotroski (2000) found that the returns were strongest in a subsample of small companies, these two factors have the possibility of explaining a substantial part of the returns on a high F-Score portfolio.
To measure the performance of the F-Score portfolios within the Fama and French (1993) framework, the following equation is estimated:
𝑅𝑝𝑡−𝑅𝑓𝑡= 𝑎 + 𝛽1(𝑅𝑚𝑡− 𝑅𝑓𝑡)+ 𝛽2𝑆𝑀𝐵𝑡+ 𝛽3𝐻𝑀𝐿𝑡+𝜀𝑡, (2)
where
- 𝑎 is the abnormal return measure of the portfolio (i.e. part of the return which is not explained by the different factors)
- 𝑅𝑝𝑡is the raw return on the portfolio in calendar month t
- 𝑅𝑓𝑡 is the one month treasury bill rate
- 𝑅𝑚𝑡 is the market index return in calendar month t
- SMB is the return on a portfolio of small stocks minus the returns on a portfolio of large stocks
- HML is the return on a portfolio with high book-to-market ratios minus the return to a portfolio with low book-to-market ratio stocks.
15 For example, there is no strong evidence that Size and in particular B/M proxies for default risk (Bird and Casavecchia.
Carhart (1997) proposes to add another factor which had proven to be a source of returns, the momentum factor, to explain returns of mutual funds. Combining these factors makes it possible to investigate whether returns can be contributed to market risk, the high Book-to-Market, small company premiums or the momentum factor.
To measure the performance of the F-Score portfolios within the Carhart (1997) framework, the following equation is estimated:
𝑅𝑝𝑡−𝑅𝑓𝑡= 𝑎 + 𝛽1(𝑅𝑚𝑡− 𝑅𝑓𝑡)+ 𝛽2𝑆𝑀𝐵𝑡+ 𝛽3𝐻𝑀𝐿𝑡 + 𝛽4𝑀𝑂𝑀𝑡+ 𝜀𝑡, (3)
where
- MOM is the return on high momentum stocks minus the return on low momentum stocks.
In equation 2 and 3, all factor loadings are estimated using a time series regression over the period under investigation. The alpha value is the intercept of the time series regression and shows the average abnormal return of the portfolio which cannot be explained by the different risk factors. The 𝛽′𝑠 give the sensitivity of the portfolio to the risk/explanatory factors [(𝑅𝑚−
𝑅𝑓), SMB, HML and MOM].
3.7 The Sharpe (1966) Ratio
The previous segment considers only systematic (non-diversifiable risk) but if an investor invests only in one portfolio, the actual risk of the portfolio is higher than indicated by the beta’s related to the before mentioned risk/explanatory factors. A typical investor will not only care about systematic risk as he will not always be able to diversify all his non-systematic risk away. Consider an investor who only invests in either one of the before considered portfolios [High Score, (Adjusted) Low Score and Entire Value], the risk this investor faces is not the systematic risk of the portfolio but the entire amount of risk (volatility) of the portfolio.
The Sharpe ratio (Sharpe, 1966) measures the reward per unit of (non-systematic & systematic) risk. By comparing the Sharpe ratios of different F-Score portfolios, I am able to evaluate the performance relative to the total risk.
The Sharpe ratio is calculated as follows:
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =𝑅𝑝−𝑅𝑓
𝜎𝑝 , (4)
where
𝑅𝑝 = Expected portfolio return16 𝑅𝑓 = Risk-free rate 𝜎
𝑝= Standard deviation of portfolio
returns.
4. Results
As Piotroski (2000) and Woodley et al. (2011) show, returns and risks of the high and low F-Score portfolios were quite different during the period studied by Piotroski (2000) compared to the period after his study. To compare both periods, I divide my sample in two subsamples: (1) formation years 1975 till 199517 and (2) formation years 1996 till 201218.
