Uppsala University
siness studies utumn 2010
Department of Bu
Bachelor Thesis, A Tutor: Jiri Novak Date: 2011‐01‐05
A Value Relevant Fundamental Investment Strategy
The use of weighted fundamental signals to improve predictability
Martin Eliasson, Khawar Malik, and Benjamin Österlund
1Abstract
The aim of this study is to investigate the possibility to improve the investment model defined in Piotroski (2000) and the subsequent research carried out on this model. Our model builds further upon the original fundamental score put forth by Piotroski. This further developed model is tested in two different contexts; firstly, a weighted fundamental score is developed that is updated every year in order to control for any changes in the predictive ability of fundamental signals over time. Secondly, the behavior of this score is analyzed in context of recession and growth cycles of the macro economy. Our findings show that high book‐to‐
market portfolio consist of poor performing firms, as shown by Fama and French (1995) and is thereby outperformed by both Piotroski's F_score and our own developed scores. The score based on a rolling window correlation is performing a little better then F_score, but the score based on correlations for prior Up and Down periods is not. The conclusions we draw from the results are that improvements have to be made, both to F_score and our own developments, to sort winners from loser to get an even more profitable zero‐investment hedge strategy.
1
We would like to thank our superior tutor, Jiri Novak, for his valuable support, views and ideas to our thesis. We
would also like to thank Peter Westin, for his manner of addressing and working around problems, and his way of
giving input when it is as most needed.
Table of contents
1. Introduction ... 2
2. Theory ... 4
2.1 The book‐to‐market effect: Risk versus mispricing ... 4
2.2 Fundamental analysis ... 5
2.3 The fundamental signals ... 6
2.3.1 F_score ... 6
2.3.2 Performance signals for profitability ... 7
2.3.3 Performance signals for financial leverage/liquidity ... 7
2.3.4 Performance signals for operating efficiency ... 8
2.4 Weighted F_score ... 8
2.4.1 Predictive ability of fundamental signals ... 8
2.4.2 Fundamental analysis score based on correlation ... 10
2.5 Our hypothesis ... 11
3. Research design ... 11
3.1 Data sample ... 11
3.2 Calculations ... 12
3.2.1 Calculation of returns ... 12
3.2.2 Calculation of the fundamental signals ... 12
3.3 Our models ... 13
3.3.1 Weighted score, two year rolling window ... 13
3.3.2 Weighted score, Up and Down periods of macroeconomic cycle ... 14
3.3.3 Summary of the score ... 15
4. Results ... 16
4.1 Results from the Rolling window score ... 19
4.2 Results from the Up and Down score ... 20
5. Conclusions ... 24
Appendix A1 ... 25
Appendix A2 ... 26
Appendix A3 ... 27
Appendix A4 ... 28
References ... 29
A Value Relevant Fundamental Investment Strategy
1. Introduction
Fundamental analysis employs the use of accounting information available in financial reports of firms. This analysis in turn can be used to predict the firm’s future performance and overall health. Investors can rely on fundamental analysis to make investment decisions based on its ability to predict future returns. However, there remain many unexplored opportunities to earn abnormal returns in this regard.
This research paper investigates the potential advantages of a fundamental analysis based investment strategy that builds on Piotroski (2000) high book‐to‐market portfolio. Book‐to‐
market (BM) value is the ratio between the book value and the market value of a firm’s equity.
A high book‐to‐market (BM) ratio indicates the market’s lack of confidence in the firm’s future performance whereas the opposite is true in case of a low book‐to‐market (BM) value.
The paper draws inspiration from previous research on fundamental analysis (Ball and Brown (1968), Ou and Penman (1989), Lev and Thiagarajan (1993) and Abarbanell and Bushee (1998)) that has shown the possibility to earn abnormal returns through investing in high book‐to‐
market firms. (Rosenberg, Reid and Lanstein (1985), Lakonishok, Shleifer and Vishny (1994) and Piotroski (2000)). The findings of these researchers show that firms with high BM values often perform well despite market’s lack of confidence in them. The root cause of this anomaly is that the market undervalues (overvalues) the high (low) BM firms in its anticipation of future
performance. Thus high BM firms are often undervalued thanks to market’s over pessimism and are value stocks i.e. diamonds among rocks. Low BM firms sit on the other end of the scale as they are often overvalued by the market in its overoptimism and are growth stocks.
