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CHAPTER 5
ADDING VALUE TO VALUE STOCKS
JOSEPH PIOTROSKI’S F-SCORE MODEL
5.1 INTRODUCTION
The value investing consists of buying securities which are trading at prices
lesser than their intrinsic value. The intrinsic value of the securities is determined
through their fundamentals. The company showing good performance in terms of
earnings, dividends, book value of assets, profitability etc. is said to be an
intrinsically strong company. Thus, value investment strategies are based on
fundamental analysis of a company. Firm‟s fundamental or intrinsic value is
determined by the information reflected in the financial statements. Stock prices
deviate at times from these values but slowly converge to these fundamental values
thereby enhancing the market value of such firms (Elleuch and Trabelsi, 2009). The
basic premise behind value investing strategies is that the sophisticated investors can
use historical financial information to select profitable investment opportunities.
Specifically, investors can earn returns in excess of the returns required for risk
compensation by identifying undervalued or overvalued securities through an analysis
of historical financial data (Piotroski, 2005).
Within the varied value investing strategies, the investors look for the strategy
that consistently identifies winners and the losers in the market with minimum risk
and earn returns superior to those averaged by the market index. In actual effect, the
existence of such a strategy would challenge the efficient market hypothesis, one of
the main pillars of financial market theory (Dahl et al., 2009). The efficient market
hypothesis states that the current stock price fully reflect available information about
the value of the firm, and there is no way to earn excess profits (more than the market
overall) by using any publically available or private information (Clarke et al., 2001).
Thus, no trading rule or security selection strategy which uses only publically
available information would provide an investor with the ability to earn, on average,
positive abnormal returns in the market that is efficient in the semi strong sense. The
Indian stock market, a strong emerging market, offers a unique opportunity to apply
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and test the profitability of accounting based fundamental analysis (Aggarwal and
Gupta, 2009). In addition, the Indian stock market has become comparable to other
mature markets due to various financial sector reforms initiated since early 1990s by
the Government of India. The positive fundamentals combined with fast growing
markets have made India an attractive destination for foreign institutional investors.
Significant amounts of capital are flowing from developed world to emerging
economy like India (Prassana, 2008). In such a situation, the profitability of an
accounting based fundamental analysis strategy aimed at yielding excess returns in
Indian stock market becomes imperative to explore.
Out of different financial variables aimed at assessing the intrinsic value of
securities, the book to market ratio has been considered as the most important and the
keystone of value investing studies. According to this valuation metric, the securities
that have higher book value in comparison to the market price, are called as
intrinsically strong or value securities. The book to market ratio of the companies is
calculated as:
Book to market ratio= Book value of a share for last financial year end/
Current market price of a share.
Book value per share is an accounting concept that measures what
shareholders would receive if all the firm‟s liabilities were paid off and all its assets
could be sold at their balance sheet value (Strong, 2004). The different studies, such
as, Stattman (1980), Rosenberg et al. (1985), Chan et al. (1991), Fama and French
(1992, 1998), Capaul et. al. (1993), Brouwer et al. (1996), Vos and Pepper (1997),
Vaidyanathan and Chava (1997), Mukherji et al. (1997), Bauman et al. (1998),
Arshanapalli et al. (1998), Dhatt et al. (1999), Doukas et al. (2001), Dimson et al.
(2003), Bird and Gerlach (2003), Ding et al. (2005) and Azzopardi (2006) have
studied the role of this ratio in providing value premium to investors.
The book to market ratio is one of the most extensively studied variables in the
finance literature. The reason behind the existence of value premium in high book to
market stocks has attracted multiple explanations. The explanation on the existence of
value premium has been explained first of all by Fama and French (1992) stating that
market judges the prospects of a high ratio of book to market equity firms to be poor
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in relation to the firms with low book to market equity. Further, Lakonishok et al.
(1994) offered the mispricing explanation behind existence of value effect and hence
provided evidence that value strategies yield higher returns because these strategies
exploit the suboptimal behavior of the typical investor and not because these
strategies are fundamentally riskier. Further, Vassalou and Xing (2004) conjectured
that the value stocks based on high book to market ratio have higher default risk than
the stocks having low book to market ratio. Also, Campbell et al. (2008) found that
the investors make valuation errors and overprice these stocks as they fail to
understand their poor prospects.
However, when examining the potential of book to market ratio in generating
excess returns to investors, Piotroski (2000) studied that no doubt the stocks selected
on the basis of high book to market ratio yield value premium to investors but about
44% of the high book to market firms did not show any increment in their value in 2
years of portfolio formation. Thus, a handsome group of stocks have not shown any
increment in value. He further held that value stocks earn returns because of being
abandoned in the market. As a result, they are lesser suggested by analysts and thus
less followed by investment community. Also, being financially distressed, one
should focus on the accounting fundamentals of such stocks, such as, leverage,
liquidity, profitability trends, cash flow adequacy etc. before taking investment
decision in such firms. Thus, in order to avoid the distress risk associated with the
high book to market stocks and to extract true value maximizing securities, Joseph
Piotroski conceptualized and empirically proved the viability of the financial
statement information in yielding true value securities.
5.2 JOSEPH PIOTROSKI’S F-SCORE
In order to ensure the financial soundness and profitability of financially
distressed high book to market firms, Joseph Piotroski developed a comprehensive
financial signal known as F-score that measures three constructs pertinent to a
company‟s financial position: profitability, financial leverage along with liquidity,
and operating effectiveness. The three constructs of Pitoroski‟s summary measure „F -
score’, is the sum of nine binary signals related to these three constructs (Wellman,
2011). The nine signals aim at measuring the strength and quality of historical
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performance trends are derived from the traditional financial statement analysis
(Piotroski, 2000; Fama and French, 2004). The F-score measure intends to spot out
the firms with the strongest enhancement in overall financial condition during the last
fiscal year while meeting a minimum standard of financial performance (Piotroski,
2005). Thus, the model based on set of financial variables aims to identify companies
that would actually increase in value out of total group of value stocks. The model is
called as F-score, whereby the 9 financial signals corresponding to the 3 constructs
i.e. profitability; leverage along with liquidity and the operating efficiency are used to
measure the financial performance of high book to market firms. The set of 9 binary
signals are used, where an indicator variable for the signal is equal to one (1) if the
signal‟s realization is good and zero (0) if the signal‟s realization is bad (Piotroski,
2000). Every year, firms are rated and classified on the basis of these recent signals.
“Strong” firms exhibit diverse improvements along a range of financial dimensions,
while “weak” firms have weakening (and generally poor) fundamentals along these
same dimensions (Piotroski, 2005). The score on each of the nine items are summed
to give the F score for the stock, ranging between zero and nine. The items together
with their desired properties are: (i) positive profitability, (ii) increase in profitability,
(iii) positive cash flow, (iv) negative accruals, (v) increase in profit margin, (vi)
increase in asset turnover, (vii) decrease in leverage, (viii) increase in financial
liquidity, and (ix) no issuance of new equity (Hyde, 2013). F-score, therefore, is the
sum of the nine binary signals and measures the financial stability, profitability and
the efficiency of the business.
The logical phenomenon behind the performance of F-score is the semi-strong
inefficiency of the market due to which it slowly incorporates the information present
in the fundamental values. Steadily, the investors‟ expectations are revised and the
gradual incorporation of information in security prices implies that over time,
investors who recognize that the strong financial condition stocks are undervalued,
initiate purchases of these stocks and drive prices higher and, analogously, investors
who realize weak financial condition stocks are overvalued, initiate sales of these
stocks and drive prices lower (Choi and Sias, 2012).
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Given below are the three constructs of F-score model
Figure 5.1: Three constructs of F-score
A. Signals Relating to Profitability
According to Piotroski (2000), “Current profitability and cash flow realization
provide information about the firm‟s capacity to generate funds internally”. When a
firm is generating positive earnings, it is a signal of its capability to generate funds
through its operating activities. Further, the positive earnings trend for a company
ensures its future survival and its fundamental capability to yield positive future cash
flows. This construct of profitability takes four measures of profitabi lity i.e. return
on assets, change in return on assets, cash flow from operations and accrual. Given
below is the discussion of the measures:
1.) Return on Assets (ROA):
This ratio establishes the relationship between the earnings generated by the
firms before providing for interest and taxes from the total assets that a firm has at
the beginning of the year. The idea behind considering earnings before interest and
taxes is that the companies operate with different levels of debt and differing tax
Three constructs of F-score
th
Profitability Leverage and
Liquidity
Operating
Efficiency
ROA ROA CFO Accrual
Liquidity Equity
Gross
Margin
Asset
Turnover
Leverage
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rates and through EBIT an investor can evaluate the operating earnings of different
companies without the distortions arising from differences in tax rates and debt
levels (Greenblatt, 2006). It therefore puts every company on equal footing while
comparing the return on assets of different companies. It is calculated as:
ROA= Net income before interest, taxes and extraordinary items at the end of
financial year / Total assets at the beginning of the year.
The firms generating positive ROA, obtain positive signal (i.e. F-ROA=1) and the
firms that are yielding negative ROA, get zero signal (i.e. F-ROA=0).
Positive ROA, thus, determines the stock‟s ability to produce funds internally
and represents the earnings productivity of total assets. Value is created when the
organization earns a return on its investment in excess of the cost of capital (Palepu
et al., 2010). Thus fulfillment of this signal avoids the risk of distress associated with
book to market firms. The rule, therefore, ensures that the firm has the capability to
generate funds internally (Ross et al., 2003).
2.) Change in Return on Assets ( ROA):
This signal measures the change in ROA in current year in comparison with
previous year‟s ROA. It is calculated as:
ROA= ROA for the year t – ROA for the year t-1.
The firms whose current year ROA is greater the previous year‟s ROA that
firm is given positive score i.e. if ROA> zero, the indicator variable F- ROA=1.
However if a particular firm has lesser ROA as compared to previous year‟s ROA,
that firm gets zero score i.e. F- ROA=0. Piotroski (2000) through this metric made
sure that firm has not incurred a loss in prior 2 years. Thus the metric ensures the
sound profitable position of the enterprise.
3.) Cash Flow from Operations (CFO):
By cash we mean cash and cash equivalents i.e. cash in hand, bank demand
deposits, all the short term investments which can be readily converted into cash
without delay in their value. The comprehensive view of the cash position of an
enterprise during an accounting period can be seen from the statement of cash flows.
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The statement is divided into three activities, namely, operating, investing and
financing activities (Ramachandran and Kakani, 2008). The operating activities are
the prime revenue producing activities of an enterprise. Sometimes, an enterprise can
face the situation of huge profits, sound working capital and inadequate cash/ bank
position. Such a situation hampers the short term financial planning of the business,
ability to meet obligations such as payment to creditors, repayment of bank loan,
payment of interest, taxes and dividends etc. (Bose, 2010). Thus, the company should
have a sufficient cash position so as to pay its debts as they come due. It is calculated
as:
CFO= Net cash flow from operating activities at the end of financial year /
total assets at the beginning of the year.
Positive ratio denotes the operating cash flow generation ability of total
assets. Thus, if the firm in particular year has positive CFO, then the indicator
variable for that firm is F-CFO=1 and the firm having negative CFO, is given zero
score i.e. F-CFO=0.
