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THE USE OF GENETIC ALGORITHMS TO OBTAIN HIGHER RETURNS ON
INVESTMENT STRATEGIES BASED ON FINANCIAL STATEMENT
ANALYSIS: A TEST IN BRAZIL
1. Introduction
Investing in value stocks is a recurring subject in literature (Graham and Dodd, 1934; Fama
and French, 1995). There is large evidence particularly on developed markets, that portfolios of
high book-to-market (HBM) stocks outperform portfolios of low book-to-market stocks.
Rosenberg, Reid and Lansteisn (1984), Fama and French (1992, 1995) and Lakonishok et al.
(1994), agree on the evidence that the book-to-market ratio is strongly and positively correlated
to future stock performance.
Abarbanell and Bushee (1997) document that an investment strategy based on financial
signals help investors to earn significant abnormal returns. Concerning specific accounting
signals, Sloan (1996) finds evidence that firms with higher amounts of accruals underperform
in the future. Piotroski (2000) aggregates the HBM effect to financial statement analysis and
shows that the mean return earned by a HBM investor can be increased by at least 7.5%
annually through the selection of financially strong HBM firms. Piotroski (2000) proposes a
strategy based on financial statements analysis to select value stocks with the potential to
outperform the market. The strategy consists in selecting high book-to-market (HBM)
companies and rank them according to a system of points based on financial signals. When the
signaling is positive (or “good”), the indicator of this signal equals 1; when it is negative (or
“bad”), the indicator equals 0. The sum of all indicators gives the score achieved by the
company. Nine financial signals and their respective indicators compose the strategy and were
chosen to assess profitability, capital structure and operational efficiency: return on assets,
variation of the return on assets, accrual, free cash flow, liquidity variation, leverage variation,
gross margin variation, assets turnover and public offer. Lopes and Galdi (2007) and Galdi
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(2008) adapted this strategy to the Brazilian market characteristics, also reaching significantly
higher-than-average returns.
The strategy above assumes that all indicators are equally important to the composition of
the score and thus, have similar relevance to the market. Conversely, the literature is extensive
showing the different relevance of financial indicators (Sloan 1996, Ou and Penman 1989,
Abarbanell and Bushee 1998, to mention some) and that this relevance varies within countries
(Bartov, 2001). The objective of this paper is to contribute to the identification of different
importance levels of financial indicators: if there is a set of weights λi for the indicators Fi that
optimizes the selection of stocks, the return of the strategy would be even higher than those
found in the above mentioned researches. Besides, it would empirically show which financial
figures are taken more seriously by the market.
Assigning weights to financial indicators to form a scalar value is not a new idea. For
example, Ou and Penman (1989) propose this method to predict stock returns and use a logit
model to estimate weights for the financial indicators. In this paper however, a computational
technique often used for optimization called Genetic Algorithms (GA) was applied to find the
set of weights λi that maximizes the return of a portfolio.
Our paper adds to the previous literature by proposing more discussion about the equally
weighted metric used by the most of the quoted studies. Selecting financial signals to
implement a financial statement analysis is a discretionary task, as it is to use the same weight
to these signals. Our paper analysis if a modern technique based on genetic algorithms selection
can improve returns of financial statement based investment strategies. If it is arbitrary to use
the same weight to all signals, why not try to optimize the result of an investment strategy by
allowing the weights to change? Could the weights reveal some peculiarity that could be used
in a financial statement analysis considering the characteristics of the market that firms are
immersed?
3
In the same vein that Lopes and Galdi (2007) we use Brazil, a prominent emerging market,
to test our investment strategy considering that the weights obtained by an optimization
strategy could be significantly different when comparing the implementation of the strategy in
a developed market and in a developing one.
Our results show that the obtained weights yield an increase of the market-adjusted return
from 36% to 76% (1-year buy-and-hold strategy) and from 68% to 112% (2-years buy-and-
hold strategy) when comparing the equally-weighted score to the optimized weighted score.
Our analysis show that the more relevant signals are change in cash and equivalents and change
in firm’s current firm-year turnover. These findings can raise the discussion about the
liquidity´s importance on financial statement analysis of firms immersed in a developing
country like Brazil, where the cost of capital is significantly high and most of the public firms
raise capital by issuing debt.
The remaining of the paper is organized as follows. Section 2 reviews the adapted strategy
used by Lopes and Galdi (2007) to the Brazilian market. Section 3 presents the main features of
genetic algorithms procedures. Section 4 presents our experiment description and shows how
the strategy was implemented. Results are presented in Section 5. Section 6 concludes the paper.