Piotroski’s main contribution has been to show the possibility to earn abnormal returns through applying fundamental analysis on the high BM (undervalued) firms. Piotroski’s research paper introduces a fundamental score (F_score) based on nine variables or signals based on financial accounting numbers. This F_score is used to form investment portfolio out of a set of firms with high book‐to‐market (BM) value. This selective investment strategy earns abnormal returns compared to a general high BM firms‐based portfolio as well as a market weighted index (Piotroski, 2000).
We set out to explore whether Piotroski’s abnormal gains can be improved when each of the
nine variables forming the fundamental score are assigned different weights. In the original
F_score all variables/signals are equally weighted. This basic assumption that each fundamental signal in the F_score has the same effect can be questioned. There is research evidence that Piotroski’s fundamental score when weighted (Rados and Lovric, 2009) or modified properly with respect to context can achieve further abnormal returns (Mohanram, 2005). Therefore, we think it is interesting whether a re‐weighting of Piotroski’s fundamental score can earn further improve the abnormal returns.
The next logical question is what criteria to be used when assigning weights to the nine signals in the Piotroski’s F_score. The ability of a signal to predict future returns is a good candidate, as the prime objective of any such fundamental analysis investment strategy is to be able to anticipate future performance. Use of this criterion poses one main challenge: The ability of each of the nine fundamental signals in the F_score to predict future returns is not necessarily constant over time. Therefore the historical behavior of the predictive ability of the nine signals becomes important and needs to be investigated.
The research study investigates this change in two ways. In the first part, the fundamental signals are assigned new weights every year. The weighting is based on the ability of each individual signal to predict future performance (returns) over the last two years. Therefore it is important that each fundamental signal in the F_score is assigned a new weight every year, based on how well it has been at predicting the future returns during the last two years.
In the second part of the study, it is investigated how well each fundamental signal in F_score predicts future performance during the historical growth and recession periods of
macroeconomic cycle. The changes in predictive behavior of each of the nine fundamental signals during growth/recession periods of macroeconomic cycles can provide insightful information. Whether this information can be employed in an investment strategy to achieve abnormal returns is of particular interest to us and forms the main research question of this thesis.
The rest of the paper is organized as follows; in the following section we discuss prior research on the book‐to‐market effect, risk versus mispricing, fundamental analysis and the fundamental signals. We describe our research design and method in section 3 and results of the study in section 4. In section 5 we draw our conclusions.
2. Theory
Piotroski (2000) investigated whether it is possible to find winners among high book‐to‐market firms by analyzing financial statements using fundamental signals. Already Graham and Dodd (1934) had shown that it is possible to identify undervalued companies and securities by analysis of financial statements. This was further developed by Ball and Brown (1968) who showed how the market reacts to earnings announcements. Ou and Penman (1989) showed that the fundamental signals are related to future returns. Fama and French (1992) suggested that these excess returns are the cause of risk. Piotroski (2000) showed that analysts
consistently neglect undervalued high BM firms and that it’s very profitable to create an investment strategy that sort out these firms to deliver excess returns.
We will in the following sub‐sections provide a brief overview of the research in this field and go through the BM‐effect, risk versus mispricing explanations, fundamental analysis and the fundamental signals. This prior research forms the foundation of the paper.
2.1 The booktomarket effect: Risk versus mispricing
Many research studies have shown a positive correlation between high book‐to‐market (BM) values and strong future returns / stock performance (Rosenberg, Reid and Lanstein (1985), Lakonishok, Shleifer and Vishny (1994) and Piotroski (2000)). Based on historical performance, the market ex‐ante expects high BM firms to most often perform poorly while expects low BM firms to perform strongly in the future. (Mohanram, 2005) Contrary to this market anticipation, it has been observed that BM firms on average show negative future excess returns while firms with high BM values show positive future excess returns. This contradiction or anomaly is known as the book‐to‐market effect. Though the BM effect is well‐observed across different time periods and markets, the underlying cause(s) of the BM effect remain disputed.