4.1 Characteristics of the portfolios19
Table 2. Financial characteristics of High Book-to-Market firms 1975-2012 (24.702 observations)
Descriptive statistics20 of the value firms during the entire period (1975 - 2012) can be found in table 2. Overall, the figures are in line with poorly performing companies who are struggling with profitability. This is consistent with Piotroski (2000), Woodley et al. (2011) and Fama and French (1995). Most figures are comparable to the figures presented by Piotroski (2000) and Woodley et al. (2011). The negative average Return On Assets, change in ROA/margin/turnover and the negative median change in ROA/margin/liquidity and turnover are all indicators that value firms have trouble staying competitive and profitable. Inconsistent with this notion but consistent with previous findings are the overall positive cash flow and negative accruals. In appendix 2, the financial characteristics of high Book-to-Market firms during both sub-periods are presented. In the second period the average and median Market Value of Equity and Assets increased substantially, which can be explained by the growth of the companies in the
17 Return period: 1976-05 till 1997-04 18 Return period: 1997-05 till 2014-04
19 High, low and Adjusted low F-Score portfolios are referred to as High, Low and Adjusted Low Score portfolios 20 These numbers have been winsorized at the 1 and 99th percentile
Mean Median % positive signal
MVE 147.35 20.92 -Assets 523.18 71.77 -B/M 1.8256 15454 -ROA -0.0165 0.0103 59% ∆_ROA -0.0171 -0.0081 42% ∆Margin -0.0075 -0.0040 44% CFO 0.0429 0.0507 76% ∆Liquidity -0.0762 -0.0307 45% ∆Leverage -0.0022 -0.0017 64% ∆Turnover -0.0567 -0.0153 46% Accrual -0.0600 -0.0516 79% issuance - - 51%
sample during the relatively long time-span. Most importantly, the average (change in) ROA deteriorated but most average’s, medians and % of positive signals21 stayed relatively similar.
Table 3 provides an overview of the distribution of stocks per formation year and F-Score. To be a suitable investment strategy, enough stocks should be identified to invest in and as can be seen, there are several years when there are relatively few low F-Score stocks (1975 – 1981, 1983, 2006 and 2009-2012 all have less than eight stocks in the score range of zero and one).22 To mitigate concerns regarding the implementability of such a Low Score portfolio, I evaluate the performance of an Adjusted Low Score portfolio, with a score of zero, one or two. This choice is supported by the decision of Duong et al. (2014) to regard stocks with a score of zero, one, two and even three as low F-Score stocks.
Table 3. Number of stocks per score & year
21 With the exception of the F-Issuance variable which deteriorated from 62% to 35%
22 There is one formation year (1976) with no stocks with a score below 2. For analyzing purposes I assume that the risk free
rate is earned for that specific period.
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 1975 0 2 14 54 107 148 143 106 50 15 1994 1 13 46 74 112 137 123 90 50 17 1976 0 0 9 29 67 118 136 150 120 35 1995 2 14 52 102 133 169 117 84 58 11 1977 0 1 17 44 87 127 126 124 92 19 1996 1 17 50 126 149 163 142 105 51 19 1978 0 1 11 31 96 132 136 122 81 15 1997 4 21 70 133 162 170 150 112 71 15 1979 2 0 10 40 110 132 131 115 68 4 1998 7 24 71 159 180 168 137 74 54 10 1980 0 4 16 42 120 137 142 102 47 5 1999 3 18 66 96 174 151 111 88 37 13 1981 2 3 12 43 99 136 147 111 54 17 2000 1 17 60 134 158 144 136 89 36 4 1982 0 11 29 71 117 145 122 82 44 13 2001 0 16 60 146 170 174 112 69 32 8 1983 0 4 18 52 106 128 124 127 53 12 2002 1 25 73 123 170 165 104 112 56 9 1984 5 17 32 86 103 131 120 117 58 13 2003 1 8 39 87 144 140 122 93 50 13 1985 5 14 56 97 151 152 105 91 53 10 2004 0 10 25 79 128 100 110 84 48 8 1986 1 12 48 103 140 132 138 72 52 15 2005 2 12 48 78 112 135 114 63 24 0 1987 0 10 54 74 111 139 137 89 50 12 2006 0 6 34 79 112 111 90 49 23 5 1988 1 16 38 98 122 126 121 102 60 12 2007 0 12 34 62 84 89 64 39 16 3 1989 3 10 47 102 144 136 120 87 41 18 2008 2 11 51 123 120 98 55 28 14 1 1990 3 11 44 91 139 147 124 73 44 14 2009 0 3 29 64 97 83 57 34 15 5 1991 2 10 42 88 147 157 131 92 58 13 2010 1 5 13 36 45 71 69 61 28 5 1992 0 10 46 73 117 154 134 109 73 24 2011 0 6 22 51 67 69 70 32 12 3 1993 0 10 45 93 135 168 134 91 70 14 2012 1 6 21 43 85 90 56 33 21 7
4.2 Raw returns
In table 4 and 5, descriptive statistics of the returns on High, Low, Adjusted Low Score, Value23 and the Market portfolios, during the first period,24 are presented. The average return on both Low Score portfolios are rather similar but the median return is substantially higher while the standard deviation is lower for the Adjusted Low Score relative to the original Low Score portfolio. This can be explained by the limited amount of stocks in the original Low Score portfolio which increases the volatility of returns.