4.) Accrual:
Under the cash basis of accounting, revenue is not reported until cash is
received and the expenses are not reported until cash is disbursed. Income under this
system of accounting is the excess of cash receipts over cash payments during a
particular accounting period. However, under accrual system of accounting, the items
of income or expenses are recognized when they are actually earned or incurred in an
accounting period. Actual cash receipts and actual cash payments are immaterial
under this method (Label, 2006). Accountants have long argued that the “quality” of
earnings is high for firms with low (or even negative) accruals, while the quality of
earnings is low for firms with high accruals (Ross et al., 2003). Sloan (1996) found
that earnings performance attributable to the accrual component of earnings exhibits
lower persistence than earnings performance attributable to the cash flow component
of earnings. Consequently, firms with relatively high (low) levels of accruals
experience negative (positive) future abnormal stock returns that are concentrated
around future earnings announcements. In fact, a strategy of buying stocks following
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a reduction in accruals and simultaneously selling stocks following a buildup in
accruals would have generated an average return of about 10 percent per year. Thus,
Piotroski (2000) accorded positive signal to firms whose cash flow from operations
is greater than their profits (ROA).
In order to calculate accrual, the difference between the existing year‟s net
profits before extraordinary items and cash flow from operations is estimated and
divided by the total assets a firm has in the beginning of the year.
Thus, the accrual ratio receives the negative signal if firm‟s profits (ROA) are
higher than the firm‟s cash flow from operations (CFO) i.e. F-Accrual =1, if
CFO>ROA and F-Accrual=0, if CFO<ROA.
B. Signals Related to Leverage and Liquidity
The firms with high book to market ratio are associated with high financial
distress (Fama and French, 1992; Vassalou and Xing, 2004) which can lead to the
risk of financial debt and illiquidity. Thus, Piotroski (2000) devised financial signals
to assess changes in capital structure and the company‟s capacity to meet future debt
service obligations. These signals confirm that the firm has not increased its financial
debt compared to last year; it holds enough working capital and has not resorted
towards external financing. These signals are as under:
5. Change in Leverage
The term leverage refers to the association between two interrelated
variables. According to James Horne, “leverage is the employment of an asset or
resources for which the firm pays the fixed cost or fixed return.” Thus, it denotes
the ability of a firm to use fixed financial charges to amplify the effect of changes in
earnings before interest and taxes (EBIT) on its earnings per share (EPS). The fixed
financial charges such as interest on debentures, dividend on preference shares etc.
do not vary with the firm‟s profits. They are to be paid irrespective of the amount of
profits available (Chakravarty, 2004). Higher leverage implies higher proportion of
debt in the capital structure of the company. Thus, the capital structure decisions are
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very critical for an organization as a shift in the firm‟s attitude towards leverage
could increase or decrease the financial strains on the company (Adami et al., 2010).
The impact of leverage on the value of the firm is the controversial issue.
Some authors have proposed its positive impact in enhancing overall returns and
other have opined the inverse relation of leverage with firm‟s value. Modigliani and
Miller (1958) are first to form the basis for modern opinion on capital structure.
They have asserted that in the absence of taxes and the transaction cost, the capital
structure does not have any influence on the firm‟s overall value. Therefore, it is
irrelevant whether the capital is financed by debt or equity. However, many authors
(Hamada, 1972; Ross, 1977; Heinkel, 1982; Bhandari, 1988; Mukherji et al., 1997;
Fama and French, 2002; Lasher, 2003; Ding et al. 2005; Dhaliwal et al., 2006;
Ward and Price, 2006; Sharma 2006; Tripathi, 2009) have found the positive
impact of leverage in enhancing the overall profitability and the market returns of
the firm.
On the other hand, many studies have found opposite results. Myers (1977)
stated that firms with excess debt overhang are prevented from raising funds to
finance positive net present value projects as the returns generated from such
investment would be transferred to debt holders and not the shareholders. So firms
with high growth opportunity may not issue debt in the first place and an inverse
relationship between growth opportunities and leverage is expected to hold (Niu,
2008). According to Piotroski (2000), “By raising external capital, a financially
distressed firm is signaling its inability to generate sufficient internal funds and in
addition, an increase in long-term debt is likely to place additional constraints on the
firm‟s financial flexibility”. It is defined as:
Leverage= long term debt at fiscal yearend/ Average total assets at fiscal year
end
Thus, if a firm has increased its leverage compared to previous year‟s leverage, that
firm gets zero signal i.e. F- Leverage=0 and if a firm‟s leverage has been reduced
compared to previous year, that firm gets positive signal i.e. F- leverage=1.
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6. Change in Liquidity:
Liquidity means the easiness and promptness with which assets can be
converted into cash. A firm can easily meet its short term liabilities if it has a sound
liquidity position. Thus, the probability that a firm will avoid financial distress can
be linked to the firm‟s liquidity (Ross et al., 2003). From it, insight can be obtained
into the present cash solvency of the firm and its ability to remain solvent in the
event of adversities. Essentially, it compares short term obligations with the short
term resources available to meet these obligations (Van Horne, 1994). The liquidity
position of an enterprise is assessed through its current ratio. Higher the ratio, greater
the ability the firm has for paying its bills. This indicator measures the change in
current ratio of a firm in current year as compared to previous year‟s current ratio.
The current ratio is calculated as:
Current ratio= Current assets at the fiscal year end/ Current liabilities at the
fiscal year end Higher current ratio as compared to previous year‟s ratio
acknowledges company to get positive signal. Thus, if the indicator variable F-
Liquidity is greater than zero, the firm gets positive signal and vice versa.
7. Change in Equity:
Whether a firm performs better or worse after having completed an equity
issuance compared to firms who have not issued equity has been the subject of
several studies. In order to maximize current shareholder value, a management
should issue equity when they consider their stock to be overvalued and vice versa
(Dahl et al., 2009). Ikenberry et al. (1995) observed that average abnormal return on
announcement of share repurchases of value stocks due to undervaluation is 45.3%
as compared to glamour stocks where no positive drift in abnormal returns could be
observed. Moreover, Loughran and Ritter (1995) found that the companies issuing
seasoned equity significantly underperform relative to non issuing firms for 5 years
after the offering date. Thus, Piotroski (2000) defined the indicator variable F-
Issuance to equal one if the firm did not issue common equity in the year preceding
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portfolio formation and F- Issuance equal to zero if the firm‟s number of issued
equity shares have increased in the current year compared to the previous year.
C. Measures Relating to Operating Efficiency
Operational efficiency can be defined as the ratio between the input to run a
business operation and the output gained from the business. Further, two financial
signals are intended to measure the operational efficiency of the business.
8. Change in Gross Margin Ratio:
This measure reflects the efficiency with which management produces each
unit of product. This ratio indicates the average spread between the cost of goods
sold and the sales revenue (Pandey, 1995). The ratio represents the excess of sales
proceeds during the period under observation over their cost, before taking into
account administration, selling and distribution and financial charges (Kishore,
2002). It is calculated as:
Gross margin= Gross profit at fiscal year end/ Total sales at fiscal year end. A
high gross profit margin is a sign of good management. A low gross profit margin
may reflect higher cost of goods sold due to firm‟s inability to purchase raw material
at favorable terms, inefficient utilization of plant and machinery, or over investment
in plant and machinery, resulting in higher cost of production (Pandey, 1995). The
gross margin, therefore, represents the limit beyond which reduction in sales price
falls outside the tolerance limit. The firm should have a reasonable margin to ensure
adequate coverage for operating expenses of the firm and sufficient return to the
owners of the business, which is reflected in the gross profit margin (Khan and Jain,
1994). Thus, Piotroski (2000), in order to measure the efficiency of the company‟s
operations compared the current year‟s gross margin to previous year‟s margin and
assigned the indicator variable F- Margin equal to one, if the change in gross margin
is positive and F- Margin equal to zero, if the change has been negative.
9. Change in Asset Turnover Ratio:
The assets are used to generate sales. It measures how effectively the firm
employs its resources. A firm should manage its assets efficiently to maximize sales.
The relationship between sales and assets is called as assets turnover. A firm‟s ability
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to produce a large volume of sales for a given amount of net assets is the most
important aspect of its operating performance (Pandey, 1995). The ability to produce
a large volume of sales on a small asset base is an important part of the firm‟s profit
picture. Idle or improperly used assets increase the firm‟s need for costly financing
and the expenses for maintenance and keep up. By achieving a high asset turnover, a
firm reduces cost and increases the eventual profit to its owners (Hampton, 1980).
The asset turnover ratio is calculated as:
Asset turnover= Total sales at fiscal year end/ Total assets at the beginning of
the year.
According to Piotroski (2000), “An enhancement in asset turnover implies
larger efficiency from the asset base”. Such an up gradation can occur in two cases.
First one is the more efficient operations i.e. smaller amount of assets yielding the
same levels of sales and the second situation can be of an increase in the level of
sales due to enhanced market setting for the company‟s products. Thus, the indicator
variable F- Turnover equals one, if change in assets turnover ratio in current year
compared to previous year is positive and the variable F- Turnover is zero, if change
in turnover ratio is negative.
The aggregate fundamental score, F-score, is defined as the addition of the individual
binary signals, or
ROA
F- rg
F Score F F ROA F CFO F Accrual
F Leverage F Liquidity Issuance F Ma in
F Turnover
Given the nine underlying signals, F-score can range from a low of zero to a high of
nine, where a low F-score represents a firm with very few good signals about the
firm‟s financial condition and a high F-score represents a firm with mostly good
signals about its financial position. All these components of F-score altogether help
in extracting a refined value portfolio out of stocks with high book to market ratio.
Overall, the F-score strategy aims at eliminating the negative return observations i.e.
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167
the left tail of the return distribution. The present study examines the relevance of
Piotroski‟s F-score in Indian stock market.
Table 5.1: Description of the Variables Discussed in Piotroski’s F-score and the
Formulae Applied
S.No. Variable Name Notation Description
1. Book to market
ratio
B/M ratio Book value of a share at fiscal year end/ Current
market price of a share
2. Return on
assets
ROA Net income before interest, taxes and extraordinary
items at the end of financial year / Total assets at
the beginning of the year
3. Change in
return on assets ROA ROA for the year t – ROA for the year t-1.
4. Cash flow from
operations
CFO Net cash flow from operating activities at the end
of financial year/Total assets at the beginning of
the year
5. Accrual ROA for the year t – CFO for the year t
6. Leverage Long term debt at fiscal year end/ Average total
assets at fiscal year end
7. Change in
leverage Leverage Leverage for the year t – Leverage for the year t-1.
8. Current ratio/
Liquidity
Current assets at the fiscal year end/ Current
liabilities at the fiscal year end
9. Change in
liquidity Liquidity Liquidity for the year t – Liquidity for the year t-1
10. Change in
equity Issuance Number of equity shares issued at fiscal year end t
– Number of equity shares issued at fiscal year end
t-1.
11. Gross margin
ratio
Gross profit at fiscal year end/ Total sales at fiscal
year end.