There are two main arguments that try to explain the BM effect. The first argument is that the BM effect is a general unexplained risk attributable to a number of factors and variables. Fama and French (1992), the chief proponents of a risk‐based explanation of the BM effect, argue that firms with high BM earn excess returns, precisely because it is a premium for the risk, so‐
called risk premium. Furthermore, they believe that high BM firms often are in financial distress and overall higher risk investments.
The second argument refutes this explanation and claims that the BM effect is explained by the mispricing phenomenon. Mispricing of stocks/securities is observed as a result of incorrect valuations based upon over‐ and under optimism on the part of the investors. La Porta,
Lakonishok, Shleifer and Vishny (1997) show that firms with low BM values are at much greater
risk of showing future negative results as compared to high BM firms. The market shows an overconfidence in the analysts' forecasts that in turn leads to overestimation of performance of low BM firms and underestimation for the high BM firms. La Porta (1996) shows that the
market's confidence in the analysts' biased growth forecasts are a partial cause of the poor performance of low BM firms. This is confirmed by Mohanram (2005), as he documented among the low BM firms that the highest returns from his hedge strategy was generated by large, extensively followed, firms. This is opposite to the BM‐effect among high BM firms, where high rates of return are found among firms that analysts neglect (Piotroski, 2005).
Lakonishok, Shleifer and Vishny (1994) argue in favour of incorrect valuation of high BM firms.
Investors, for example, being far too optimistic for low BM firms, overestimate the current strong returns and growth while being far too pessimistic towards high BM firms due to these companies’ financial distress (the financial stress observation is indicated by Fama and French (1992)). Lakonishok et al (1994) is backed by Griffin and Lemmon (2002), as they document that companies with high level of financial distress show the largest return reversals around
earnings announcements, which contradicts a risk‐based explanation (Mohanram, 2005).
Abarbanell and Bushee (1998) also show that the market lags behind, that the gains are realized close to earnings announcements, and that opportunities for excess returns disappear after a 12‐months period.
Therefore, there is a strong argument for mispricing, and not risk, as the explanation behind the BM‐effect. As Piotroski (2005) states, both the work of Piotroski (2000) and Mohanram (2005) suggests that a portion of the observed book‐to‐market effect relates to the mispricing of fundamentals. We in our study follow their line of argument.
2.2 Fundamental analysis
Many research papers have demonstrated the usefulness of analyzing financial statements in order to anticipate future returns. Ou and Penman (1989) showed that a number of financial ratios can be used to predict future performance. Lev and Thiagarajan (1993) and Abarbanell and Bushee (1998) examine the ability of fundamental signals to predict one‐year future returns growth and cross‐sectional test between fundamental signals and future returns.
Contribution to fundamental analysis has also been down by Sloan (1996) who examines how stock prices and the market react to accruals and the cash flow components of earnings. Sloan shows that the accruals and the cash flow components can predict future returns. But analysts tend not to assimilate this information in a timely manner, rather miss it because they
concentrate on the present returns. It is only when the effects of cash flow components and
accruals actually are translated to high returns, that investors and analysts seems to take this
information into account. Sloan documents that the market is temporarily inefficient in the interpretation of financial statements and the existence of this inefficiency contains plausible profit opportunities (Sloan, 1996).
Piotroski (2000) carries this legacy when he suggests that it can be very profitable to include fundamental analysis in an investment strategy for firms with high BM values. Piotroski argues that firms with a high BM ratio are ideal candidates to choose for fundamental analysis of financial statements, because analysts often neglect these firms. He shows that within the top quintile of high BM firms there are companies with strong fundamental signals that may have an additional return that is more than 20% larger than those with weak fundamental signals.
Piotroski succeeds well in his study through showing the utility of fundamental analysis of financial statement in separating winners from losers. Piotroski does not take into account the market and analysts' estimates, but attempts to separate the firms with the help of their historical financial data, public information that investors either miss or misinterpret (Piotroski, 2000).