2. From Fundamental Analysis to BrF_SCORE
The premise that the financial characteristics of a company may be linked to its real value
is the central theme of fundamental analysis (Damodoran 2002). There is a vast literature
showing several ways of how interpreting these characteristics may lead to the composition of a
portfolio that outperforms the market. Particularly, the selection of HBM companies has proven
to be a successful strategy (Fama and French 1992; Lakonishok, Schleifer, Vishny 1994).
Nonetheless Piotroski (2000) claims that this superior result relies upon the strong performance
of a few companies, tolerating the feeble performance of most of the others. He proposes a
strategy based on accounting numbers that aims, by means of the identification of “positive”
4
signals, to select among these HBM companies only those that would outperform the market.
He proposes the observation of nine financial figures that assess a company regarding
profitability, capital structure and operational efficiency: return on assets, variation of return on
assets, accrual, free cash flow, liquidity variation, leverage variation, gross margin variation,
assets turnover and public offer. The strategy is simple: each variable is associated to an
indicator, equal to one when the value of the variable is recognized as “good” to the
performance of the company and equal to zero when it is said to be “bad”. The sum of all nine
indicators results a score (F_SCORE). Each year, after all companies have disclosed their
results, the higher quintile of HBM firms is identified and, among these firms, those with
higher F_SCORE are chosen to be kept in the portfolio for 1 and 2 years (buy-and-hold). The
application of this technique in the US market yielded average adjusted returns (above market
average) of 13.4% and 28.7% for 1 and 2 years, respectively.
Lopes and Galdi (2007), adapting Piotroski’s (2000) proposal to the characteristics of the
Brazilian market, changed the F_SCORE and created the BrF_SCORE:
BrF_SCORE = F_ROA + F_∆ROA + F_ACCRUAL + F_CF + F_∆LIQUID + F_∆LEVER + F_∆MARGIN + F_∆TURN + EQ_OFFER
where:
F_ROA = 1 if ROA > 0, zero otherwise. ROA is defined as net income scaled by beginning-of-the-year total assets;
F_∆ROA = 1 if ∆ROA > 0, zero otherwise. ∆ROA is defined as current firm-year ROA less the previous firm-year ROA;
F_ACCRUAL = 1 if ACCRUAL < 0, zero otherwise. ACCRUAL is defined as the variations in
current assets (except cash and equivalent) less the variations in current liabilities (except short term debt). This value is scaled by beginning-of-the-year total assets. (This calculation was
applied because Brazilian accounting standards did not require cash flow statements until
2008);
F_CF = 1 if CF > 0, zero otherwise. CF is defined current firm-year change in cash and
equivalents, scaled by beginning-of-the-year total assets;
F_∆LIQUID = 1 if ∆LIQUID > 0, zero otherwise. ∆LIQUID measures the changes in the
firms’s current ratio in relation to previous year. The current ratio is defined as the ratio of
current assets to current liabilities at the end of the year;
F_∆LEVER = 1 if ∆LEVER <0, zero otherwise. ∆LEVER is the change in the ratio of total
gross debt to total assets in relation to prior year;
5
F_∆MARGIN = 1 if ∆MARGIN > 0, zero otherwise. ∆MARGIN is the change in firm-year current gross profit scaled by total sales (gross margin ratio) compared to previous year;
F_∆TURN = 1 if ∆TURN > 0, zero otherwise. ∆TURN is the change in firm’s current firm-year
Sales scaled by beginning-of-the-year total assets (asset turnover ratio);
OF_PUB = 1 if the firm did not issue equity in the year preceding portfolio construction, zero
otherwise.
Similar to previous research, this one has also shown that the use of this technique in the
Brazilian market yielded higher adjusted returns1 for 1 and 2 years periods.
3. Genetic Algorithms
Genetic Algorithms (GA) are an Evolutionary Computation (EC) technique, one of the
Artificial Intelligence branches that proposes a new paradigm, alternative to conventional data
processing, in which previous knowledge about problem solving is not required to find a
solution. Its mechanism is based on Charles Darwin’s theory of natural selection, where the
best adapted individuals have higher chance to reproduce, leading to the evolution of the
population (Bittencourt, 1998).