12. Change in gross
margin Margin Gross profit for the year t – Gross profit for the
year t-1
13. Asset turnover
ratio
Total sales at fiscal year end/ Total assets at the
beginning of the year
14. Change in asset
turnover ratio Turnover Asset turnover for the year t – Asset turnover for
the year t-1
5.3 HIGH BOOK TO MARKET STOCKS
In order to examine the relevance of F-score in Indian stock market, at first all the
stocks listed at Bombay Stock Exchange (excluding the financial stocks) with relevant
book to market information are screened. Further, the book to market ratio of all the
selected stocks is calculated using following formula:
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Book to market ratio= Book value of a share for last financial year end/ Current
market price of a share.
A company's book value explains how much money would be left for
shareholders if the company were to immediately liquidate, sell all of its assets and pay
off all its liabilities. As per CMIE's (Centre for Monitoring Indian Economy) definition,
the outstanding reserve plus the paid-up capital at the end of a year is considered for the
calculation of book value. The net profit (net of prior period and extra-ordinary items)
earned in the interim period and adjusted for dividend outgo is added to the total net
worth to reflect the latest book value of the company (prowess.cmie.com)
Further, the stocks are divided into quintiles on the basis of book to market ratio.
The stocks in the highest quintile of book to market ratio are designated as value stocks.
Table 5.2 shows the number of value stocks selected each year from 1996 to 2010.
Table 5.2: Number of Stocks Selected in Highest Book to Market Quintile Each
Year
S.No. Year Number of stocks in high book to market quintile
1 1996 298
2 1997 298
3 1998 240
4 1999 233
5 2000 271
6 2001 249
7 2002 254
8 2003 253
9 2004 272
10 2005 302
11 2006 317
12 2007 354
13 2008 405
14 2009 416
15 2010 435
16 Across the period 4597
Table 5.2 shows that in the year 1996, the number of stocks forming the part of
portfolio is 298. In 1997 also, 298 stocks form the part of portfolio, 240 in 1998, 233 in
1999, 271 in 2000, and 249 in 2001. Across the period of 15 years, 4597 stocks form the
part of the study. The performance of these stocks selected is analyzed as under:
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169
5.3.1 Analyzing the Performance of Stocks with High Book to Market Ratio
In order to analyze the performance of stocks falling in the highest book to market
quintile, the market adjusted returns of all such stocks have been calculated for two holding
periods i.e. 12 months, 24 months. Further, the significance of the returns has been
examined through one sample t-test. Thus, we proceed to test the following hypothesis:
H01 : The market adjusted returns of high book to market stocks is equal to
zero
The results examining the above hypothesis in both the holding periods are listed
in Table 5.3
Table 5.3: Results of the Significance of Market Adjusted Returns of High Book
to Market Stocks
Year No. of
stocks
12 months holding period 24 months holding period
Mean
(Annual) Std. Dev. T-Value P-Value
Mean
(Annualized) Std. Dev. T-Value
P-
Value
1996 298 -21.0625
(13.8021) 238.0280 -1.52591 .128
-1.0152
(3.726853) 64.33546 -0.2724 .786
1997 298 78.20839
(10.14116) 175.0635 7.711979 .000***
40.47185
(3.450373) 59.56268 11.7297 .000***
1998 240 77.03241
(9.92424) 153.7458 7.762039 .000***
56.77972
(3.706807) 57.4256 15.31769 .000***
1999 233 134.1327
(12.49738) 190.7643 10.73286 .000***
47.34687
(3.44252) 52.54779 13.75355 .000***
2000 271 28.62323
(4.15069) 68.32903 6.896013 .000***
49.77847
(2.379566) 39.1726 20.91914 .000***
2001 249 111.9621
(5.17454) 81.65298 21.63708 .000***
53.63793
(2.179734) 34.39562 24.60756 .000***
2002 254 61.39512
(7.507327) 119.6471 8.178027 .000***
28.20791
(2.805267) 44.7086 10.05534 .000***
2003 253 67.06019
(8.185056) 130.1913 8.193003 .000***
65.46658
(2.607224) 41.47044 25.10969 .000***
2004 272 193.157
(6.856627) 113.0824 28.17085 .000***
48.53954
(2.229048) 36.7624 21.77591 .000***
2005 302 -20.1481
(4.244383) 73.7595 -4.747 .000***
-5.74701
(2.092294) 36.3602 -2.74675 .000***
2006 317 24.12948
(4.108321) 73.14657 5.873321 .000***
13.64269
(1.846413) 32.87446 7.388753 .000***
2007 354 26.69862
(3.83673) 72.18781 6.958674 .000***
13.39258
(1.694185) 31.87591 7.905027 .000***
2008 405 19.15687
(2.017917) 40.6098 9.493387 .000***
23.29422
(1.217385) 24.4994 19.13464 .000***
2009 416 44.53731
(2.787409) 56.85221 15.97803 .000***
9.756745
(1.51241) 30.84724 6.451122 .000***
2010 435 -11.8571
(2.52908) 52.74815 -4.68831 .000***
-8.97528
(1.690349) 35.25503 -5.30972 .000***
Across
the period 4597
47.78089
(1.90865)
129.4111
25.033 .000***
25.47815
(0.706398) 47.89462 36.064 .000***
Note:
1. *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
2. Standard error of mean has been reported in parenthesis
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
170
Table 5.3 shows that high book to market portfolio has yielded higher return than
the market in all the years except 1996, 2005 and 2010. In year 1997, 1998, 1999, 2000,
2001, 2002, 2003, 2004, 2006, 2007, 2008 and 2009, the returns of high book to market
portfolio have been significantly higher than the market returns in 12 months as well as
24 months holding periods. Across the period of 15 years, the high book to market
portfolio has yielded an annual return of 47.78% (significant at 1% level of significance)
in case of 12 months holding and an annualized rate of return of 25.47% (significant at
1% level of significance) in case of 24 months holding period. However, out of three
years with negative market adjusted return, the returns have been significant only in year
2005 and 2010. Thus, the portfolio of high book to market stocks has the potential to
outperform the market in Indian stock market.
The market adjusted performance showed above was based on the total portfolio
of high book to market stocks. The further, section shows the number of stocks out of
total portfolio of stocks that actually showed an increment in their value.
5.3.2 Stocks not showing the Increment in their Value
In this section attempt is made to know the number of stocks in the portfolio of
high book to market stocks which are not showing the increment in their value. The
returns of all the stocks are observed and the number of stocks with no increment in their
value in 12 months as well as 24 months period is listed. Table 5.4 reports the results.
Table 5.4: Number of High Book to Market Stocks that did not show an
Increment in their Value
Year Total book
to market
stocks
Number of stocks with
no appreciation in 12
months holding period
% of stocks with no
appreciation in 12
months holding period
Number of stocks with
no appreciation in 24
months holding period
% of stocks with no
appreciation in 24
months holding period
1996 298 237 79.5302 173 58.05369
1997 298 87 29.19463 70 23.48993
1998 240 81 33.75 38 15.83333
1999 233 34 14.59227 35 15.02146
2000 271 104 38.37638 58 21.40221
2001 249 12 4.819277 10 4.016064
2002 254 76 29.92126 65 25.59055
2003 253 77 30.43478 13 5.13834
2004 272 2 0.735294 22 8.088235
2005 302 210 69.53642 187 61.92053
2006 317 142 44.79495 115 36.2776
2007 354 143 40.39548 124 35.02825
2008 405 137 33.82716 63 15.55556
2009 416 78 18.75 136 32.69231
2010 435 293 67.35632 262 60.22989
Across
the period
4597 1713 37.26343 1371 29.8238
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
171
Table 5.4 shows that out of 298 high book to market stocks selected in year 1996,
237 (i.e. 79.53%) stocks did not showed an increase in their value in12 months holding
period. In case of 24 months holding period, 173 (i.e. 58.05%) stocks did not showed any
improvement. Thus, majority of the high book to market stocks did not increase in their
value in 12 months, 24 months period. In year 1997, out of total 298 stocks, 87 stocks
(i.e. 29.19%) did not showed any improvement in 12 months period and 70 (23.48%)
stocks did not increase in 24 months holding period. Similarly in all the years, the
number of stocks not showing any improvement in their value can be elicited from Table
5.4. Across the period of 15 years, the value of 1713 stocks out of 4597 stocks (i.e.
37.26%) did not increase in 12 months holding period and about 29.82% stocks did not
rise in their value in 24 months holding period. Therefore, it can be inferred that, no
doubt, the overall portfolio of high book to market stocks yield excess market returns to
investors but handsome number of stocks in high book to market portfolio have not
shown the increment in their value in 12 as well as 24 months holding period.
Piotroski (2000) found that less than 44% of the stocks in high book to market
portfolio earn positive market-adjusted returns in the two years following portfolio
formation in US stock market. He thus made an attempt to distinguish the stocks with
positive market adjusted returns from the stocks with negative market adjusted returns
through financial statement based heuristic, called as F-score. The further study explores
whether the F-score applied on high book to market stocks in Indian stocks market can
enhance the performance of value portfolio
5.4 F-SCORE APPLICATION
5.4.1 Descriptive statistics
In order to apply F-score on the stocks in value portfolio i.e. high book to market
stocks, the financial signals embedded in F-score are calculated for all high book to
market stocks. Table 5.5 contains the information regarding the basic characteristics of
high book to market portfolio. The mean, median, standard deviation and the positive
proportion of each of the individual financial signal attributed to 4597 observations for
the period 1996 to 2010 is shown as under:
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
172
Table 5.5: Financial and Return Characteristics of High Book to Market Stocks (4597
Observations across the Period of Study)
Variable Mean Median Standard
deviation
Proportion with
positive signal (%)
Market capitalization
(in millions)
253.816762 44.430000 1714.6507815 n/a
Assets (in millions) 1824.458612 443.100000 8568.4496308 n/a
Book to market ratio .301946 .240000 .2234880 n/a
ROA .048376 .044196 .1266639 81.25
Change in ROA -0.073993 -0.006928 3.0398143 40.69
Change in margin -0.057371 -0.005241 8.2404905 42.84
CFO (in millions) 105.990605 14.900000 1723.4411711 73.48
Change in liquidity -0.143910 -0.051110 25.4715463 47.15
Change in leverage -0.003192 -0.001332 .0832847 46.76
Change in turnover -1.581886 -0.025164 99.7809612 42.93
Accrual .005170 -0.008572 .2058045 45.41
Table 5.5 provides the descriptive statistics regarding the financial characteristics
of high book to market firms. It can be seen that average (median) firm in the value
portfolio (highest book to market quintile) has a mean (median) book to market ratio of
0.302 (0.240) and the market capitalization of 253.816 (44.43) million rupees. Further,
the average return on assets (ROA) realization is 0.0483 (0.0441) and about 81.25% of
high book to market firms have shown the positive value of ROA. This finding cannot be
considered with Piotroski (2000) findings of negative average realization of ROA (-
0.0054). Furthermore, the average and median firms in high book to market stocks shows
decline in respect of change in ROA (-0.0739, -0.00692), gross margin (-0.0573, -
0.00524), liquidity (-0.1439, -0.0511) and turnover (-1.5818, -0.02516) in current year as
compared to last year. No doubt the decline in the average and median firms in the
portfolio of high book to market firms in terms of leverage (-0.00319, -0.00133) in
current year compared to last year shows the lesser reliance of these firms on outside
funds but such stocks did not show any improvement in current year in terms of return on
assets, gross margin, liquidity and turnover compared to last year.