Mohanram (2005) shows that fundamental analysis works best when the fundamental signals are adapted according to the economic context in which they are used. He employs further development of the fundamental signals that Lev and Thiagarajan (1993) examined. Mohanram adapts the fundamental signals for growth in order to assess firms with low BM and then he compares his own G_score with Piotroski's F_score. He concludes that the G‐score (F_score) which was adapted for low BM (high BM) firms did not work for high BM (low BM) firms. All information used by Piotroski's and Mohanram's studies is extracted from the financial statements. They only use public information that investors and analysts tend to overlook.
(Piotroski (2000) and Mohanram (2005)).
Rados and Lovric (2009) follow Piotroski’s (2000) study and show that a weighted F_score could increase the results from Piotroski’s investment strategy. They assign weights to every
fundamental signal in F_score . The weights are assigned based on the values of correlation coefficient between individual fundamental signals and one year future returns for the period 1976‐1996. Thereafter they carry out Piotroski’s investment strategy for the subsequent period, 1997‐2007. (Rados and Lovric, 2009)
2.3 The fundamental signals 2.3.1 F_score
According to Piotroski (2000), we need to sort out deteriorating firms from the high
book‐to‐market firms, as the majority of the high BM firms are in financial distress (Fama and
French, 1995). The nine fundamental variables that form the F_score are discussed in the rest of this section. Piotroski defines these 9 fundamental signals so that collectively they measure an individual firm’s positions in three areas: profitability, financial leverage/liquidity and
operating efficiency. Each signal is assigned a binary value either 1 or 0 in Piotroski’s model. The sum of these nine values gives the value of the F_score, which has a value range between 0 and 9. A high score indicates a positive outlook for future performance of the firm, while a low score predicts a weak future performance.
2.3.2 Performance signals for profitability
This area contains the four binary signals of Piotroski (2000) which measures the firms potential to generate funds internally. Historical conditions in earning cash flow and profits is said to be a good indicator of future performance and the ability to generate cash flow. The four signals used are ROA, CFO, ∆ROA and ACCRUAL. Piotroski (2000) defines ROA as net income before extraordinary items scaled by beginning‐of‐the‐year total assets, CFO as cash flow from
operations scaled by beginning‐of‐the‐year total assets and ∆ROA as current year’s ROA less the prior year’s ROA. If these three the variables have a positive sign, the signals are assigned value 1, otherwise 0.
Piotroski (2000) defines ACCRUAL as current year’s net income before extraordinary items less cash flow from operations scaled by beginning‐of‐the‐year total assets (i.e. ROA less CFO). If CFO is greater than ROA this should be interpreted as a positive signal and assigned binary value 1 else 0 in F_score. The motivation for this is that if earnings are driven by positive accrual adjustments, this would be considered as a bad signal about future profitability potential, especially for high BM firms where there are strong incentives to manage earnings through positive accruals (e.g. Sweeney (1994)).
2.3.3 Performance signals for financial leverage/liquidity
These signals aim to capture the capital structure of the firm and hence the firm’s preparedness and ability to service debt. Three binary signals are used in Piotroski’s (2000) F_score to proxy this construct namely: ∆LEVER, ∆LIQUID and EQ_OFFER.
Piotroski (2000) defines ∆LEVER as historical change in the ratio of total long‐term debt to
average total assets. A decrease in this variable is seen as a positive sign i.e. the firm has lesser
financial leverage compared to last year. Therefore an increase in this variable results in a value
of 1 otherwise 0. Piotroski draws motivation from previous research that shows that increased
financial leverage of a firm is an indicator of the inability to generate internal funds (Myers and
Majluf, (1984) and Miller and Rock (1985)). Also a highly leveraged business is dependent on its
interest coverage issues and therefore becomes inflexible to changes in its short and long term business strategy.
Piotroski (2000) defines ∆LIQUID as change in current ratio compared to last year. Since current ratio is the ratio of current assets to current liabilities, an increase in current ratio means more current assets and less current liabilities and therefore higher liquidity. Higher liquidity is interpreted as a positive signal about the firm’s ability to service current debt obligations.
