Fundação Getúlio Vargas
Escola De Pós-Graduação Em Economia
Marcelo Paranaguá de Vasconcelos Teixeira
VALUE AND MOMENTUM STRATEGIES
IN THE BRAZILIAN STOCK MARKET:
THE 2008 FINANCIAL CRISIS AND ITS
AFTERMATH
Rio de Janeiro
2011
Marcelo Paranaguá de Vasconcelos Teixeira
VALUE AND MOMENTUM STRATEGIES
IN THE BRAZILIAN STOCK MARKET:
THE 2008 FINANCIAL CRISIS AND ITS
AFTERMATH
Dissertação submetida à Escola de PósGraduação em Economia da Fundação
Getulio Vargas como requisito parcial para
obtenção do grau de mestre em economia.
Área de Concentração: Finanças
Orientador: Marco Antônio Cesar Bonomo
Rio de Janeiro
2011
Ficha catalográfica elaborada pela Biblioteca Mario Henrique Simonsen/FGV.
Teixeira, Marcelo Paranaguá de Vasconcelos
Value and momentum strategies in the Brazilian stock market : the
2008 financial crisis and its aftermath / Marcelo Paranaguá de
Vasconcelos Teixeira. – 2011.
ix, 41 f.
Dissertação (mestrado) - Fundação Getulio Vargas, Escola de PósGraduação em Economia.
Orientador: Marco Antônio Cesar Bonomo.
Inclui bibliografia.
1. Bolsa de valores. 2. Investimentos. 3. Ações (Finanças). 4. Crise
financeira global, 2008-2009. I. Bonomo, Marco Antônio Cesar. II.
Fundação Getulio Vargas. Escola de Pós-Graduação em Economia. III.
Título.
CDD – 332.6322
Marcelo Paranaguá de Vasconcelos Teixeira
VALUE AND MOMENTUM STRATEGIES
IN THE BRAZILIAN STOCK MARKET:
THE 2008 FINANCIAL CRISIS AND ITS
AFTERMATH
Dissertação submetida à Escola de Pós-Graduação em Economia
da Fundação Getulio Vargas como requisito parcial para obtenção
do grau de mestre em economia. Área de Concentração: Finanças
E aprovado em 01/07/2011 pela banca examinadora.
Marco Antônio Cesar Bonomo
EPGE/FGV
Axel André Simonsen
EPGE/FGV
Marcelo de Sales Pessoa
IPEA
Rio de Janeiro
2011
RESUMO
Esta dissertação analisa o desempenho de três estratégias de investimento em
carteiras de custo zero (“value”, “momentum” e uma combinação 50/50 delas,
que é chamada de “combo”) no mercado de ações brasileiro durante a última
década. Os resultados são comparados aos encontrados por Asness, Moskowitz e
Pedersen (2009) para quatro mercados: EUA, Reino Unido, Europa Continental, e
Japão. Uma análise específica é feita em torno da crise financeira de 2008,
comparando os resultados pré- e pós-crise. O índice de Sharpe é usado para
ajustar os desempenhos por seus riscos, e para classificar as estratégias para
diferentes horizontes de investimento. Os resultados mostram um ótimo
desempenho da estratégia “combo” nos últimos três anos, período que inclui a
crise de 2008, mas considerando todo o período analisado a estratégia “value”
obteve o melhor desempenho. Esse resultado difere dos resultados encontrados
para os quatro mercados de referência, onde a estratégia combo tem o melhor
desempenho. A análise do horizonte de investimento mostra que a escolha do
investidor pode mudar com diferentes horizontes.
Palavras-chave: Estratégias “value” e “momentum”, crise financeira, índice de
Sharpe, horizonte de investimento.
ABSTRACT
This dissertation analyzes the performance of three zero-cost portfolio strategies
(value, momentum and a 50/50 combination of those, which is called combo) in
the Brazilian stock market during the last decade. The results are compared to
the ones found by Asness, Moskowitz and Pedersen (2009) for four markets: US,
UK, continental Europe, and Japan. A specific analysis is made around the 2008
financial crisis, comparing the pre- and post-crisis results. The Sharpe ratio is
used to adjust the performances by their risks, and to rank the strategies for
different investment horizons. The results show that the combo performed very
well on the last three years, period that includes the 2008 crisis, but considering
the entire period the value strategy had the best performance. This result is
different from the results found for the four benchmark markets, where the
combo strategy has the best performance. The investment horizon analysis
shows that the investor’s choice may change with different horizons.