Further, Table 5.6 shows the 12 months, 24 months buy and hold returns for
complete portfolio of high book to market firms, with the percentage of firms with
positive raw and market adjusted returns.
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
173
Table 5.6: Return Distribution of the Stocks in High Book to Market Portfolio
Mean 10th
percentile
25th
percentile
Median 75th
percentile
90th
percentile
Percent
positive
(%)
12 months holding period
Raw returns 63.66213 -37.543444 -5.805557 35.907332 97.605512 197.299210 71.321
Market adjusted 47.78089 -52.500941 -19.721234 20.796098 81.569808 177.373127 62.693
24 months holding period
Raw returns 38.57398 -16.471807 8.053941 33.288619 63.848194 100.734062 52.686
Market adjusted 25.47581 -27.257827 -4.345306 21.495459 50.216663 84.261128 70.872
Table 5.6 shows that the mean and median market adjusted return in case of
one year period is 47.78% and 20.796% respectively. The two year holding period
shows the mean and median return of 25.475%, 21.495% respectively. It implies that
the mean as well as median market adjusted return of high book to market stocks have
been positive in 12 as well as 24 months holding period. Thus, high book to market
firms earn positive market adjusted returns in one, two year after the portfolio is
formed. It is consistent with the finding of Fama and French (1992), Lakonishok et al.
(1994) and Piotroski (2000). However, it is important to note that only 62.693% of
firms have positive market adjusted returns in 12 months holding period. Thus,
37.307% of the firms had zero or negative market adjusted returns in that period.
Therefore, the implementation of a strategy which could eliminate the negative values
from the return distribution will greatly improve the portfolio‟s mean return
performance.
5.4.2. Return Distribution Statistics Pertaining to High Book to Market Stocks
Table 5.7 and Table 5.8 show the distribution of the returns earned by the
highest quintile of book to market firms. For all the firms, the fundamental measure
F-score has been calculated as the sum of the nine individual binary signals as under:
ROA
F- rg
F Score F F ROA F CFO F Accrual
F Leverage F Liquidity Issuance F Ma in
F Turnover
Here, each binary signal is equal to one if the underlying variable is a good signal
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
174
about the future performance of the firm and the signal is set equal to zero if the
underlying realization is a bad signal regarding the future performance of a firm. Overall,
the total F-score equal to nine represents the fulfillment of the firm on all favorable set of
financial signals and the F-score equals to zero represents lack of fulfillment of the firm
on any of the favorable financial signal. Also, the firms having F-score of 8 or 9 are
accredited as high score firms and the firms having F-score of 1 or 2 are recognized as
low score firms. The return distribution of all the firms as well as different categories of
F-score along with the number of firms are shown in Table 5.7 and 5.8.
Table 5.7: Return Distribution of 12 Months Holding Period Market Adjusted
Returns to a value Investment Strategy based on Fundamental Signals
Mean 10th
percentile
25th
percentile
Median-
50th
percentile
75th
percentile
90th
percentile
%
positive
No. of
stocks
All
firms
47.780 -52.50094 -19.721234 20.796098 81.569808 177.373127 62.693% 4597
F-score
1 42.3705583 -122.1810 -38.179497 39.214676 96.368109 278.607971 52.631% 19
2 35.470623 -62.9225 -28.068712 7.6039213 66.16829 180.622 55.221% 134
3 32.161 -65.14982 -27.106796 10.738751 62.857590 140.456726 56.294% 421
4 36.301724 -60.73468 -27.358952 12.643242 67.849315 159.695358 58.221% 821
5 52.446492 -52.30267 -17.094806 21.149794 85.884505 187.095681 62.983% 1086
6 50.594022 -52.55888 -19.613851 24.921367 87.059939 185.271541 63.645% 993
7 37.47869 -43.188 -14.1829 27.93234 80.86259 170.126 66.39% 723
8 69.67008 -35.96663 -9.811126 38.272218 107.954141 197.382240 71.084% 332
9 49.16197 -54.58711 -3.929840 24.545073 95.707068 168.191531 70.588% 68
Low
score
36.32748 -63.27908 -29.676331 7.732254 68.595673 184.842333 54.248% 153
High
score
66.1837 -38.362941 -7.346701 36.099792 103.911244 192.765805 71.25% 400
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
175
Table 5.8: Return Distribution of 24 Months Holding Period Market adjusted
returns to a Value Investment Strategy based on Fundamental Signals
Mean 10th
percentile
25th
percentile
Median-50th
percentile
75th
percentile
90th
percentile
%
positive
No. of
stocks
All
firms
25.4780
-27.257827 -4.345306 21.495459 50.216663 84.261128 70.827% 4597
F-score
1 6.15643483 -71.475642 -36.777933 13.821805 58.841285 85.546457 57.894% 19
2 18.369136 -58.513943 -15.396339 22.22965 50.78732 88.67977 61.194% 134
3 18.919 -30.388811 -9.058623 13.396351 41.159449 78.409220 63.895% 421
4 20.185281 -36.053428 -8.113825 16.096589 45.023150 78.095235 66.747% 821
5 27.284321 -25.644070 -2.914118 24.393756 52.878989 85.783365 72.375% 1086
6 26.714918 -28.967615 -3.932375 22.758816 51.832613 86.467542 71.5005% 993
7 16.13732 -20.3655 0.090245 22.78009 50.148 81.15417 74.965% 723
8 34.24404 -17.289779 3.063441 26.195031 60.563508 98.448643 76.204% 332
9 35.06779 -18.374019 1.208544 31.416098 58.547406 84.318525 76.470% 68
Low
score
16.85253 -58.763618 -16.828178 17.418834 50.880058 87.911156 60.130% 153
High
score
34.38408 -17.496362 2.925959 27.430862 59.437687 96.926354 76.5% 400
Table 5.7 shows the return distribution statistics pertaining to 12 months holding
period and Table 8 shows the return classification information regarding 24 months
holding period. As evident from these tables, maximum number of observations i.e. 1086
observation out of 4597 observations is clustered around F-score of 5, followed by 993
observations around F-score of 6 and further, 821 observations are clustered around F-
score of 4. The number of firms having high score i.e. 8 or 9 are 400 and the number of
observations having low score 1 or 2 are 153. Thus, high F-score portfolio represents
8.7% (400 out of 4597) of the entire portfolio and the low F-score represents 3.33% (153
out of 4597) of the entire portfolio across the period of 15 years.
Table 5.7 further shows that the 12 months mean and median market adjusted
return of highest quintile of book to market firms is 47.78% and 20.79% respectively.
Out of sample of all high book to market firms i.e. 4597 observations across the period of
15 years, 62.69% of the firms have positive market adjusted returns in 12 months holding
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
176
period. Further, 52.63% of the firms having F-score 1 have positive market adjusted
return in 12 months holding period. It is important to note that the percentage of firms
having positive market adjusted return continued to increase with successive increase in
F-score. Along with it, different return partitions i.e. 10th
percentile, 25th
percentile, 50th
percentile, 75th
percentile and 90th
percentile also showed an increase in 12 months
market adjusted return with the successive increase in composite measure F-score.
Table 5.8 reports that when the holding period has been extended from 12 months
to 24 months, the mean and median market adjusted annualized rate of return of highest
quintile of book to market firms is 25.47% and 21.49% respectively. Further, 70.827% of
the firms in entire sample show the positive market adjusted returns in 24 months holding
period as compared to 62.69% in case of 12 months holding period. Similarly, 57.89% of
the firms with F-score equals to 1 have positive market adjusted return in 24 months
holding period compared to 52.63% in case of 12 months period. Also, 61.19% of the
firms with F-score equals to 2 had positive market adjusted return in 24 months holding
period compared to 55.22% in case of 12 months period. Along with it, different return
partitions i.e. 10th
percentile, 25th
percentile, 50th
percentile, 75th
percentile and 90th
percentile also showed an increase in 24 months market adjusted return with the
successive increase in composite measure F-score. Thus, F-score strategy helps in
shifting the distribution of returns (towards right) earned by a value investor.
The mean market adjusted return of high score portfolio is 66.18% in case of 12
months holding period and 34.38% in case of 24 months holding period. This return of
high score portfolio is greater than that of low score portfolio in both the holding periods
(low score portfolio has 36.32% return in 12 months period and 16.85% in case of 24
months period). Also important to note that return of high score portfolio even exceeds
the return of all high book to market firms. Thus, high score portfolio outperforms both
low score as well as all firms in respect of mean market adjusted returns in both the
holding periods. Thus, the evidence regarding the success of strategy to discriminate
between future winners and future losers can be elicited from the above results.
5.4.3 Examining the Significance of Difference in Returns
In order to examine the significance of the return difference between the portfolio
of high score stocks and the portfolio of low score stocks, independent sample t-test has
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
177
been used. Along with it, the significance of return difference amongst the high score
stocks and all stocks in high book to market portfolio is also examined using t-test. The
following hypothesis is tested:
H02 : There is no significant difference between the mean returns of the
stocks having high F-score and all the stocks having high book to
market ratio
H03 : There is no significant difference between the mean returns of the
stocks having high F-score and the stocks having low F-score
In order to examine H02, two groups of stocks are formed; one containing all high
book to market stocks and another containing stocks that have the F-score of 8 or 9.
Further, independent sample t-test has been used on the 12 months as well as 24 months
market adjusted returns of the two groups. In order to examine the H03, two groups are
formed; one containing the high score stocks (i.e. the stocks having 8 or 9 as the F-score)
and another containing the low score stocks (i.e. the stocks having 1 or 2 as the F-score).
Further, independent sample t-test has been used on the market adjusted returns of these
stocks. The analysis will help to determine whether the high score firms significantly
outperform the low score and all the value stocks. Table 5.9 reports the results.
Table 5.9: Results of t-test Employed on Firms with High Score- Low Score
Group, Firms with High Score- All High Book to Market Firms
criteria No. of
stocks
12 months market adjusted returns 24 months Market Adjusted Returns
Mean
returns
(Annual)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
T-value
Mean
returns
(Annualized)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
T-value
High 400 66.183 124.11 18.402 0.627 2.737*** 34.384 47.150 8.908 0.165 3.572***
All 4597 47.780 129.41 25.475 47.894
High 400 66.183 124.11 29.856 0.265 2.618*** 34.384 47.150 17.531 4.985** 3.601***
low 153 36.327 108.38 16.852 52.681
Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
Table 5.9 shows the results of significance of return difference between high
score stocks and all the stocks in high book to market portfolio in case of 12 months as
well as 24 months holding period. The F-value of Levene‟s test that measures the
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
178
equality of variances of two groups is 0.627 in case of 12 months holding period and
0.165 in case of 24 months holding period. The insignificant F-value of Levene‟s test
leads to acceptance of null hypothesis of equal variance in two groups. Further, the return
difference between the portfolio of high score and all high book to market stocks being
18.402% in case of 12 months holding period and 8.908% in case of 24 months holding
period, is significant at 1% level of significance. It therefore leads to rejection of null
hypothesis (H02) of no significant difference between the mean returns of the stocks
having high F-score and all the stocks having high book to market ratio. Thus, the firms
with F-score 8 or 9 significantly outperform all the firms in value portfolio in both the
holding periods.