Piotroski (2000) assigns ‘1’ in F_score to ∆LIQUID if it has a positive value (i.e. an increase) otherwise zero.
Piotroski (2000) defines EQ_OFFER to be ‘1’ in F_score if no common equity has been issued by the company in the year proceeding portfolio formation. On the other hand issuance of
common equity means that the financially distressed high BM firm is need of capital from external sources. This shows a lack of ability in generation of capital internally through normal course of business operations (Myers and Majluf (1984) and Miller and Rock (1985)) which then is an indicator of poor financial condition.
2.3.4 Performance signals for operating efficiency
Two signals are used by Piotroski (2000) to measure changes in efficiency of the firm’s operations. They are named ∆MARGIN and ∆TURN.
∆MARGIN is defined as current gross margin ratio (net sales less cost of goods sold scaled by net sales) less the prior year’s gross margin ratio. An increase indicates an improvement in efficiency of the business operations which is considered a positive signal for the firm’s
operating efficiency, Piotroski (2000). Therefore an increase from previous year is translated to binary value ‘1’ in F_score and vice versa.
∆TURN is defined as current year asset turnover ratio (net sales scaled by average total assets for the year) less the prior year’s asset turnover ratio. An increase in asset turnover shows efficient utilization of the assets employed in the business. If the signal is positive then it is assigned value ‘1’ in the F_score otherwise ‘0’.
2.4 Weighted F_score
2.4.1 Predictive ability of fundamental signals
Relevance and reliability are two corners stones of financial accounting and reporting. Value
relevance of accounting information presented by a firm is of prime importance to the financial
analysts and investors in order to form their expectations about future performance of the business. The construct value relevance means how precise and how well the accounting information of a firm follows/predicts the present and the future performance of the firm.
Value relevance of an accounting variable is usually proxied in accounting research by the correlation between the accounting variable and future returns. The financial statement information has been shown to be value relevant over decades (Francis and Shipper, 1999).
There is empirical evidence that the ability of a financial variable in predicting future return does not remain constant, since many of the accounting numbers are correlated to external contextual variables such as macroeconomic cycle, industry growth etc.
Ling and Ohlsson (2010) showed the value relevance of Piotroski’s fundamental signals over time. Although the study was conducted over a limited period and on the Stockholm Stock Exchange, it showed clearly that the signals’ ability to follow future returns changes over time.
This becomes especially important when signals should be weighted. Rados and Lovric (2009) based their weighting on correlations between fundamental signals and future returns over two decades and used the average value of the correlation coefficients. In doing so they missed the changes in the explanatory power of the signals exhibited in Ling and Ohlsson study and seen in Figur 1 (2010).
Figur 1. Value relevance for Piotroski’s nine fundamental signals. (Ling and Ohlsson, 2010)
2.4.2 Fundamental analysis score based on correlation
F_score (described above in detail) assigns a binary value 1 or 0 to each fundamental signal.
Therefore it relies on the change in sign of the fundamental signals every year and not the magnitude of change in one particular direction. Piotroski indicates two issues in this respect;
firstly, the effect of each signal is not uniform, secondly, the possible loss of information due to binary grading of the score.
Rados and Lovric (2009) remove both considerations, when they modify F‐score through assigning weights to each signal in the F_score.
First, the weights are assigned based on the magnitude of the co‐efficient of correlation between each signal and 1‐year returns. For example, if ROA has a correlation with returns of 0.10, the signal ROA is weighted 10. This score is called A_score by Rados and Lovric (2009) and controls for the problem of non‐uniform effect of each signal in predicting future returns. Rados and Lovric (2009) used Piotroski’s (2000) correlation table, as shown in Appendix A1.
Secondly, for each of the nine signals, the firms with positive signal values are divided into size quintiles. This means for nine signals there are in total nine different sets of data, each divided into five quintiles based on the size of the particular signal in consideration. The firms in the highest quintile are awarded a score of 1. The firms are awarded 0,8 if they are in the second highest, 0,6 if they are in the third highest quintile, 0,4 for fourth highest quintile and in the last signal quintile the firms are awarded 0,2 points. This is named by Rados and Lovric (2009) as the B_score. This B_score scheme controls for the loss of information caused by a simple binary grading in Piotroski’s original work.