When using GAs, the problem to be optimized is the environment and the population is a
set of individuals, each of them a possible solution to the problem. Individuals are composed by
genes, the solution’s parameters, and their capability to solve the problem is evaluated by
means of a fitness function. As an example, given a situation where one wants to optimize fuel
consumption of transporting a load between two known points, where it is possible to define
the load’s weight and the vehicle’s average speed, each individual would be composed by a
couple of genes (weight, speed) and would be assessed by the fuel consumption that this
combination would produce. GA are usually applied to the solution of search and optimization
problems, specially when they are not differentiable, present multiple local optima or its
mathematical model is too complex or simply does not exist.
Figure 1 represents GA’s mechanism using as example individuals with eight genes. An
initial population (a) is assessed by the fitness function (b). It sets the values 24, 23, 20 and 11
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to the four individuals: the better the individual, the higher the value assigned and the greater
chances it will have to reproduce. In this particular example, the probability an individual has
to reproduce is directly proportional to the result of the fitness function. In (c) couples are
randomly selected for reproduction following probabilities in (b). In this example, one of the
individuals was selected twice, while another one was not even once selected. Still in (c), the
crossover points are also randomly selected, creating in (d) the next generation individuals.
This mechanism consists in combining the first part (before the crossover point) of a genitor
with the later part of the other genitor: the first descendent of the first couple inherited its first
three genes from the gray individual and the five last from the white individual, while the
second descendent inherited its first three genes from the white individual and the five last from
the gray individual. Finally, in (e) each individual can suffer random mutation at one of its
genes, producing genes that could be not present in the initial population (Russel and Norvig,
2003).
2 4 7 4 8 5 5 2 24 31% 3 2 7 5 2 4 1 1 3 2 7 4 8 5 5 2 3 2 7 4 8 1 5 2
3 2 7 5 2 4 1 1 23 29% 2 4 7 4 8 5 5 2 2 4 7 5 2 4 1 1 2 4 7 5 2 4 1 1
2 4 4 1 5 1 2 4 20 26% 3 2 7 5 2 4 1 1 3 2 7 5 2 1 2 4 3 2 2 5 2 1 2 4
3 2 5 4 3 2 1 3 11 14% 2 4 4 1 5 1 2 4 2 4 4 1 5 4 1 1 2 4 4 1 5 4 1 7
(b)(a)
Initial Population
(c)
SelectionFitness Function
(d)
Crossover
(e)
Mutation
Figure 1 – Genetic Algorithm. Initial population (a) is assessed and ranked (b), selecting
couples for reproduction (c). The generated descendents (d) may have their genes affected
by mutation (e).
Source: Russell and Norvig (2003)
In a good GA implementation it is said that the population must “converge”, or
successively evolve and become more homogeneous, while the evaluation of the best
individual converges to the global optimum. However, given the characteristics of the method,
it is not sure that a global optimum will be found. Yet, “acceptably good” optima can be
usually found in acceptable time (Beasley, Bull, Martin 1993).
1 Using Bovespa’s IBrX-100 index as benchmark.
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4. Experiment Description
Non financial or insurance firms listed at Bovespa between 1997 and 2008 were selected.
Data was extracted from Economatica database and refer to the period from 1997 to 2006
(financial reports) and from 1997 to 2008 (1 and 2 years market adjusted returns). For each
firm-year, 1 and 2 years buy-and-hold market adjusted returns are calculated using the first
price information available in the 100 days following May 1st. Bovespa’s index IBrX-100 was
used as benchmark to market-adjust the returns.
In Brazil, both common and preferred shares are considered as equity and in many cases
there is even more than one type of preferred shares. The most liquid2 shares for each firm-year
were selected, excluding firm-year missing data to calculate book-to-market indexes, indicators
or returns.
Then, the HBM portfolio for each year was composed by the firms in the top quintile of
BM, resulting 370 observations. The cut-off BM ratios are presented in Table 1 and the
descriptive statistics in Table 2. Finally, the 1% higher and lower firm-year returns (3 for 1-
year return and 3 for 2-years return) were excluded, resulting 367 firm-year observations.
Table 1 – Cut-off BM ratios
One can notice in Table 1 the reduction of the BM ratio since 2003 caused by the market
value growth of firms listed on Bovespa and, possibly, indicating the formation of a bubble that
ended up bursting at the end of 2008.
2 Liquidity is measured by the formula )/()(100 VvNnPpLa ⋅⋅⋅⋅⋅= , where p is the number of days in
which the share was traded at least once in the chosen period, P is the number of days in the chosen period, n is the number of times the share was traded in the chosen period, N is the total number of trades
with all shares in the chosen period, v is the share’s trade volume (in cash terms) in the chosen period and
V is the total volume traded of all shares in the chosen period.
Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
BM 3.68 4.94 2.91 2.95 2.91 2.98 2.13 1.92 1.47 1.06
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Table 2 – Descriptive Statistics
Descriptive Statistics of HBM firms’ financial indicators (Firm-year observations from 1997 to 2006)
Mean Standard
Deviation Min Q1 Median Q3 Max n
BM 5.4763 4.9631 1.0581 2.9939 4.2462 6.5059 61.0257 370
Mkt Cap
(R$ thousand) 622,401 3,092,327 510 10,685 31,138 112,142 33,247,392 370
Assets
(R$ thousand) 3,769,002 16,383,111 19,717 117,280 332,411 1,057,393 121,891,641 370
Share Liquidity 0.0979 0.4271 0.0000 0.0000 0.0004 0.0059 4.0458 370
ROA -0.0076 0.0820 -0.4477 -0.0345 0.0040 0.0240 0.5284 370
CF -0.0018 0.0807 -0.9132 -0.0088 0.0003 0.0144 0.3267 370
∆ROA -0.0027 0.1075 -0.6643 -0.0306 -0.0031 0.0270 0.8952 370
Accrual -0.0199 0.1069 -0.4489 -0.0657 -0.0269 0.0154 0.7450 370
∆Liquid -0.1771 2.8207 -47.3857 -0.2087 -0.0239 0.1970 7.9159 370
∆Lever -0.0035 0.0905 -0.4658 -0.0270 0.0000 0.0322 0.4371 370
∆Turn 0.0038 0.2053 -0.8631 -0.0592 0.0035 0.0777 1.3805 370
∆Margin 0.0067 0.1442 -1.0611 -0.0346 0.0000 0.0427 1.5088 370
BM – book-to-market ratio, or end-of-the-year equity divided by end-of-the-year Mkt. Cap. Mkt. Cap.(R$ thousand) - share price at the end of the year multiplied by the number of outstanding shares. Assets (R$ thousand) – firm’s total assets at the end of the year. Share Liquidity – index representing the liquidity of shares traded at Bovespa. The higher the value, the more liquid
the share is. Defined as: )/()(100 VvNnPpLa ⋅⋅⋅⋅⋅= , where p is the number of days in which the share was
traded at least once in the chosen period, P is the number of days in the chosen period, n is the number of times the share was traded in the chosen period, N is the total number of trades with all shares in the chosen period, v is the share’s trade volume (in cash terms) in the chosen period and V is the total volume traded of all shares in the chosen period. ROA – return on assets, or net profit divided by the firm’s beginning-of-the-year total assets.. FCF – free cash flow, defined as the variation of cash and equivalent divided by firm’s beginning-of-the-year total assets.
∆ROA – variation of the return on assets, or current firm-year ROA less previous firm-year ROA. Accrual – variations of current assets (except cash and equivalent) less the variations of current liabilities (except short-term debt) less depreciation in the period. This value is scaled by firm’s beginning-of-the-year total assets (this calculation was applied because Brazilian accounting standards did not require cash flow statements until 2008). ∆Liquid – variation of firm’s current ratio in relation to previous year. The current ratio is calculated dividing firm’s current assets by firm’s current liabilities in the end of the year. ∆Lever – leverage variation in relation to previous year. Leverage is calculated as the total debt divided by firm’s asset in the beginning of the year. ∆Turn – variation of assets turnover. Assets turnover is calculated as the firm’s net revenue divided by total assets in the begining of the year. ∆Margin – variation of firm’s current gross margin scaled by beginning-of-the-year assets. Gross margin is calculated dividing firm’s gross profit by sales.
For the sake of simplification the original method was modified: the indicator EQ_OFFER
was excluded from the model since, in the analyzed period, very few firms listed at Bovespa
raised capital issuing shares. Rather, companies financed themselves mostly by means of debt,
following a more common way to raise funds in the Brazilian market. Besides, Galdi (2008)
9
shows that this indicator shows a significantly smaller correlation to returns than the other
indicators.