It should be noted that the yearly average raw return on the High Score (Low Score) portfolio is lower (higher) than was documented by Piotroski (2000) and Woodley et al. (2011). Although the difference in average return between the High and Low Score portfolios is lower, it is still substantial and in line with previous findings.
Table 4. Monthly raw returns (1976m05 - 1997m04: 252 monthly observations)
Table 5. Yearly raw returns (1976m05 - 1997m04: 21 observations)
Table 6 and 7 provide the descriptive statistics of the monthly and yearly returns on the five portfolios during the second period.25 Comparing the Adjusted Low and original Low Score portfolio leads to the conclusion that the return characteristics of these portfolios are quite different for the period of May 1997 to April 2014. Not only the yearly median returns and standard deviation differ substantially in this period, but also the difference in average returns
23 These are the returns to the entire portfolio of all value stocks 24 May 1976 to April 1997
25 May 1997 to April 2014
High Score Low Score Adj. Low Score Value Market
Mean 0.0190 0.0091 0.0099 0.0173 0.0125 Median 0.0153 0.0030 0.0073 0.0193 0.0149 Std. Dev. 0.0478 0.0937 0.0625 0.0473 0.0424
High Score Low Score Adj. Low Score Value Market
Mean 0.2525 0.1193 0.1228 0.2256 0.1564 Median 0.2013 0.0317 0.1264 0.1693 0.1507 Std. Dev. 0.2195 0.3831 0.2321 0.2023 0.1467
increased. The median monthly return is substantially higher for the Adjusted Low Score portfolio, while its monthly standard deviation is substantially lower.
The average return on the High Score portfolio is considerably lower than the average return on the other high Book-to-Market portfolios, while the median return on the High Score portfolio is higher compared to the other portfolios. Notably, only the Market portfolio (which is per definition very well diversified) has a lower standard deviation than the portfolio consisting of high F-Score stocks. The low standard deviation of the returns on the High Score portfolio is a first indication of the relatively low risk of this portfolio.
Comparing the return characteristics in the period between May 1997 and April 2014 with the raw returns documented by Woodley et al. (2011) leads to the same conclusions as for the first period. Although the difference in average return between the High and Low Score portfolios is lower, it is still substantial and in line with previous findings.
Table 6. Monthly raw returns (1997m05 - 2014m04: 252 monthly observations)
Table 7. Yearly raw returns (1997m05 - 2014m04: 17 observations)
Comparing tables 4 (5) and 6 (7) leads to the conclusion that the average return on a portfolio of high F-Score stocks has decreased considerably while the average returns of both Low Score portfolios have increased. Returns on the Value portfolio slightly increased while the average return of the Market portfolio decreased. From comparing these figures, it looks like value stocks performed relatively well during May 1997 and April 2014 with a yearly average return of over 24% but that the high F-Score stocks performed relatively weak in this period. This is a first indication that the F-Score was able to separate winners from losers in the period
High Score Low Score Adj. Low Score Value Market
Mean 0.0109 0.0169 0.0129 0.0155 0.0073 Median 0.0168 0.0036 0.0104 0.0163 0.0138 Std. Dev. 0.0581 0.1123 0.0848 0.0644 0.0474
High Score Low Score Adj. Low Score Value Market
Mean 0.1629 0.2452 0.2132 0.2440 0.0953 Median 0.1990 0.1148 0.0794 0.1398 0.1418 Std. Dev. 0.3390 0.5294 0.5070 0.4525 0.2013
studied by Piotroski (2000) but not anymore after 1997. This is consistent with findings of Woodley et al. (2011).
I use the t-test (Wilcoxon signed rank test) to formally test whether the difference in average (median) returns to the various portfolios are significantly different from zero. Table 8 shows that the difference in mean returns between the High and Low, High and Adjusted Low and Adjusted Low and Value portfolios are significantly different from zero and that all differences in medians are significantly different from zero in the period April 1976 - May 1997.