Eventually, the A_score is multiplied by the B_score. For example: ROA, with an A_score of 10 is multiplied with B_score for a company in the last size quintile of the signal gets 2 points (10 x 0,2), while a company with a strong signal is assigned 10 points (10 x 1). This final score after multiplication is called C_score.
The net effect of the weighting scheme described above is that any bias due to non‐uniform effect of a signal or binary grading is removed. Results of this study show a considerable improvement in returns over Piotroski’s returns, thus proving the loss of information hypothesis.
2.5 Our hypothesis
The predictive ability of each fundamental signal in F_score changes over time and the first part of our study investigates this issue. We hypothesize that an investment strategy that re‐assigns (updates) weights every year taking into account these changes during previous two years should provide abnormal returns. Whether these returns are in excess of the returns earned with the help of unweighted and non‐updated F_score is investigated.
In the second part of our study, we hypothesize that an investment strategy that takes into account the variations of the fundamental signals during growth and recession periods of the macroeconomic cycles should provide abnormal returns. We investigate whether it is possible to exploit this variation to earn excess returns in line with the first part of our hypothesis.
3. Research design 3.1 Data sample
For each year
21983‐2008;
We select our sample from NASDAQ and New York Stock Exchange using data available in Datastream provided by Thomson Reuters. We collect primary quotes, major securities and adjusted prices. We discard firms that do not have necessary information to calculate book‐to‐
market. We discard firms with no return or price index data available on the day of portfolio formation (i.e. 31st May). Firms with reporting zero returns are retained in the sample. Return for the firms that are delisted over the years is assumed to be zero. Market adjusted returns are equal to the buy‐and‐hold return minus the value‐weighted market return.
We filter our returns data sample for outliers in two stages. First, we take away the outliers detectable through inspection of descriptive statistics of the entire sample. Thereafter we remove all firm observations for which returns are greater than two standard deviations plus and minus the mean. We do this to get a uniform data sample without any personal judgments.
We discard firms without necessary information to calculate the signals. For every year, the firms are classified into BM quintiles according to the prior fiscal year’s BM distribution. This
2
The year is the investment year. For example, 2008 is using the fundamental signals from 2007 and the returns
for the one year (two years) buy and hold strategy from May 2008 to May 2009 (May 2010). This to avoid hind
sight biases.
leaves us with a final sample of 10 685 high BM firm‐year observations
3.
The database available for our study is Datastream provided by Thomson Reuters. This is different from the database Compustat used in Piotroski’s study. One important issue is the difference between data available in Compustat and Datastream. The Cash flow from
operations signal provided in Compustat has its most equal replacement in Datastream by Net Cash flow less Operating activities. The signal EQ offer isn’t either available in Datastream.
Therefore we proxy equity offers by changes in total outstanding shares.
3.2 Calculations
3.2.1 Calculation of returns
The buy‐and‐hold returns are calculated from the fifth month after the end of the fiscal year, in order to allow for information dissemination among all market actors. We calculate both one and two year returns, from 31st May the investment year to the 31st May in year one or two.
For short positions, we calculate the returns as following:
(P
t+1 / P
t) ‐ 1
where P is the return without dividends, and t is the investment year. We calculate the returns from long positions the same way, except we assume that paid dividends are re‐invested the day of payment at closing time. A few words on why returns from short and long positions are calculated in different manner. The primary reason is that short positions can be exploited through use of borrowed shares, and in such a transaction any dividend rights are usually not transferred from the lender to the borrower. On the other hand, long positions involve
complete ownership of the shares being traded and as a result the trader/investor has the right to dividends and their subsequent reinvestments.
3.2.2 Calculation of the fundamental signals
The nine fundamental signals are calculated as described in the Theory section (2.3).