Keywords: Value and momentum strategies, financial crisis, Sharpe ratio,
investment horizon.
CONTENTS
1
INTRODUCTION……………………………………………………………………………………
2
LITERATURY REVIEW…………………………………………………………………………….
2.1 The Value Strategy……………………………………………………………………………….
2.2 The Momentum Strategy……………………………………………………………………..
2.3 The Value and Momentum Combination Strategy (Combo Strategy)..
3
METHODOLOGY……………………………………………………………………………………
3.1 Data……………………………………………………………………………………………………..
3.2 Portfolio Construction………………………………………………………………………….
3.3 Adjusting the performances for the risk………………………………………………
3.4 Correlation…………………………………………………………………………………………..
4
RESULTS……………………………………………………………………………………………….
4.1 Performance………………………………………………………………………………………..
4.2 Risk-adjusted Performance…………………………………………………………………..
4.3 Correlations…………………………………………………………………………………………
4.3.1 Ibovespa………………………………………………………………………………………………
4.3.2 Stocks Correlation………………………………………………………………………………..
4.3.3 Foreign Capital Flow…………………………………………………………………………….
5
CONCLUSIONS………………………………………………………………………………………
REFERENCES………………………………………………………………………………………………….
APPENDIX……………………………………………………………………………………………………..
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35
37
7
1. INTRODUCTION
The traditional finance paradigm tries to understand financial markets through
models in which agents are rational, i.e., they process new information correctly
(updating their beliefs accordingly to the Bayes’ law), and given their beliefs, they
make optimal choices, maximizing their utility. Although this traditional framework is
very attractive, their predictions usually are not confirmed in data, and it has faced
some difficulties explaining some stock markets facts, as well as some individual
trading behaviors observed in the real world.
The field of behavioral finance comes as a new approach for financial markets,
arguing that some phenomenon can be better explained if the agents are not
considered fully rational. The literature of the area shows that a lot of aspects of the
investors’ actions that seem to point to rationality deviations can be observed through
empirical evidence.
One of the observed actions is the insufficient diversification. There is strong
evidence that the investors diversify their portfolios much less than some traditional
financial models would recommend when choosing a portfolio, and when they
diversify, most of them do it in a very naive way, as shown by Benartzi and Thaler
(2001).
Another common characteristic of investors’ behavior is the excessive trading,
as observed by Barber and Odean (2000). Rational models generally expect few
transactions to happen, because in a world where rationality is common knowledge,
an agent would be reluctant to buy if another one would be willing to sell. A
transaction would not be justified by new information or by asymmetric information,
but only if an agent had some external shock in its wealth. However, with a sample
from 1991 to 1996 from a large broker, taking in consideration the transaction costs,
the authors found that the average return of the investors was much lower than the
returns of the standard benchmarks, due to the high number of transactions in the
period.
8
Other aspects of the behavior of the investors are connected to the buying and
selling decisions. Shefrin and Statman (1985) observe that the agents avoid selling
stocks when they worth less than the value for which they were bought, calling it
“disposition effect”, and Odean (1998) observes that the agents are more willing to sell
a stock when its price is higher than the price they paid for it.
Regarding the buying decision, Odean (1999) noticed that the agents’
preferences are split between stocks with recent gains and stocks with recent losses,
but in both cases they prefer the extreme cases. This phenomenon may be explained
by an “attention effect”, because some agents may just not pay attention to certain
stocks until they have some kind of abnormal behavior, such as great gains or losses.
Barberis and Thaler (2003) argue that the reason for these rationality
deviations is that the agents generally base their decisions on a limited number of
heuristic principles, which simplify complex tasks of probability evaluation and price
prediction, and can lead to systematic ad serious mistakes.
De Bondt and Thaler (1985) also found evidence of irrational behavior by
investors, this time related to “overreaction” to recent news, which would lead to
abnormally high returns on the short-run, followed by a reversal effect on the longrun.
These irrational behavior from the non-rational agents, who are called “noise
traders”, lead to mispricing on the markets, and the traditional finance theory argues
that the rational agents should recognize the opportunities of arbitrage, correcting the
mispricing and excluding the noise traders from the market. However, there is a lot of
empirical evidence of persisting mispricing, due to arbitrage limits, mostly connected
to the short-term investment horizon of the agents, as argued by Shleifer (2000).
So, the existence of irrational behavior created space to a new research area, in
which the authors try to predict the return of the stocks based on past information,
relying on the known behavioral pattern of the agents to construct the strategies.