Table 8. Differences between the monthly returns of the portfolios in the first period (1976m05 - 1997m04)
This table shows the difference in the average and median monthly returns between the various portfolios. Probability and significance levels are determined by applying the t-test (Wilcoxon signed rank test) for the mean (median) differences in monthly returns.
Table 9 shows that only the difference in average (median) return between the High Score and Value portfolio (Adjusted Low Score and value) is significantly different from zero in the period April 1997 – May 2014.
Table 9. Differences between the monthly returns of the portfolios in the first period (1997m05 - 2014m04)
This table shows the difference in the average and median monthly returns between the various portfolios. Probability and significance levels are determined by applying the t-test (Wilcoxon signed rank test) for the mean (median) differences in monthly returns.
High - Low High - adj. Low High - Value Low - Value adj. Low - Value
Mean 0.0099* 0.0091*** 0.0018 -0.0081 -0.0073*** Probability (0.0592) (0.0002) (0.1121) (0.1058) (0.0006) Median 0.0166*** 0.0110*** 0.0022** -0.0156*** -0.0077*** Probability (0.0048) (0.0001) (0.0290) (0.0076) (0.0002) std.dev 0.0831 0.0388 0.0176 0.0797 0.0335 * sig. at 10% level ** sig. at 5% level *** sig. at 1% level
High - Low High - adj. Low High - Value Low - Value adj. Low - Value
Mean -0.0060 -0.0019 -0.0045* 0.0015 -0.0026 Probability (0.3675) (0.6653) (0.0968) (0.7833) (0.3237) Median 0.0084 0.0009 -0.0020 -0.0110 -0.0050* Probability (0.7894) (0.5757) (0.1860) (0.3229) (0.0682) std.dev 0.0948 0.0643 0.0389 0.0754 0.0374 * sig. at 10% level ** sig. at 5% level *** sig. at 1% level
While the difference between the average High and (Adjusted) Low Score portfolio returns in the second period are significantly positive, they are insignificantly negative in the period between May 1997 and April 2014. The difference in median return between the High and (Adjusted Low) Score portfolio returns is significantly positive in the first period but insignificantly positive in the second period.
It can be concluded that a portfolio of high F-Score stocks earns significantly higher average and median returns than a portfolio consisting of low F-Score stocks during the first period (May 1976 – April 1997) but not anymore during the second period (May 1997 – April 2014). Hypotheses H126 and H1b27 can therefore be accepted.
4.3 Change in portfolio value
To illustrate the change in portfolio value an investor would have experienced, graph 1 shows the change in portfolio value if one dollar was invested in May 1976.
Graph 1. The change in portfolio value if 1$ was invested in May 1976 till April 2014
26 A portfolio of high F-Score stocks earns higher return than a portfolio consisting of low F-Score stocks during the first
period (May 1976 – April 1997)
27 A portfolio of high F-Score stocks does not earn higher returns than a portfolio consisting of low F-Score stocks during the
Over the entire period, the High Score portfolio performed relatively well, only the overall Value stock portfolio had a higher portfolio value in April 2014. Investing in one of the two Low Score portfolios would have earned an investor less than he would have earned by investing in the overall Market portfolio. But, as shown by table 4, 5, 6 and 7, the High Score portfolio performed particularly well during the first period but not anymore during the second period. This is illustrated by graph 2 and 3 who show the change in portfolio value during the two sub-periods.
Graph 2. The change in portfolio value if 1$ was Graph 3. The change in portfolio value if 1$ was
invested in May 1976 (till April 1997) invested in May 1997 (till April 2014)
Graph 2 shows the change in portfolio value till April 1997 if one dollar was invested in May 1976. The end value of the High Score portfolio is almost $86,56 while that of the original Low Score portfolio is $3,26 and that of the Adjusted Low Score portfolio $7,45. The end value of the High Score portfolio is also substantially higher than that of the overall Value ($56,02) and Market portfolio ($18,07). Graph 3 shows the performance of one dollar invested in May 1997. The entire Value stock portfolio has the highest end value in April 2014 ($15,15) and all portfolios had higher ending values than the Market portfolio. The ending value of the original Low Score portfolio ($9,22) is considerably higher than that of the High Score portfolio ($6,53) and the ending value of the Adjusted Low Score portfolio ($6,74) is only slightly higher than that of the High Score portfolio ($6,53). The graph clearly shows the big impact of the
HML SMB MOM Mean 0.0053 0.0026 0.0032 0.0039 0.0020 Median 0.0124 0.0020 0.0019 0.0052 0.0015 Maximum 0.1135 0.1388 0.2202 0.1839 0.0056 Minimum -0.1723 -0.1261 -0.1640 -0.3472 0.0000 Std. dev. 0.0475 0.0342 0.0359 0.0570 0.0018 (𝑅𝑚𝑡− 𝑅𝑓𝑡) 𝑅𝑓𝑡
2008/2009 stock market crash on value stocks with portfolio values decreasing in excess of 50% and it seems that the Low as well as the High Score portfolios were affected in the same magnitude.