Cash flow statements were not a mandatory part of the financial reporting in the US markets before 1989, and not fully implemented before 1990. Therefore, while we use the CFO (cash flow from operations) variable after 1990, we have to proxy the cash flows from operations for
3
The years 1983‐1984 are only used to calculate the weight of the fundamental signals for the investment strategy starting year 1985, and are therefore not included in any portfolio. The sample available for the portfolios (1985‐
2008) consists of 10 316 high BM firms across 24 years.
the year before. Sloan (1996) uses an approximation which we employ (with simplification, e.g.
we do not take into account cash flow pertaining to taxes). The cash flow is calculated by us using the following equation:
Cash flow from operations = Net income + Depreciation ‐ Changes in Working Capital.
Where Working capital = Current operating assets ‐ Current operating liabilities.
We use this approximation the first seven years of our study.
3.3 Our models
3.3.1 Weighted score, two year rolling window
Each year, the weights of the nine fundamental signals are assigned. The weights are calculated in three stages as described in the theory section (2.4.2) with three sets of scores, namely:
A_score, B_score and C_score. Spearman’s correlation is selected as the method of choice since it is less vulnerable to biases caused by outliers. Spearman’s correlation is calculated between each signal and the following year’s returns, for all years.
For each year, for each of the nine signals (e.g. ROA, CFO, etc.) Spearman correlation is calculated between the fundamental signals and the returns for the two prior years (this to avoid hind sight biases, and therefore the return used in the correlation is before the
investment date). For any given year, the Spearman correlation between fundamental signals and returns are calculated for the two previous years. The co‐efficients of these correlations are then used to assign weights to the fundamental signals for the coming investment year. (For example, 1985 investment year’s weighted score uses the correlation between 1982 and 1983 years fundamental signals and 1983 and 1984 years returns respectively). This we call the Rolling score since it provides our weighted score, based on previous two years, through a rolling window that will update each investment year.
Secondly, for each signal, we scale the firms into five quintiles, based on the size of their signals relative magnitude. The firms in the lowest quintile are awarded 20% of the signal’s worth, and firms in the higher quintiles are assigned 20% incremental values continuing all the way up to the firms in the highest quintile that are awarded 100% of the signal’s worth.
The weighting of the final score consists of two components. The first component of the final
score is weighted by the magnitude of the co‐efficient of correlation between fundamental
signal and future returns. The second component of the final score is weighted by the relative
strength of each fundamental signal for each firm when compared with the entire sample (our
Rolling score is simply multiplied by each firm’s quintile score, e.g. 1 for the largest quintile, 0,2 for the smallest). Based on this final score next year’s portfolio is formed. Our hypothesis holds true if excess returns are earned using this strategy. If successful, this method can be used to ex‐ante predict abnormal returns based on the value relevant score. This score draws its value relevant weight from previous two years data.
3.3.2 Weighted score, Up and Down periods of macroeconomic cycle
A similar approach is taken regarding growth and recession periods of the macroeconomic cycle. First weighted score values are calculated for Up (growth) and Down (recession) periods of economy year 1983‐1996. These values are then used to test the second part of our
hypothesis. If excess returns are successfully predicted with the help of this strategy the second part of our hypothesis is also true.
Growth and Recession periods need to be classified for the second part of our study. These can be inferred on the basis of business cycle indicators and market trends observed over the years.
Financial markets are the earliest indicators of macroeconomic ups and downs, while the real economy often lags by two or three quarters. Therefore we define recession (Down) and growth (Up) periods of macro economy using the S&P 500 index with a 200 days simple moving average (SMA) curve. Standard and Poor’s 500 is one of the largest, leading equity lists on the US market, thereby following the macro economy effects on the stock markets very closely.
Historical values of this index between 1983 and 2009 graphically show how and when Up and Down cycles start, prevail and end.
First we determine what years during the period 1983 and 1996 were Up (growth) years and what years were Down (recession) years, with help from the 200 days SMA curve on S&P 500 index. Spearman’s correlations are calculated between fundamental signals and returns for all Up years in this period. A similar calculation is carried out for all Down years. This provides us with two measures: An average value of the correlation co‐efficient between each fundamental signal and returns for all Up years and a similar average value for all Down years. These ex‐post average values of co‐efficients of correlations are then used to predict future Up and Down market returns ex‐ante in the period 1997 to 2009.