Table 3 shows the returns of the strategy based on BrF_SCORE for the set of firm-year
observations considered. One can observe that the returns are lower, for instance, than those
obtained by Lopes and Galdi (2007): 1-year (2-years) accumulated return of 12.9% (23.9%)
above all HBM firms, against 20.9% (77,7%) obtained by the quoted research. Besides, one can
also notice that the difference between high-score firms’ returns and the average return is not,
contrary to the observed by Galdi (2008), statistically significant. This difference may be due to
the time frame difference of the two samples (our sample contemplates also 2005 and 2006
financial reports) or due to the way the returns were calculated (tolerance to find the first
quotation after May 1st). Nevertheless, this does not invalidate our results, for its objective is to
check whether the optimization of weights yields returns higher than those obtained with
uniform weights (BrF_SCORE). As mentioned above, the effectiveness of BrF_SCORE was
demonstrated by previous research (Piotroski, 2000 and Lopes and Galdi, 2007).
In this experiment an individual is composed by eight genes, each of them being the weight
for one of the indicators. The individual is assessed by the fitness function, defined as the
yearly average adjusted return between 1997 and 2004. In this way, the individuals whose
genes (or weights) lead to a better assessment (higher return) will have higher chances to
reproduce, spreading its genes and generating better adapted descendents, able to select shares
that will produce higher returns.
It was set an initial population of 100 individuals that reproduce up to 1000 generations.
The algorithm is also interrupted if no new individual with a better fitness result arises in 500
generations. The initial population is randomly defined, with its genes ranging from +0.5 to -
0.5, and then evolutes according to the reproduction and mutation mechanisms. No restrictions
are applied to the range of values a gene can assume (i.e. negative values are allowed).
Different experiments were carried out for 1-year and 2-years adjusted returns.
10
A new score (O_BrF_SCORE) was created to combine the weights into the strategy:
∑=
i
ii FSCOREBrFO λ__
The strategy based on BrF_SCORE assigns to each firm-year a score that ranges from 0 to
9 and selects those with high score (7 to 9) to form the portfolio. However, the values
O_BrF_SCORE can assume do not have a fixed range, once the weights may assume any value
during the optimization process. Therefore, “high score” is defined as the higher third of
O_BrF_SCORE for a given set of weights (or a given individual). High score firm-year
observations are then selected to compose the portfolio of that year. It was arbitrated that at
least five companies would compose the portfolio. If less then five companies achieve a high
score in a given year, the subsequent companies in the O_BrF_SCORE ranking would
complete the portfolio.
Despite the highest adjusted returns (1% of HBM firm-year observations) were excluded
from the sample, there were still observations whose adjusted return was still much higher than
the average. This represents a robustness problem to the optimization algorithm, once it tends
to “choose” weights so that these companies remain in the portfolio, even if these weights end
up picking also low-return firms. This situation was by-passed imposing a limit to the 1 and 2-
years adjusted returns of the 2% highest-return firm-year observations (n=6), being this limit
equal to the sixth highest adjusted return (for 1 and 2 years). It is important to mention that this
limitation was imposed only to the set of data used for weight optimization, while the final
result obtained with the optimized weights was calculated using the original adjusted returns.
The mutation mechanism, described in the previous section, exists to help the algorithm
escape from a local optimum, but it does not ensure finding a global optimum. Thus, in the
attempt to increase the chances to find a better result, the optimization process was repeated 20
times for each experiment and then, among these 20 set of weights, the best one was selected.
At last, the weights were normalized (i.e. scaled by the highest weight in modulus) to ease
the comparison between different sets of weights.
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Table 3 – Returns of the strategy based on BrF_SCORE
This table presents in panels A and B, respectively, the 1 and 2-years buy-and-hold returns based on the financial signals extracted from the financial statements of HBM firms. Low-score firms are those with BrF_SCORE from 0 to 2, while high-score firms are those ranging from 6 to 8.