In further analysis, the significance of return difference between high F-score
firms and the low F-score firms is examined. The F-value of Levene‟s test of equality of
variances is .265 in case of 12 months holding period showing that variances of two
groups are equal. In case of 24 months holding period, the value of Levene‟s test is 4.985
(significant at 5% level of significance) showing that the variance between two groups is
not equal. Thus, the results of Welch t-test become applicable in such a situation. The
mean difference between two groups (29.856% in case of 12 months holding period and
17.53% in case of 24 months holding period) is significant at 1% level of significance. It
also leads to rejection of null hypothesis (H03) of no significant difference between the
mean returns of the stocks having high F-score and the stocks having low F-score. Thus,
high F-score portfolio significantly outperforms the low F-score firms in both the holding
periods.
The above results show that high F-score portfolio significantly outperform the
entire value portfolio based on book to market ratio as well as the low F-score portfolio
on the basis of mean market adjusted returns. The following sections explore whether the
outperformance of high score stocks over low score stocks is attributed to small firm
effect. It is due to the reason that Piotroski (2000) opined that if the return predictability
is concentrated in smaller firms, an investor would not be interested in investing in such
stocks due to riskiness and low level of liquidity associated with such stocks. Thus, the
performance of the F-score strategy across size, share price level and trading volume
partitions is examined as under.
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
179
5.4.4 Return Conditional on Firm Size
Piotroski (2000) attempted to explore whether the excess returns observed
using the F-score based strategy is strictly a small firm effect or can be useful across
all size categories. In order to determine whether the excess returns to high score
portfolio and the outperformance of high score portfolio over low score portfolio is
due to small size effect, we took the data available on book to market ratio, market
capitalization of all the stocks listed on BSE every year on 30th
June. On basis of
market capitalization of all the stocks, the 33.3 percentile and 66.67 percentile are
calculated every year. The stocks with market capitalization up to 33.33 percentile are
classified as small stocks, the stocks having market capitalization in the range of
33.33 to 66.67 percentile are categorized as medium size stocks and the stocks
exceeding the percentile of 66.67 in terms of market capitalization are classified as
large size stocks. Thereafter, these percentiles are used to classify the high book to
market stocks into small, medium and large size portfolios.
5.4.4.1 Market Adjusted Returns of F-Score Stocks in Different Size Categories
After classifying the stocks into different size categories, out of total of 4597
high book to market stocks across the period of 15 years, 2512 stocks have small size,
1699 stocks have medium size and 386 stocks have large size. Table 5.10 shows that
out of 2512 small stocks, only 12 stocks have F-score of 1, further, 73 stocks have F-
score of 2, 219 stocks have F-score of 3, followed by 39 stocks having F-score of 9.
Similarly, amongst the medium size stocks, out of 1699 stocks, only 4 stocks have F-
score of 1 and 21 stocks have F-score of 9. Out of stocks with large size group, only 3
stocks have F-score of 1, only 8 stocks have F-score of 9 and the maximum number of
stocks i.e. 83 stocks have F-score of 6. The mean as well as median returns of the
stocks falling in different categories of F-score, low and high group in three size
partitions have been shown in Table 5.10 and Table 5.11.
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
180
Table 5.10: 12 Months Market Adjusted Returns Earned Using Value Investment
Strategy Based on Fundamental Signals in Different Size Partitions
Small firms Medium firms Large firms
Mean Median No. of
stocks
Mean Median No. of
stocks
Mean Median No. of
stocks
All
firms
66.249 30.8220 2512 28.563 11.218 1699 12.180 3.703 386
F- score
1 84.004 46.344 12 -33.887 -27.874 4 -22.488 -52.801 3
2 42.394 18.558 73 34.934 3.070 49 -4.460 -2.303 12
3 55.477 18.912 219 9.741 -1.272 164 -5.461 -23.923 38
4 58.576 24.809 434 14.461 9.087 320 -3.670 -9.410 67
5 75.976 36.995 560 29.211 10.172 433 18.941 1.836 93
6 68.587 34.078 557 30.359 11.760 353 15.901 15.925 83
7 65.159 33.383 414 36.930 14.377 249 15.091 16.907 60
8 75.463 35.741 204 63.249 43.501 106 47.138 32.475 22
9 41.748 21.864 39 69.644 25.049 21 31.535 18.967 8
Low 48.268 20.262 85 29.740 -1.755 53 -8.065 -12.338 15
high 70.029 32.472 243 64.306 43.436 127 42.977 28.719 30
Table 5.10 shows that mean and median of 12 months market adjusted returns of
all stocks having high book to market ratio and small size is 66.249%, 30.822%
respectively. Medium size group has mean and median return of 28.563%, 11.218%
respectively. The larger size group has mean return of 12.18% and median return of
3.703%. The small size portfolio thus has larger mean and median return than medium,
large size portfolio. It shows the presence of small firm effect i.e. stocks of small size
firm outperform the stocks with large size. Further, in all F-score categories, the small
size stocks outperform the larger size stocks in terms of 12 months mean market adjusted
returns. In respect of low score and high score portfolio also, the mean, median market
adjusted return of the small size portfolio is larger than that of medium size and large size
portfolio in case of 12 months holding period of such stocks. Table 5.11 shows the
similar return classification when the holding period is extended from 12 months to 24
months holding period.
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
181
Table 5.11: 24 Months Market-Adjusted Returns Earned Using Value Investment
Strategy Based on Fundamental Signals in Different Size Partitions
Small firms Medium firms Large firms
Mean Median No. of
stocks
Mean Median No. of
stocks
Mean Median No. of
stocks
All
firms
33.339 26.309 2512 17.263 16.635 1699 10.452 11.466 386
F- score
1 26.5140 20.929 12 -25.110 -12.795 4 -33.584 -58.819 3
2 25.525 28.365 73 15.126 17.418 49 -11.922 -2.621 12
3 29.949 21.840 219 5.942 4.425 164 11.361 7.169 38
4 28.709 21.652 434 13.130 12.587 320 -1.335 4.352 67
5 36.182 29.872 560 18.189 17.871 433 16.050 18.559 93
6 36.979 28.976 557 15.018 17.861 353 7.572 12.308 83
7 32.444 24.861 414 22.628 21.394 249 16.960 11.691 60
8 34.518 24.593 204 34.635 30.255 106 29.815 30.876 22
9 31.120 24.070 39 49.031 51.137 21 17.654 1.564 8
Low 25.664 20.262 85 12.089 3.2667 53 -16.254 -3.040 15
high 33.973 24.462 243 37.015 32.795 127 26.572 25.101 30
Table 5.11 shows that the 24 months annualized mean, median market adjusted
return of small size firms is 33.33%, 26.309% respectively. The medium size firms have
the mean, median market adjusted annualized rate of return of 17.26% and 16.635%
respectively. Further, the large size portfolio has the mean return of 10.452% and the
median return of 11.466%. It is again important to note that in respect of 24 months
holding period also, the small size portfolio outperforms both medium as well as large
size portfolio. Further, in all F-score categories, the small size stocks outperform the
larger size stocks in terms of 24 months mean market adjusted returns. In respect of low
score and high score portfolio also, the mean, median market adjusted return of the small
size portfolio is larger than that of medium size and large size portfolio in case of 24
months holding period of such stocks. However, in order to see whether small firm effect
is accountable for excess returns on high score portfolio and to mark the outperformance
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of high score portfolio over low score portfolio, the difference between high score and
low score has to be statistically significant. The following section will explore whether
the difference between the high score and low score portfolio in different size categories
is statistically significant or not.
5.4.4.2 Examining the Significance of Return Difference between High F-Score
and Low F-Score Stocks in Different Size Categories
Independent sample t-test has been used to determine the significance of
difference between high score and low score portfolio in different size categories. The
following hypothesis is tested and reported in Table 12 as under:
H04 : There is no significant difference between the mean returns of the
stocks having high F-score and the stocks having low F-score across
different size partitions
Table 5.12 shows that in case of large size portfolio, the F-value of Levene‟s test
intended to measure the equality of variances in two groups (high score portfolio and low
score portfolio) is insignificant (at 5% level of significance) in 12 months holding periods
leading to the acceptance of null hypothesis of equal variance in two groups. In case of
24 months holding period, the significant value of Levene‟s test implies that the variance
of two groups are not equal. Hence, the results of Welch‟s t-test become applicable.
Further, the mean difference of 51.043% between high F-score and low F-score portfolio
in case of 12 months holding period is significant at 1% level of significance and the
difference of 42.827% between the two is significant at 5% level of significance in case
of 24 months holding period showing that in case of stocks with larger size, the high F-
score portfolio significantly outperforms low F-score portfolio. Similar results have been
found in case of medium size portfolio wherein high F-score portfolio significantly
outperforms low F-score portfolio.
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Table 5.12: Results of t-test Employed on Firms with high F-score as well as low F-score Across Different Size
Partitions
Size
No. of
stocks
Criteria
12 months market adjusted Returns 24 months Market Adjusted Returns
Mean
returns
(Annual)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
t-value
Mean
returns
(Annualized)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
t-value
Large
30 High 42.974 64.356 51.043 0.543 2.312**
26.572 27.472 42.827 10.798*** 3.041***
15 Low -8.065 79.935 -16.254 50.969
Medium 127 High 64.306 94.924
34.566 0.014 2.145** 37.015 41.738
24.925 11.384*** 2.70*** 53 Low 29.740 106.762 12.089 61.570
small 243 High 70.029 141.866
21.760 0.371 1.280 33.973 51.542
8.308 0.448 1.325 85 Low 48.268 112.299 25.664 44.199
Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
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In case of small size portfolio, the value of F-value (0.371 in case of 12 months;
0.448 in case of 24 months) of Levene‟s test is insignificant in both the holding periods
leading to the acceptance of null hypothesis of equal variance in two groups. The mean
difference between high F-score and low F-score portfolio (21.76% in case of 12 months
holding period; 8.3% in case of 24 months holding period) is statistically insignificant
showing that the high F-score portfolio does not significantly outperforms low F-score
portfolio in respect of stocks with small market capitalization. Thus, excess returns on
high F-score portfolio as well as outperformance of high F-score over low F-score
portfolio could not be attributed to small firm effect.
Returns Conditional on Alternative Partitions
Along with the size effect, the outperformance of high score portfolio over the
low score portfolio is examined taking other partitions such as trading volume and share
price level.
5.4.5 Trading Volume Partitions
Trading volume means the share turnover which is total number of shares traded
during the prior fiscal year scaled by the average number of shares outstanding during the
year. Similar to firm size, all the high book to market companies are placed into trading
volume partitions. Each year, all the firms on BSE with trading volume data and book to
market data are ranked on the basis of June end trading volume. On basis of trading
volume of all the stocks, the 33.3 percentile and 66.67 percentile are calculated every
year. The stocks with trading volume up to 33.33 percentile are classified as low volume
stocks, the stocks having volume in the range of 33.33 to 66.67 percentile are categorized
as medium volume stocks and the stocks exceeding the percentile of 66.67 in terms of
trading volume are classified as large volume stocks. Thereafter, these percentiles are
used to classify the high book to market stocks into low, medium and large volume
portfolios (Piotroski, 2000). The mean and median return of high book to market stocks,
low F-score stocks and high F-score stocks across different trading volume partitions
have been reported in Table 5.13.