Our Up years between 1983 and 1996 are 1983, 1985, 1986, 1989, 1991, 1992, 1993, 1995 and 1996. These years together form the average value of correlation co‐efficients for the future Up years.
Our Down years between 1983 and 1996 are 1984, 1987, 1988, 1990 and 1994. These years
together form the average value of correlation co‐efficients for the future Down years.
To determine which score to use (Up or Down) in the investment strategy, we must decide if the coming investment year is an Up or a Down year. To do this we check the simple moving average (SMA) curve for Standard & Poor’s 500 index in May each year. If the curve is pointing upwards, the coming year is an Up year, and if the curve is pointing downwards, the coming year is a Down year. This may seem a little arbitrary, but is close enough since the 200 days SMA curve changes direction very slowly, and therefore pretty well describes the current overall trend.
3.3.3 Summary of the score
We introduce a further innovation to the scoring scheme explained in the theory section.
Previous research either assigns a binary grading to all fundamental signals (Piotroski, 2000) or a decimal grading only to the positive fundamental signals (Rados and Lovric, 2009). Binary grading means that each of the nine fundamental signals can either be assigned a value of 1 or 0 as defined in Piotroski’s original work. A decimal grading as used by Rados and Lovric on the other hand assigns a value between 0,2 and 10 to all fundamental signals that originally had a binary score ‘1’ according to Piotroski’s method. This means that all signal values equal to ‘1’
according to the original Piotroski’s F_score binary grading are translated into a decimal score.
However all binary scores of ‘0’ are discarded and this leads to loss of information. Therefore, in our scoring scheme we assign decimal scores to both positive as well as negative signals,
thereby avoiding any loss of information in discarding the non‐positive signal values.
We calculate the weighted score using decimal grading, as described in section 2.4.2. The calculation takes place in three stages. First, the A_score is calculated that takes into account the effect of correlation that exists between the individual fundamental signal and the returns observed in the following year.
Secondly, B_score is calculated that assigns for each firm and fundamental signal a decimal value between 0,2 and 1 based on the strength of the signal. The effect of magnitude of the signal for each firm is included in this way. What sign in B_score is given to a firm for a signal depends on how that particular observation would have been scored if the original Piotroski binary F_score was applied. If the signal has a binary score ‘1’ according to Piotroski’s original scoring method then it is assigned a positive signal. Conversely, if the signal has a binary score
‘0’ in Piotroski’s method it is assigned a decimal value between ‐0,2 and ‐1.
In the third step, the final score is calculated through multiplication of A_score and B_score.
The final score therefore translates the effect of the direction and magnitude of the change represented by a fundamental signal compared to previous year, as well as the effect of the correlation between the signal and future returns.
We sum up all positive signals and take long positions in the firms over 70% of maximum score (absolute value). The same way we sum up all the negative signals and take short positions in the firms with more than minus 70% of the maximum score (e.g. if the absolute maximum score is 100, the limit for long positions is firms with over 70 in positive score and the limit for short positions is firms with below ‐70 in positive score).
We carry out our Rolling window (Up and Down) buy‐and‐hold strategy for one, respectively two years, taking long positions in the companies that have received the highest score, while taking short positions in the companies that have received the lowest score. We do this for the period 1983‐2008 (1997‐2008)
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4. Results
Table 1 shows our portfolio for all high book‐to‐market firms between 1985‐2008. The returns are represented in the two columns for each year, one and two years buy and hold strategy respectively. The high book‐to‐market portfolio is performing with 10% up for the one year buy and hold strategy and 25% for two years. Still, the one year buy and hold portfolio for high book‐to‐market is only negative for 6 out of 24 years, and for two years buy and hold it is only negative for 3 out of 24 years. This is a little surprising, however, only 43,8% (41,3%) of the high book‐to‐market firms have a positive one year (two years) market adjusted return. The fact stated by Fama and French (1995) that high book‐to‐market consists of many poor performing firms seems to be correct, but overall our high book‐to‐market sample performs well, especially on a two year horizon.
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