Panel A – 1-year market adjusted return (firm-year observations from 1997 to 2006)
Mean Percentile
10%
Percentile
25% Median
Percentile
75%
Percentile
90% n
All firms 0.2350 -0.4728 -0.2951 0.0309 0.4922 1.1875 367
BrF
_S
CO
RE
0 -0.2864 - -0.7568 -0.2855 0.1822 - 4
1 -0.0180 -0.5038 -0.3618 -0.2888 0.2577 0,7810 20
2 0.0209 -0.5491 -0.3750 -0.2294 0.3758 0,7082 41
3 0.3727 -0.3675 -0.1948 0.0938 0.6272 1,2884 57
4 0.0966 -0.5385 -0.2820 -0.0153 0.4065 0,7158 84
5 0.3494 -0.4121 -0.2277 0.1392 0.7694 1,5427 70
6 0.3562 -0.4728 -0.1899 0.1689 0.5417 1,2170 57
7 0.3689 -0.4777 -0.3142 0.0148 0.4218 1,6049 28
8 0.4072 - -0.4475 0.0729 1.3572 - 6
Low Score (0-2) -0.0100 -0.5491 -0.3750 -0.2520 0.3525 0,7162 65
High Score (6-8) 0.3635 -0.4728 -0.2654 0.1281 0.5385 1,3572 91
High – Low 0.3734 0.0763 0.1096 0.3801 0.1861 0.6410
estat-t 3.0624
p-Value 0.0013
High – All 0.1285 0.0000 0.0297 0.0972 0.0463 0.1697
estat-t 1.1714
p-Value 0.1219
Panel B – 2-years market adjusted return (firm-year observations from 1997 to 2006)
Mean Percentile
10%
Percentile
25% Median
Percentile
75%
Percentile
90% n
All firms 0.4380 -0.5739 -0.3664 0.0507 0.9607 2.1624 367
BrF
_S
CO
RE
0 -0.5746 - -0.9139 -0.5457 -0.2932 - 4
1 0.2348 -0.7901 -0.6099 -0.2118 0.8378 2,4004 20
2 0.0986 -0.7132 -0.5164 -0.0926 0.3083 1,4264 41
3 0.6670 -0.5487 -0.3363 0.2763 1.2733 2,4793 57
4 0.1923 -0.6042 -0.4672 -0.1036 0.4526 1,4113 84
5 0.5521 -0.5800 -0.2269 0.1552 1.2250 2,0800 71
6 0.6114 -0.5179 -0.2819 0.3672 1.0930 2,2326 56
7 0.7230 -0.5058 -0.2876 0.1138 1.0043 3,5245 28
8 1.0730 - -0.2151 1.0336 2.1025 - 6
Low Score (0-2) 0.0991 -0.7521 -0.5365 -0.1765 0.3585 1,4667 65
High Score (6-8) 0.6769 -0.4057 -0.2523 0.3329 1.0930 2,4974 90
High – Low 0.5778 0.3464 0.2841 0.5094 0.7345
estat-t 3.1804
p-Value 0.0009
High – All 0.2389 0.1683 0.1140 0.2822 0.1323
estat-t 1.5886
p-Value 0.0574
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5. Results
Figure 2 and Figure 3 show the results of the optimization experiments for 1 and 2-years
periods, comparing them with the original strategy of uniform weights. The results are
significantly higher (α=5%) than the original strategy both for 1- and 2-years-ahead returns.
Two points call the attention already at first glance: the difference between weights for 1
and 2-years holding period and the presence of negative weights.
F_ROA F_CF F_∆ROA F_ACCRUAL F_∆LIQUID F_∆LEVER F_∆MARGIN F_∆TURN
Uniform Weights 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Optimized Weights - 1 year -0.03 1.00 -0.70 -0.60 -0.18 0.99 0.27 0.62
Optimized Weights - 2 years -0.53 0.91 0.40 -1.00 0.79 0.38 0.22 0.82
-1.00
-0.50
0.00
0.50
1.00
Uniform Weights Optimized Weights - 1 year Optimized Weights - 2 years
Figure 2 – Weights of Indicators
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1 year 2 years
Uniform Weights 0.3635 0.6769
Optimized Weights 0.7614 1.1215
p-Value 0.0183 0.0351
Uniform Weights
Uniform Weights
Optimized Weights
Optimized Weights
0.0000
0.4000
0.8000
1.2000
Figure 3 – Average Adjusted Returns of 1 and 2-years buy-and-hold strategy (1997 to
2006)
From the first observation one can notice that companies that have the best 1-year
performance will not necessarily be among the top performers in the 2-year period (otherwise
weights would be similar). Moreover, it shows that these firms’ characteristics are different.
The existence of negative weights is even more interesting given that, by definition, all
indicators should point to “good” conditions. Nevertheless, analyzing the weights jointly, not
individually, may shed light to some hypothesis, argued below.
Among the optimized weights for 1-year return the two most important are those related to
free cash flow and leverage reduction. Together they could indicate that the firm used cash
generated by operations to reduce leverage. Asset turnover and margin increase also had
positive weight, but lower in modulus. ROA’s weight was inexpressive, while ∆ROA’s weight
indicate firms that reduced their return on assets. One hypothesis for this apparently
contradictory result would be the fact that the portfolio is built in May, some time after the
disclosure of companies results and possibly providing enough time for the market’s negative
reaction (maybe excessively), creating opportunities for superior results. These hypothesis is
14
coherent with the evidences of conservatism found in the North-American (Basu 1997) and
Brazilian (Costa, Lopes and Costa 2006; Almeida, Scalzer and Costa 2008) markets.