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Table 5.13: Market Adjusted Returns Earned Using Value Investment Strategy
Based on Fundamental Signals in Different Trading Volume
Partitions
Panel A showing market adjusted returns in case of 12 months holding period
Low volume Medium volume Large volume
Mean
(%)
Median
(%)
No. of
stocks
Mean
(%)
Median
(%)
No. of
stocks
Mean
(%)
Median
(%)
No. of
stocks
All firms 63.087 32.479 1611 42.912 17.946 1791 34.415 12.896 1195
Low 65.079 29.799 50 26.498 -3.502 50 18.475 -0.047 53
high 63.625 41.225 168 70.282 34.162 142 64.492 31.091 90
Panel B showing the market adjusted returns in case of 24 months holding period
All firms 32.092 27.067 1611 24.099 21.437 1791 18.647 14.250 1195
Low 33.815 33.776 50 20.451 24.463 50 -2.546 -7.082 53
high 35.861 31.879 168 33.148 24.131 142 33.575 22.985 90
Table 5.13 shows that out of total of 4597 high book to market firms, 1611 firms
are categorized into low volume firms, 1791 as firms having medium trading volume and
1195 firms as firms with large volume. It is further important to note that the 12 months
mean market adjusted returns of high F-score portfolio have been greater than all firms as
well as low F-score portfolio in all levels of trading volume except the low volume
portfolio. The low F-score portfolio in case of low trading volume has the mean market
adjusted rate of return of 65.079% and the high F-score portfolio in similar group has the
mean market adjusted rate of return of 63.625%. Further, in case of 24 months holding
period, the mean market adjusted return of high score portfolio exceeds the mean return
of low score as well as all the firms in all levels of trading volume that shows the
outperformance of high F-score firms over low F-score as well as all firms having high
book to market ratio, irrespective of the trading volume. However, in order to prove the
existence of excess returns on high score portfolio over low score portfolio irrespective of
trading volume partitions, the difference between high score and low score has to be
statistically significant. The following section will explore whether the difference
between the high F-score and low F-score portfolio in different trading volume categories
is statistically significant or not.
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5.4.5.1 Examining the Significance of Return Difference between High F-Score
and Low F-Score Stocks in Different Trading Volume Categories
In order to examine whether the difference between the high score and the low
score portfolio across different categories of trading volume is statistically significant or
not, the independent sample t-test has been used. Thus, we examine the following
hypothesis:
H05 : There is no significant difference between the mean returns of the
stocks having high F-score and the stocks having low F-score across
different trading volume categories.
Table 5.14 reports the results as under
Table 5.14 shows that the F-value of Levene‟s test, which means the equality of
variance between two groups (high and low F-score portfolio) in case of low share
turnover firms is 0.914 in case of 12 months holding period and 0.164 in case of 24
months holding period, which is statistically insignificant. It shows that the variances of
two groups are equal. Further, the insignificant t-values in case of both the holding
periods make it evident that there is no difference in the mean market adjusted return of
the stocks that have high F-score and the stocks that have low F-score, in the category of
low trading volume. Thus, high returns to high F-score firms are not present when the
firms have low trading volume.
In case of firms with medium trading volume, the difference between the high
score and low score portfolio is significant (at 5% level of significance) in case of 12
months holding period and insignificant in case of 24 months holding period. Further, in
case of firms with large trading volume, the F-value of Levene‟s test (1.953 in case of 12
months; 0.742 in case of 24 months holding period) is insignificant in both the holding
periods leading to the acceptance of null hypothesis of equal variance in two groups. In
addition, the difference of 46.016% in case of 12 months and 36.122% in case of 24
months period between high F-score and low F-score firms is statistically significant. It
shows that high F-score stocks significantly outperform low F-score firms, if they have
huge trading volume.
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Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
Table 5.14: Results of t-test Employed on Firms with High F-score as well as low F-Score Across Different Trading
Volume Partitions
Trading
volume
Criteria
12 months market adjusted Returns 24 months Market Adjusted Returns
Mean
returns
(Annual)
Std.
Dev.
Mean
difference
F-value of
Levene’s
test
T-
value
Mean
returns
(Annualized)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
T-value
Low 168 High 63.625 98.137
-1.453 0.914 -0.090 35.861 42.239
2.045 0.164 0.291 50 Low 65.079 106.59 33.815 47.691
Medium 142 High 70.282 135.669
43.783 0.170 2.035** 33.148 51.868
12.697 0.357 1.489 50 Low 26.498 115.691 20.451 51.785
Large 90 High 64.492 147.595
46.016 1.953 2.016** 33.575 48.473
36.122 0.742 4.168*** 53 low 18.475 99.012 -2.546 52.626
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Thus, we draw an inference through the above results that for F-score strategy to
work, the firms ought to have huge trading volume. The statistically significant
outperformance of high F-score strategy over low F-score strategy will disappear, if the
firms are thinly traded or have small share turnover.
5.4.6 Share Price Partitions
To examine, whether the performance of F-score strategy exists, irrespective of
low share price effect, all high book to market firms are classified into share price
partitions based on prior year‟s cut offs for all BSE firms. Similar to firm size, all the
high book to market companies are placed into share price partitions. Each year, all the
firms on BSE with sufficient share price and book to market data are ranked on the basis
of June end closing share prices. On basis of closing share prices of all the stocks, the
33.3 percentile and 66.67 percentile are calculated every year. The stocks with share
prices up to 33.33 percentile are classified as small priced stocks, the stocks having
closing prices in the range of 33.33 to 66.67 percentile are categorized as medium priced
stocks and the stocks exceeding the percentile of 66.67 in terms of closing share prices
are classified as large priced stocks. Thereafter, these percentiles are used to classify the
high book to market stocks into small, medium and large price portfolios. The mean and
median return of high book to market stocks, low F-score stocks and high F-score stocks
across different share price partitions have been reported in Table 5.15
Table 5.15: Market-Adjusted Returns Earned Using Value Investment Strategy based
on Fundamental Signals in Different Share Price Partitions
Panel A showing market adjusted returns in case of 12 months holding period
Small price Medium price Large price
Mean Median No. of
stocks
Mean Median No. of
stocks
Mean Median No. of
stocks
All firms 63.043 28.605 2559 31.252 13.634 1667 16.768 6.120 371
Low 46.874 17.820 95 22.622 6.194 46 5.363 -18.575 12
high 71.860 34.717 241 59.553 36.615 134 47.00 43.436 25
Panel A showing market adjusted returns in case of 24 months holding period
All firms 32.815 26.964 2559 17.584 15.589 1667 10.307 11.290 371
Low 22.159 26.247 95 7.614 2.773 46 10.251 18.719 12
high 36.927 27.647 241 29.071 26.489 134 38.344 31.688 25
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Table 5.15 shows that, out of total of 4597 high book to market firms, 2559 firms
have small share price, 1667 firms have medium price and only 371 firms have large
price. The 12 months market adjusted mean return of high F-score firms in all the
categories of share price (71.860% in small price; 59.553% in case of medium price;
47.00% in case of large price) exceeds the mean return of all high book to market firms
(63.043% in case of small price; 31.252% in case of medium price; 16.768% in case of
large price) as well as low score firms (46.874% in case of small price; 22.622% in case
of medium price; 5.363% in case of large price). The same results hold in case of 24
months holding period. It, thus, implies that the high F-score firms outperform all the
firms in high book to market portfolio as well as low F-score firms across all categories
of share prices.
However, in order to examine the statistically significant outperformance of high F-
score portfolio over low F-score portfolio irrespective of share price partitions, the
difference between two has to be statistically significant. The following section will
explore whether the difference between the high F-score and low F-score portfolio in
different share price categories is statistically significant or not.
5.4.6.1 Examining the Significance of Return Difference between High F-Score
and Low F-Score Stocks in Different Share Price Categories
In order to examine whether the difference between the high score and the low
score portfolio across different categories of trading volume is statistically significant or
not, the independent sample t-test has been used. Thus, we examine the following
hypothesis:
H06 : There is no significant difference between the mean returns of the
stocks having high F-score and the stocks having low F-score across
different share price categories.
Table 5.16 reports the results of testing the above hypothesis.
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Table 5.16: Results of t-test Employed on Firms With High F-Score as well as low F-Score Across Different Share Price
Partitions
Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
Share
price
No. of
stocks
Criteria
12 months market adjusted Returns (Annual) 24 months Market Adjusted Returns (Annualized)
Mean
returns
(Annual)
Std.
Dev.
Mean
difference
F-value of
Levene’s test
T-
value
Mean
returns
(Annualized)
Std.
Dev.
Mean
difference
F-value
of
Levene’s
test
T-value
Small 241 High 71.860 133.885
24.985 0.112 1.597 36.927 40.153
14.767 1.796 1.616 95 Low 46.874 116.108 22.159 50.169
Medium 134 High 59.553 112.138
36.931 0.723 1.996** 29.071 46.207
21.456 4.474** 2.527** 46 Low 22.622 95.905 7.614 58.722
Large 25 High 47.000 78.730
41.637 0.150 1.487 38.344 48.246
28.092 0.459 2.505** 12 low 5.363 81.815 10.251 49.665
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Table 5.16 shows that in case of stocks with small share price, the F-value of
Levene‟s test is insignificant showing no difference in the variances of the two groups
(high score and low score group). The difference in the mean market adjusted returns
of two groups (24.98% in case of 12 months; 14.76% in case of 24 months holding
period) in case of stocks with small share price is statistically insignificant in both
the holding periods. Further, significant difference is observed between two groups
in case of medium price in both the holding periods. In case of large price portfolios,
the market adjusted mean difference of 41.63% between high F-score and low F-
score portfolio is statistically insignificant in case of 12 months holding period of
such stocks. Nevertheless, statistically significant mean market adjusted difference of
28.092% between high F-score and low F-score portfolio is observed in case of 24
months holding period.
In a nutshell, the statistically significant outperformance of high F-score
stocks over low F-score stocks is channelized to firms with large size, huge trading
volume and medium to large price in Indian stock market. Hence, the risk involved
in investing in small and illiquid firms is not implicated in this investment strategy.
5.4.7 Analyzing the Predictive Ability of F-score Strategy
The prior results of significant difference between the high F-score and low
F-score shows the capability of F-score in predicting the returns. The model
development and estimation of the relationship between F-score and the overall
returns is as under:
5.4.7.1 Model Development
5.4.7.1 (A) Dependent variable-
In order to study the predictive ability of the criteria in explaining the risk
adjusted returns, the market adjusted stock return (annual in case of 12 months,
annualized in case of 24 months) variable has been taken as dependent variable as
advocated in Piotroski (2000), Michou (2007), Dahl et al. (2009) and Dosamantes
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(2013). The reason behind taking excess of portfolio‟s return over market is to know
whether the excess returns yielded by the stocks are explained by F-score or not.
5.4.7.1 (B) Explanatory variables and hypothesis development
According to Piotroski (2000), there are certain known effects also which
could have strong relationship with F-score. Thus, before determining the role of F-
score in predicting stock returns, the following effects need to be controlled for. A
brief discussion of the explanatory variables used in the model is given below.