With this in mind, in this work we analyze the performance of value and
momentum strategies, as well as a combination of both strategies, on the Brazilian
9
stock market, examining their behavior during the last decade (from 2001 to 2010) in
order to rank the strategies. A special attention is given to the 2008 crisis.
Following the methodology of Asness, Moskowitz and Pedersen (2009), we
construct the value, momentum, and combo zero-cost portfolios, compute their
returns, and analyze the results for the entire period, as well as for the pre- and postcrisis periods. We adjust the performances of the strategies by their risks through the
Sharpe ratio, and analyze the results over different choices of investment horizon.
Finally, for further analysis, we compute the correlation between the performances of
the strategies and some financial variables.
The results show during the 2008 crisis/recovery the combo strategy had the
best performance, but considering the entire period the value strategy performed
better than the combo, even after adjusting by the risk. Besides, investment horizon
analysis shows that the strategies’ ranking may change with different horizon choices.
On the next section we present a literature review; on the third section we
present the used methodology; on the fourth section we analyze the performance of
the strategies; and on the fifth section we present the conclusions of the work.
10
2. LITERATURE REVIEW
2.1. The Value Strategy
The “value” strategy is based on idea that the existent mispricing on the market
will be corrected. It consists on, based on some value signal, buying stocks with a
“good” signal and selling stocks with a “bad” signal. An example of a value signal is the
book-to-market (BM) ratio, which is in fact one of the most used value signals. The
idea is that if a price is below its fundamental level, it should increase, and similarly, if
a price is above its fundamental level, it should decrease.
Fama and French (1992), studying the US stock market, found that the
portfolios composed of stocks with high BM had higher average monthly return then
the portfolios composed by stocks with low BM, and that this abnormal return wasn’t
justified by a higher risk.
Lakonishok, Shleifer and Vishny (1994) also found that stocks with high BM
continuously present higher returns in comparison with stocks with low BM, and the
risk could not justify the difference of returns. They found yet that these results were
valid for both “bear” and “bull” market periods.
Later, in a more comprehensive work, Fama and French (1998) found
effectiveness of the value strategies for several countries, including Brazil.
Analyzing the Brazilian case, Braga and Leal (2000) found that portfolios of
stocks with high BM had much better performances than portfolios of stocks with low
BM, even after adjusting the performances by the portfolios’ risk.
On another work, Lacerda (2007) analyzed the performance of the value
strategy on the Brazilian stock market from 1987 to 2006. He found that the strategy
presented abnormal returns on all analyzed periods, and once more the excessive
returns could not be justified by a higher risk.
11
2.2. The Momentum Strategy
The “momentum” effect is the relation between an asset’s return and its recent
performance history. The momentum strategy consists on buying stocks with high
momentum (that is, high past returns) and selling stocks with low momentum,
believing on the continuity of the trend.
Jegadeesh and Titman (1993) found evidence on momentum effectiveness on
the US market, for several formation periods as well as several portfolio maintenance
periods. They also found that the momentum return wasn’t justified by a higher risk.
Chopra, Lakonishok and Ritter (1992) also found a short-run momentum trend for the
US market.
For the Brazilian market, Lemos and Costa Jr. (1997) found reversal effect
instead of a momentum effect, where the stocks with low momentum had better
performance than the stocks with high momentum.
Bonomo and Dall’Agnol (2003), following the methodology of Chopra,
Lakonishok and Ritter (1992), also found a reversal trend in the Brazilian stock market
instead of a momentum one.
2.3. The Value and Momentum Combination Strategy (Combo Strategy)
The “combo” strategy consists on a 50/50 combination of the value and
momentum strategies. Asness, Moskowitz and Pedersen (2009) argue that studying
the interaction between value and momentum is more powerful than examining each
one in isolation.
The explanation for this result is that the negative correlation between value
and momentum strategies makes the volatility of the combo strategy smaller than the
volatilities of the value and momentum strategies. Adding to that their high expected
returns, it makes a simple equal-weighted combination of the two a powerful strategy
12
that produces a significantly higher Sharpe ratio than the ones of the individual
strategies.
They show that the combo strategy has a higher Sharpe ratio than both
individual strategies for four analyzed markets: United States, United Kingdom,
Continental Europe and Japan.
13
3. METHODOLOGY
3.1. Data
The stock sample used to compute the performance of value and momentum
strategies consists of 1140 stocks negotiated at Bovespa, from July of 2000 through
December of 20101. From the “Economatica” system, we collected the stocks’ daily
closure prices, book-to-market information2, and quarterly average traded volume.