The reduction of liquidity (negative F_∆LIQUID), despite being the second least important
indicator, may indicate that a part of the noncurrent liabilities could have turned into current
liabilities and be, together with a negative ∆ROA, one of the reasons for the negative reaction
of the market. F_ACCRUAL’s weight was not coherent with those from F_ROA and F_CF:
with a negative (or close to zero) profit and a positive cash flow, a negative accrual was
expected (remember that F_ACCRUAL = 1 if ACCRUAL < 0, i.e. a negative weight tends to
select positive accruals). However, observing the way the accruals were calculated may lead to
other hypotheses:
Accruals = (∆CurrAssets – ∆Cash&Eq) – (∆CurrentLiab– ∆STDebt) – Depreciation
If the firm negotiates with its suppliers the extension of liabilities’ payment term, these
liabilities could be transferred to the non-current liabilities account. Alternatively, the
shareholders may decide to invest more money in the company and this money is used to pay
claimants other than debtholders. These situations would have a positive impact on the accrual
calculated as above and overestimate it, but would not affect the real accrual. It is possible that
this kind of situation happens to financially distressed firms. As a matter of fact, a closer look
at firms with negative ROA, positive CF and positive ACCRUAL (unreported) revealed these
situations. As a summary, the indicators seem to sketch firms that were about to go bankrupt
but didn’t. Maybe because of that these firms have a high 1-year return, as the market corrects
its too pessimistic expectations, but are not among those with the highest 2-year return, as in a
longer term their performances still don’t look so bright.
In the set of weights for 2-year returns F_ROA is negative and F_∆ROA is positive,
meaning companies that were not profitable, but that improved their performance. Not being
profitable may have contributed for the firm to be a HBM one, while the improvement of ROA
might indicate the beginning of operational performance improvement leading to higher future
returns. The hypothesis of performance improvement is also reflected on the positive (and
15
relevant) weights of cash generation, asset turnover and liquidity increase, indicating that the
company is somehow becoming more prepared for the operations in the long term. Leverage
reduction and margin increase are also aimed, but less important. F_ACCRUAL’s negative
weight could be interpreted in the same way as for 1-year-return weights, specially the
hypothesis of shareholders’ investment to liquidate liabilities other than debt (coherent with
liquidity improvement). Differently from the 1-year-return weights, these apparently seek
companies that have been improving operational results and with growth perspectives.
Obviously, the above mentioned hypotheses are merely speculative and require further
investigation.
Table 4 presents the distribution of returns by O_Br_SCORE ranges. Panel A shows that
firms with high score obtained 1-year-adjusted return 49 p.p. higher than those with low score
and 53 p.p. higher than all HBM firms from 1997 to 2006. The results are statistically
significant at 1%. Similarly, panel B shows companies with high score obtaining 2-years-
adjusted returns 89 p.p. above those with low score and 68 p.p. higher than all HBM firms in
the same period. Also in this case the results are significant at 1%.
16
Table 4 – Return of the strategy using optimized weights
The figures below show the performance of the optimized weights year by year comparing
them with the uniform weights. It can be observed that the optimized weights yield higher
Panels A and B present the 1 and 2-years buy-and-hold returns yielded by the weights optimized using Genetic Algorithms applied to financial data from 1997 to 2006. For 1-year (2-years) weights, firms ranked as high score obtained O_BrF_SCORE from 1.42 to 2.88 (from 1.84 to 3.52), while firms ranked as low score obtained O_BrF_SCORE from -1.51 to -0.05 (from -1.53 to 0.15).