4.4 Performance measurement of the F-Score portfolios
The previous segment shows that investing in high F-Score stocks was, at least by looking at the return, a good strategy in the first period but that an investor would have earned higher returns by investing in the low F-Score portfolios or the Value portfolio after April 1997. As explained before, the average risk-averse investor primarily cares about the risk-return trade-off and therefore, higher amounts of risk can potentially explain higher average returns. In the next section it will be investigated whether the raw returns on the different constructed portfolios can be explained by the Fama and French (1993) three-factor or Carhart (1997) four-factor models.
First, the descriptive statistics of the independent variables during both sub-periods are shown in table 10 and 11. The tables give the average, median, minimum and maximum returns on the different factors [Market (𝑅𝑚𝑡− 𝑅𝑓𝑡), High minus Low, Small Minus Big and Momentum
premium] and the return on the Risk-Free rate. Most notably, while the average return on the SMB factor increased, the average return on the other factors decreased.
Table 10. Descriptive statistics of independent return variables (1976m05 - 1997m04: 252 observations)
Table 11. Descriptive statistics of independent return variables (1997m05 - 2014m04: 204 observations)
HML SMB MOM Mean 0.0067 0.0036 0.0019 0.0089 0.0058 Median 0.0098 0.0039 0.0021 0.0089 0.0053 Maximum 0.1247 0.0760 0.0846 0.1524 0.0135 Minimum -0.2324 -0.0845 -0.0990 -0.0958 0.0021 Std. dev. 0.0426 0.0251 0.0249 0.0312 0.0024 (𝑅𝑚𝑡− 𝑅𝑓𝑡) 𝑅𝑓𝑡
4.4.1 Fama and French (1993) three-factor model
Table 12 provides the results to the Fama and French (1993) three-factor regression model28 for the period of May 1976 – April 1997. As expected, the High Score portfolio earns a significant positive alpha and the Adjusted Low Score portfolio earns a significant negative alpha during this sub-period. This is consistent with Piotroski (2000) and Woodley et al. (2011) who find that high (low) F-Score stocks earn abnormal positive (negative) returns. Surprisingly, the negative alpha of the original Low Score portfolio is not significant. A possible cause is the big volatility of this portfolio due to its low number of stocks. It follows that hypothesis H229 can partially be accepted as the High (Adjusted Low) Score portfolio earns a significant positive (negative) alpha in the Fama and French (193) three-factor model, while the negative alpha of the original Low Score portfolio is not significant in the period May 1976 – April 1997.
Piotroski (2000) found that the abnormal returns were primarily earned by small companies, this is supported by table 12 as the factor loadings on the SMB factor are relatively high for all the portfolios. The returns are thus particularly sensitive to the performance of small relative to big companies. When the relatively high SMB factor loadings are taken into consideration, the market factor loadings are also quite substation.
Moreover, three ‘hedge’ portfolios are constructed to determine whether the alpha’s are significantly different from each other. It can be concluded that the alpha’s of the High Score and Adjusted Low Score portfolios are significantly different from each other as the alpha is significant at the 1% level. The alpha’s of the High Score – Low Score portfolio30 and High Score – Value portfolio are not significant and it therefore cannot be concluded that these alpha’s are significantly different from each. This indicates that the abnormal monthly returns on a portfolio of high F-Score stocks are significantly higher than the abnormal returns on the
28 All Fama and French (1993) and Carhart (1997) regressions have been tested for, and if necessarily adjusted for,
heteroscedasticity
29 The high (low) F-Score portfolio earns abnormal positive (negative) returns in the Fama and French (1993) three-factor
model during the first period (May 1976 – April 1997)