F-score- A comprehensive financial signal known as „F-score‟ measures three
constructs pertinent to a company‟s financial position: profitability, f inancial
leverage along with liquidity, and operating effectiveness. The three constructs of F-
score of a stockis the sum of nine binary signals related to these three constructs
(Wellman, 2011). In order to determine the relation between F-score and market
adjusted returns, the following null hypothesis is tested.
H07 : F-score of the stock has no significant impact on its market
adjusted returns
Under reaction or momentum effect: Chan et al. (1996) found the delayed reaction
of stock prices to the information in past returns and in past earnings. It is due to the
fact that there is tendency of the market to anchor too heavily on the past trends. The
investors therefore cut down the new information which is at odds with their
mindsets and alter their perceptions steadily. This fact of under reaction over
intermediate horizons suggests that a stock with high past returns will on average
experience high subsequent returns. Moreover, a substantial portion of under reaction
or momentum effect is concentrated around subsequent earnings announcements.
Thus, if the market is surprised by good or bad earnings news, then on an average the
market continues to be surprised in same direction for at least six months. Asness
(1997) however found the inverse relation between the momentum effect and the
value premium. As F-score comprises of the company‟s information regarding
profitability, it is necessary to control this effect, to examine the robustness of F-
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
193
score. Thus, the six months prior return on a particular stock has been used as the
control variable before estimating the relation between F-score and stock returns.
The following null hypothesis is tested.
H08 : The momentum effect of the stock has no significant impact on its
market adjusted returns.
Recent equity offering: Ikenberry et al. (1995) observed that average abnormal
return on announcement of share repurchases of value stocks due to undervaluation
is 45.3% as compared to glamour stocks where no positive drift in abnormal returns
could be observed. Moreover, Loughran and Ritter (1995) found that the companies
issuing seasoned equity offering significantly underperform relative to non issuing
firms for 5 years after the offering date. Thus, the companies issuing equity in the
preceding financial year are said to have negative stock returns in the current period.
Since the equity issuance variable is incorporated in the F-score, it is thereby
correlated to aggregate return metric. Thus, equity issuance variable has been taken
as control variable in order to estimate the relationship between F-score and overall
returns. The following null hypothesis is tested.
H09 : The issue of equity shares by a company in preceding financial
year has no significant impact on its market adjusted returns in
current period.
Accrual: Sloan (1996) observed that the firms with relatively high (low) levels of
accruals experienced negative (positive) future abnormal stock returns which were
concentrated around future earnings announcements. He also observed that the
strategy of buying stocks following a reduction in accruals and simultaneously
selling stocks following a buildup in accruals would have generated an average
return of about 10 percent per year in US stock market. Also, Takamatsu and Favero
(2013) found that current accruals were incapable of explaining future abnormal
return behavior in the firms that were analyzed. In addition, no significant abnormal
Adding Value to Value Stocks -Joseph Piotroski’s F-score Model
194
returns were reached in an accruals-based investment strategy. Therefore, the
companies having increased level of accruals in current fiscal year compared to the
level of accruals in previous fiscal year are said to have negative stock returns.
Again, the accrual variable is built-in in the F-score, it is thereby correlated to
aggregate return metric. Thus, the accrual variable has been taken as control variable
in order to estimate the relationship between F-score and overall returns.
H010 : The level of accrual of a company has no significant impact on its
market adjusted returns.
Size- The term „size‟ is measured as the market value of the equity shares (a stock‟s
price times shares outstanding). The different studies have found significantly
negative impact of size in explaining stock returns, see for example, Banz (1981),
Fama and French (1992), Mukherji et al. (1997), Anderson et al. (2003), Dunis and
Reilly (2004), Kumar and Sehgal (2004), Kyriazis and Diacogiannis (2007) and
Tripathi (2009). Thus, the variable „size‟ acts as control variable in order to estimate
the relationship between market adjusted returns and the total score. The following
hypothesis is formulated and tested.
H011 : The size of the stock has no significant impact on its market
adjusted returns.
Book to market effect- It is measured as the ratio of the book value of the company
to number of shares outstanding. Along with size, different studies have found the
significant role of book to market equity in explaining stock returns, see for example,
Lakonishok et al. (1991), Mukherji et al. (1997), Vos and Pepper (1997), Arshanaplli
et al. (1998), Dhatt et al. (2001), Sehgal (2001), Anderson et al. (2003), Karan and
Gonenc (2003), Malin and Veeraraghavan (2004), Bahl (2006), Bundoo (2008),
Senthilkumar (2009), Tripathi (2009). Thus, book to market ratio acts as control
variable in order to estimate the relationship between market adjusted returns and the
total score. The following hypothesis is formulated and tested.
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H0 : The book to market equity of the stock has no significant impact
on its market adjusted returns.
5.4.7.2 Model Estimation
As the present data set entails both a spatial (cross sectional units i.e.
companies) and temporal dimension (periodic observations of a set of variables
characterizing these cross-sectional units over a particular time span); thus to
examine these issues, panel data analysis has been used. The following model is
examined:
1 2 3
4 5 6
logit it it it
i it it it
Marketadjustedreturns size booktomarket momentum
accrual equityoffer F score u
Here, 2~ 0,it uu N , 1,...,i N (N= no. of cross-sectional units), and 1,...,t T (T=
no. of time-series units).
It is important to mention that size means the market capitalization of the
stocks at fiscal yearend; momentum means the six-month market adjusted return1
over the six months directly preceding the date of portfolio formation; accrual means
the excess of ROA over CFO (as described in section 5.2) and the equity offer acts as
indicator variable where it is set equal to one if the firm raised equity during the
prior fiscal year and zero otherwise. In order to estimate the said model, the value of
momentum and accrual variables for all the observations (4597) are ranked in
ascending order and divided into deciles so as to assign ranks to the firms.
Thereafter, the values of these variables are replaced with their portfolio decile
ranking i.e. 1 to 10 in order to estimate the regression model. Before proceeding to
further analysis, Pearson‟s correlation matrix has been formed. Table 5.17 provides
Pearson correlation coefficients between the dependent variable (market adjusted
returns) and the explanatory variables (size, book to market, accrual, equity offer,
1 The six months market adjusted return of the stocks have been calculated by summing up the
monthly market adjusted returns of the stocks for a period of 6 months directly preceding the date
of portfolio formation.
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196
momentum and F-score) and amongst different explanatory variables for the period
1996-2010.
Table 5.17: Pearson’s Product Moment Correlation Matrix
Size B/M ratio Equity
offer Accrual Momentum F-score
12 months
market
adjusted
return
(annual)
24 months
market
adjusted
return
(annualized)
Size 1 -.422*** .175*** .078*** .014 -.051*** -.290*** -.382***
B/M ratio -.422*** 1 -.063*** -.093*** .099*** -.002 .220*** .293***
Equity offer .175*** -.063*** 1 .056*** .001 -.189*** -.045*** -.098***
Accrual .078*** -.093*** .056*** 1 -.015 -.203*** -.035** -.061***
momentum .014 .099*** .001 -.015 1 .130*** -.117*** -.157***
F-score -.051*** -.002 -.189*** -.203*** .130*** 1 .062*** .087***
12 months
market
adjusted return
(annual)
-.290*** .220*** -.045*** -.035** -.117*** .062*** 1
24 months
market
adjusted return
(annualized)
-.382*** .293*** -.098*** -.061*** -.157*** .087*** 1
Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
Table 5.17 makes it evident that the explanatory variable; book to market ratio
has significantly positive correlation with the market adjusted returns (-0.220 in case of
12 months; -0.293 in case of 24 months holding period) in both the holding periods.
Also, significantly negative correlation has been observed between the market adjusted
returns and the size factor (-0.290 in case of 12 months; -0.382 in case of 24 months
holding period). It implies that increase in size results in fall in market adjusted returns.
Along with size factor, the variables; accrual, equity offer and momentum have also been
negatively associated with the returns in both the holding periods. In addition, F-score
has significantly positive association with the market adjusted returns (-0.062 in case of
12 months; -0.087 in case of 24 months holding period) which implies that as the value
of F-score increases, there would be an increase in market adjusted returns. As far as
correlation amongst the explanatory variables is concerned, it is lesser than the
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197
prescribed rule of thumb i.e. 0.8 (Gujarati and Sangeetha, 2007). We further proceed to
apply regression analysis.
In order to determine the relationship between F-score and the stocks returns, the
data regarding returns, accruals, equity offering, size, book to market ratio and
momentum returns have been calculated for all high book to market firms across the
period of 15 years i.e. 1996 to 2010. The total number of high book to market
companies across the period of study is 4597 which results in formation of 1462
mutually exclusive groups of companies across the period of 15 years. Since the present
data set entails both a spatial (cross sectional units i.e. companies) and temporal
dimension (periodic observations of a set of variables characterizing these cross-
sectional units over a particular time span); therefore to examine these issues, the panel
data analysis has been used (Agrawal and Khan, 2011). Broadly there are three methods
of estimating such a data set- pooled regression analysis, fixed effects panel data
analysis and random effects panel data analysis. Further, the time invariant and the
individual invariant effects can be estimated by including (N-1) individual dummies and
(T-1) time dummies in the existing model. Since the number of individuals (groups)
across the period of study are 1462, the introduction of 1461 (n-1 dummies are
introduced to avoid the dummy trap) dummies in the regression model would lead to an
enormous loss in degrees of freedom (Baltagi, 2005). Thus, the time invariant effects are
estimated using T-1 time dummies i.e. d2 for 1997, d3 for 1998, d4 for 1999,…….,d15
for 2010 in the existing regression model.
The different diagnostic tests have been used to determine an appropriate model
for estimation. The Chow test helps in determining whether the fixed effects panel data
model or pooled regression model is more appropriate to use and Lagrange Multiplier
(LM) test helps to find out whether the random effects panel data model or pooled
regression model is more suitable to use. Thereafter, Hausman test helps to choose
between fixed effects and random effects panel data model. The Table 5.18 reports the
results as under:
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Table 5.18: Results of Chow test, LM Test and Hausman Test to Determine an
Appropriate Model
Chow test
H (0): Pooled
OLS
H (a): Fixed
effects model
Lagrange Multipler
test
H (0): Pooled OLS
H (a): Random effects
model
Hausman test
H (0): Random
effects
H (a): Fixed effects
Final
model
12 months holding
period
45.89
(0.000)***
78.67
(0.000)***
79.42
(0.000)***
Fixed
effects
Fixed effects Random effects Fixed effects
24 months holding
period
44.57
(0.000)***
84.73
(0.000)***
160.49
(0.000)***
Fixed
effects
Fixed effects Random effects Fixed effects
Note: Significance at: p-values * , 0.10, * * , 0.05 and * * * , 0.01
Table 5.18 shows that the value of the Chow test in both the holding periods has
been significant at 1% level of significance. It leads to the rejection of null hypothesis of
no differences in coefficients across time. Hence, fixed effects panel data model is more
appropriate to use in such a situation. In addition, the Chi-squared statistic of Lagrange
Multiplier (LM) test is also significant in both the holding periods leading to the rejection
of null hypothesis of lack of presence of random effects in residuals. Thus, random
effects panel data model is more suitable to use in this situation. Further, to decide
whether fixed effects or random effects model is more appropriate to use, Hausman test
has been applied. The significant test statistic of Hausman test in both the holding periods
leads to the rejection of null hypothesis of no correlation between the individual effects
and the explanatory variables of the model. Hence, fixed effects panel data model is
considered more appropriate to apply in this situation.