Panel A – 1-year market adjusted return (firm-year observations from 1997 to 2006)
Mean Percentile
10%
Percentile
25% Median
Percentile
75%
Percentile
90% n
All firms 0.2350 -0.4728 -0.2951 0.0309 0.4922 1.1875 367
O_B
rF_S
CO
RE
-1.51 to -0.78 0.4594 -0.5491 -0.1932 -0.0251 0.2499 3.5690 9
-0.78 to -0.05 0.2409 -0.4019 -0.3082 0.0671 0.4471 1.3551 54
-0.05 to 0.69 0.0247 -0.5385 -0.3441 -0.1345 0.2837 0.7162 142
0.69 to 1.42 0.2344 -0.4475 -0.2655 0.1038 0.4917 0.9888 112
1.42 to 2.15 0.8531 -0.2654 -0.0692 0.4790 1.5092 2.3862 43
2.15 to 2.88 0.3792 -0.7477 -0.0705 0.4752 1.1967 1.2222 7
Low Score 0.2721 -0.4019 -0.3082 0.0628 0.4471 1.5095 63
High Score 0.7614 -0.2699 -0.0705 0.4764 1.2989 2.0133 50
High-Low 0.4893 0.1320 0.2378 0.4136 0.8518 0.5039
estat-t 2.5689
p-Value 0.0060
High-All 0.5264 0.2028 0.2247 0.4455 0.8066 0.8258
estat-t 3.1319
p-Value 0.0014
Panel B – 2-year market adjusted return (firm-year observations from 1997 to 2006)
Mean Percentile
10%
Percentile
25% Median
Percentile
75%
Percentile
90% n
All firms 0.4380 -0.5739 -0.3664 0.0507 0.9607 2.1624 367
O_
BrF
_S
CO
RE
-1.53 to -0.69 0.2586 -0.6880 -0.5293 -0.1765 0.9670 1.2588 27
-0.69 to 0.15 0.2169 -0.5979 -0.4679 -0.0704 0.5325 1.6498 79
0.15 to 1.00 0.3688 -0.5499 -0.3675 0.0474 0.7619 1.7360 108
1.00 to 1.84 0.3796 -0.5487 -0.3395 0.1375 0.7424 1.5487 103
1.84 to 2.68 1.2038 -0.3320 -0.0485 0.6591 2.1025 4.0301 37
2.68 to 3.52 1.0110 -0.3432 0.2037 1.2968 1.8718 2.1624 13
Low Score 0.2275 -0.6838 -0.4696 -0.0774 0.6695 1.5867 106
High Score 1.1215 -0.3432 -0.2003 0.7546 2.0800 2.6274 50
High-Low 0.8940 0.3406 0.2693 0.8320 1.4105 1.0407
estat-t 3.8414
p-Value 0.0001
High-All 0.6836 0.2308 0.1660 0.7039 1.1193 0.4650
estat-t 3.1371
p-Value 0.0014
17
returns in all 10 periods (1-year returns) and in 9 out of 10 periods (2-years returns). Such a
result was already expected, since all periods were used in the optimization process. The
robustness of the weights (i.e. its performance in periods not used in the optimization process)
were not tested and could be a matter for further studies.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Uniform Weights Optimized Weights
Figure 4 – Yearly returns (1-year buy-and-hold)
0
0.5
1
1.5
2
2.5
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Uniform Weights Optimized Weights
Figure 5 – Yearly returns (2-years buy-and-hold)
As mentioned above, the optimization process was repeated 20 times for each experiment
and only the best set of weights was explored in this paper. Hence there are other sets of
18
weights that, even not yielding returns as high as those here presented, also lead to much higher
returns than those with uniform weights. These other sets of weights also reveal different
profiles of firms that achieved superior returns. A deeper analysis of them could be the subject
of further studies, as well as the variation of the relative importance of the weights indicating a
possible change in market’s assessment criteria.
6. Conclusion
This paper tries to identify which financial indicators are more important when identifying
firms whose shares would have future returns higher than the market average and speculates
about the relation of these indicators. It is based on a strategy developed by Piotroski (2000)
and adapted to the Brazilian market by Lopes and Galdi (2007) and Galdi (2008), which
observes 9 financial indicators and selects firms with more “positive” signals. The empirical
approach here presented associates weights to these indicators and, by means the computational
technique Genetic Algorithms, optimizes the selection of firms (and the return of the portfolio)
by choosing these weights.
The results showed that the obtained weights yield an increase of the adjusted return from
36% to 76% (1-year buy-and-hold strategy) and from 68% to 112% (2-years buy-and-hold
strategy) when compared to uniform weights, being both results significant at 5%, but not at
1%. More than that, it shows significant differences in the importance of the financial
indicators and reveals that the relation among them is not trivial. It also shows that companies
with the best return in 1-year period are not the same as those with the best return in 2 years,
since different sets of weights were found when optimizing the portfolio for 1 and 2-years
returns.
Given the nature of the employed method it is possible that the weights found yield
significantly higher returns only for the period used in the optimization. In this sense, further
research could test the robustness of the weights in subsequent periods, not used in the
optimization process. Another alternative for further studies would be the testing an investment
19
strategy combining more than one set of weights (result of other optimization processes), so it
would be possible to increase the number of shares and allow the formation of higher volume
portfolios, given the reduced liquidity of many HBM firms.
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