After determining the choice of the model, the error term has to be free from
disturbances. Table 5.19 shows the results of testing of different assumptions of panel
data regression model.
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Table 5.19: Results of Testing Different Assumptions of Panel Data Regression
Model
Assumptions 12 months holding
period
24 months holding
period
Stationarity
Fisher type unit root test based on ADF tests
(Inverse chi-sq)
H(0): panel contains unit root
H (a): panel is stationary
Variables
Returns 3515.3462
(0.000)***
1877.1634
(0.000)***
F-score 2446.7234
(0.000)***
Bp ratio 2260.9789
(0.000)***
Equityoffer 2271.6692
(0.000)***
Accrual 3810.3653
(0.000)***
Momentum 3690.7845
(0.000)***
Size 2078.5712
(0.000)***
Autocorrelation
Woolridge test for autocorrelation (F-Statistic)
H (0): no autocorrelation
H (a): autocorrelation
0.770
(0.3806)
365.602
(0.000)***
Heteroskedasticituy
Breusch Pagan/ Cook Weisbery test (chi-sq statistic)
H (0): constant variance
H (a): heteroskedasticity
361.74
(0.000)***
75.26
(0.000)***
Multicollinearity
Vif test (mean vif)
1.89
Note:
1. P-value of the statistics has been reported in parenthesis
2. *** shows significant at 1% level of significance
Table 5.19 shows the results of testing of various assumptions on the given panel
data. The Fisher type unit root test based on Augmented Dickey Fuller test shows that all
the variable in the regression analysis are stationary i.e. unit root are not present in the
dataset. Further, the Woolridge test for autocorrelation shows the lack of presence of
autocorrelation in case of 12 months holding period. However, the 24 months data shows
the presence of autocorrelation. Also, the data is not homoskedastic in both the holding
periods. The mean value of variance inflation factor (VIF) lesser than 10 shows the lack
of presence of multicollinearity amongst the independent variable of the regression. The
analysis is said to be efficient only if the error term is free from all kind of disturbances.
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200
Thus, to remove the problem of autocorrelation and heteroskedasticity in the data set,
cluster (i) command (see Appendix IV) has been used in Stata and the robust standard
errors have been reported for the purpose of analysis. Table 5.20 shows the results of
panel data regression analysis.
Table 5.20: Results of Role of F-Score In Predicting The Stock Returns
Dependent
variables
12 months holding period 24 months holding period
Independent
variables
coefficient Robust
std. error
T-
value
P-value coefficient Robust std.
error
T-
value
P-value
F-score 4.93198 1.09944 4.49 0.000*** 1.507012 0.3687852 4.09 0.000***
Accrual 0.99023 .6061497 1.63 0.102 -0.119797 0.1986197 -0.60 0.546
Momentum -6.3174 1.021306 -6.19 0.000*** -2.108179 0.3222178 -6.54 0.000***
Size -27.5837 3.010006 -9.16 0.000*** -11.56885 0.8677475 -13.33 0.000***
Book to
market ratio
1.043611 .5500355 1.90 0.058* 0.428626 0.2297475 1.87 0.062*
Equity offer 7.66700 6.424987 1.19 0.233 -0.436018 2.309823 -0.19 0.850
D2 76.0292 12.73776 5.97 0.000*** 29.79618 3.94224 7.56 0.000***
D3 89.8549 13.63969 6.59 0.000*** 47.63443 4.574263 10.41 0.000***
D4 148.942 15.53715 9.59 0.000*** 41.23242 4.521249 9.12 0.000***
D5 42.6054 11.19391 3.81 0.000*** 44.90643 4.104481 10.94 0.000***
D6 122.9632 11.9297 10.31 0.000*** 45.401 4.012941 11.31 0.000***
D7 81.35074 13.20463 6.16 0.000*** 24.00364 4.48029 5.36 0.000***
D8 78.97681 13.72568 5.75 0.000*** 57.32358 4.416907 12.98 0.000***
D9 198.5947 12.41263 16.00 0.000*** 37.86312 3.937776 9.62 0.000***
D10 48.54385 9.902109 4.90 0.000*** 8.772375 3.879429 2.26 0.024**
D11 78.93341 9.806639 8.05 0.000*** 23.76946 3.5606 6.68 0.000***
D12 98.19876 9.623107 10.20 0.000*** 30.38913 3.660238 8.30 0.000***
D13 70.8737 9.464793 7.49 0.000*** 35.44618 3.440297 10.30 0.000***
D14 111.7876 9.797515 11.41 0.000*** 26.79123 3.709172 7.22 0.000***
D15 68.318 9.022126 7.57 0.000*** 13.87954 3.597484 3.86 0.000***
constant 77.05165 19.79172 3.89 0.000*** 45.82804 5.772199 7.94 0.000***
R-square 0.2148 0.2900
Wald chi-
square
(P-value)
1546.87
(0.000)
1621.99
(0.000)
Note: *, **, *** denotes p-values significant at 10, 5 and 1 percent level respectively
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Table 5.20 shows that Wald chi- square of the model which is joint significance
test for all the variables is significant at 1% level of significance showing the goodness of
fit of the model. Table 5.20 further reports the results of the predictability of stocks
returns through F-score after holding size, value, momentum, equity offer and accrual
constant in 12 months as well as 24 months holding period. The coefficient of the
momentum effect has been significantly negative in both the holding periods leading to
the rejection of null hypothesis (H08) of no significant impact of momentum of stocks on
their market adjusted returns. It therefore shows that the return six months prior to the
date of portfolio formation of high book to market stocks, affects the overall returns
negatively. It could be due to the fact that pursuing a value strategy (the strategy of
buying high book to market stocks) entails to buying the firms with poor momentum. The
value and momentum measures are negatively correlated (Asness, 1997). Since the
sample consists of only the value stocks, the momentum effect in such case could not be
positively affecting the stocks returns. These findings are consistent with that of (Dahl et
al., 2009) and inconsistent with the findings of Piotroski (2000) who found the
statistically positive relation between the returns and the momentum.
The coefficient of size factor has been significantly negative in both the holding
periods leading to the rejection of null hypothesis (H011) of no significant impact of size
on stock returns. It therefore shows the presence of size effect in the data i.e. the stocks
with lower market capitalization outperform the stocks with higher market capitalization.
Along with the size effect, the value effect i.e. the tendency of high book to market stocks
to outperform low book to market stocks is also present in the sample. The book to
market coefficient is positive and statistically significant (significant at 10% level of
significance) in both the holding periods leading to the rejection of null hypothesis (H012)
of no significant impact of book to market equity on market adjusted returns. It therefore
confirms the presence of value effect in Indian stock market.
Further, the coefficient of the accrual effect has been positive in case of 12
months holding period and negative in case of 24 months holding period. However, the
coefficients have been statistically insignificant in both the holding periods leading to the
acceptance of null hypothesis (H010) of no significant impact of level of accruals on the
market adjusted returns. The findings are not in line with the findings of developed
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economies where the significantly negative relation has been observed between the
returns and the accruals (Piotroski, 2000). However, in contrast with the findings of the
developed markets, high accrual portfolios tend to provide higher returns as compared to
low accrual portfolios in Indian stock market (Sehgal et al., 2012). The study however,
finds the positive relation up till one year holding periods only. When the holding period
is extended, the relationship turns negative. Nevertheless, the relation remains
statistically insignificant.
Along with accrual effect, the coefficients of the equity offer variables are
positive in both the holding periods showing that the firms that issued equity in the prior
fiscal years positively affect the subsequent returns. These findings are also inconsistent
with the findings of Loughran and Ritter (1995), Piotroski (2000) who found that the
companies that had issued equity in the preceeding financial year significantly
underperform relative to the non-issuing firms in the current year. However, the current
findings have been statistically insignificant leading to the acceptance of null hypothesis
(H09) of no significant impact of equity issuance by a company on its market adjusted
returns.
In respect of F-score we notice that, after controlling for size effect, book to
market effect, accrual effect, momentum effect and equity issuance effect, the
coefficients of F-score is positive and significant at 1% level of significance in both the
holding periods leading the rejection of null hypothesis (H07) of no significant impact of
F-score on market adjusted returns. It therefore implies that one point improvement in the
aggregate score is associated with an approximate 4.93% increase in one year market
adjusted return and about 1.5% increase in two year annualized market adjusted rate of
return earned subsequent to portfolio formation. Moreover, the addition of variables
designed to capture size effect, value effect, momentum effect, accrual reversal, and a
prior equity issuance has no impact on the capability of F-score to predict future returns
in Indian stock market.
5.5 CONCLUSION
The study examines the relevance of an accounting based fundamental strategy in
enhancing the overall returns of value stocks. For this, the fundamentals based investment
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strategy „F-score‟ given by Piotroski (2000) has been used on stocks having high book to
market ratio in order to eliminate the firms with poor future prospects from the entire
portfolio of value stocks. The F-score model is the sum of nine financial signals that
measures three constructs pertinent to a company‟s financial position: profitability,
financial leverage along with liquidity, and operating effectiveness. The results revealed
the presence of significant difference in the mean market adjusted return of stocks,
meeting all constructs of F-score as compared to the mean market adjusted return of the
entire value portfolio (18.402% in case of 12 months, 8.908% in case of 24 months)
across the period of study. Further, the significant mean return difference (29.856% in
case of 12 months, 17.531% in case of 24 months) found between the high F-score firms
and the low F-score firms, suggests that an investor could constitute a hedge portfolio
that generate positive return by selling expected losers stocks and buying expected
winners. Thus, an F-score strategy can help in shifting of the returns earned by an
investor.
In further analysis, the attempt was made to know if the excess returns earned
using fundamental analysis strategy is strictly a small firm effect or could be applied
across all categories of size, trading volume and share price partitions. The results did not
find the evidence of the statistically significant outperformance of high F-score stocks
over low F-score stocks in respect of firms with smaller size. However, the statistically
significant outperformance of high F-score stocks over low F-score stocks is found to be
channelized to firms having large size, huge trading volume and medium to large price in
Indian stock market. Thus, the risk involved in investing in illiquid and small firms is not
implicated in this investment strategy
Further, the role of F-score in predicting the overall returns is examined. Before
examining this relationship, there are certain known effects which could have a strong
relation with F-score are controlled. These effects include size effect, book to market
effect, momentum effect, recent equity offering and accrual effect. The results revealed
that after controlling for these known effects, one point improvement in aggregate F-
score is associated with an about 4.93% increase in market adjusted return and about
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1.5% increase in two year annualized market adjusted return earned subsequent to
portfolio formation. Thus, the addition of variables designed to capture size effect, value
effect, momentum effect, accrual reversal, and a prior equity issuance has no impact on
the capability of F-score to predict future returns in Indian stock market. Thus, an
investor can apply this strategy for enhancing the returns on value portfolio in Indian
stock market.