The database was divided in time in 20 one-year-window subsamples
(overlapping every six months), so that in the middle point of each subsample it would
be possible to analyze 6-month past information to create the value and momentum
portfolios, and then calculate their returns over the following 6 months. As this is an
ex-post exercise, the idea is that, starting in January of 2001, the investor would have
analyzed available information from the last six months to create the portfolio, and in
July of 2001 he would have “sold” this portfolio, computing its returns, and created a
new one based on the new recent information. He would have repeated the process in
every six months until December of 2010.
Since the signal used in the value strategy (BM) is different from the one used
in the momentum strategy (past returns), specific filters were created for each
approach in order to construct the portfolios: for the value strategy, in each
subsample, the stocks with at least one BM information in the past six months were
kept; for the momentum strategy, in each subsample, the stocks with six months of
past return history were kept.
Besides these individual filters, two other ones were created that were
common to both strategies. First, to avoid abnormalities on the returns, the stocks
with price smaller than R$ 0.1 at some point of a subsample were excluded from it.
Second, to avoid liquidity problems, all stocks with an average traded volume smaller
1
Bonomo and Dall'Agnol (2003) show that the efficiency of the Brazilian stock market seems to have
improved since the Brazilian macroeconomic changes in the 90’s, which may affected the returns of the
these strategies. So, in order to avoid these changes to affect the results, we chose to analyze the
performance of these strategies based only on last decade information, from 2001 to 2010.
2
As a proxy to book-to-market, it was used the P/PVS ratio (price / patrimonial value per stock).
14
than R$ 300,000.00 in the last quarter were excluded from that subsample. After all
the filters, we end up with on average 204 and 216 available stocks to be used in the
value and momentum portfolios, respectively.
3.2. Portfolio Construction
Once the stocks to be used have been selected, we followed the methodology
of Asness, Moskowitz and Pedersen (2009) to construct the value, momentum, and
combo portfolios and compute their returns. Zero-cost portfolios were constructed for
each strategy and each period, simulating an investor that based on the signals would
create a portfolio, keep it for six months3, and then rebuilt the portfolio based on the
new signal information. The idea is to create a unique portfolio’s construction
algorithm, but keeping the portfolio a dynamic characteristic.
It is worth mentioning that the goal here is not to come up with the best
predictors of the returns of the stocks, but to introduce a simple approach that should
give good results and doesn’t demand a constant attention to the portfolio, since the
investor will keep it for six months without making any changes.
For the value strategy, the used signal was the last BM information available for
each stock. We sorted the stocks based on their BM, split them in three groups4 (high,
middle, and low), and constructed zero-cost portfolios that go long stocks with high
BM and short stocks with low BM. This way, we are using on average approximately
136 stocks (2/3 of 204) on the value portfolios.
The stocks
3
are weighted in the value portfolio as follows:
Asness, Moskowitz and Pedersen (2009) used 12-month signal information to construct their
portfolios, and keep them for twelve months, but due to the reduced database we are using (compared
to the databases of other papers in the literature), we chose to make new portfolios in every 6 months,
so that we could have more portfolio return information to analyze.
4
If the number of available stocks is not divisible by three, the middle group will be slightly bigger, so
that the high group will always have the same number of stocks as the low group.
15
where
is the number of stocks composing the portfolio at time
exclusion of the middle group), and
(after the
are the weights, which clearly sum to zero,
representing a zero-cost long-short portfolio. Notice that the weights were chosen
such that the overall portfolio is scaled to R$1 long and R$1 short.
Then, the return of the value portfolio is:
where
is the individual return of stock .
For the momentum strategy, we used as signal the 6-month past cumulative
raw return of the stocks, skipping the most recent month’s return5, which was called
MOM2-6. Then we did the same thing we did for value: sorted the stocks based on
their MOM2-6, divided them in three groups (high, middle, and low), and constructed
zero-cost portfolios that go long stocks with high MOM2-6 and short stocks with low
MOM2-6. So, the momentum portfolios are composed on average by 144 stocks.
The stock weighting methodology of the momentum portfolio is the same used
to the value portfolio, just replacing BM for MOM2-6.
We also consider the return on a 50/50 equal combination of value and
momentum strategies, which will be called “combo strategy”. Then, the return of the
combo is:
3.3. Adjusting the performances by the risks
To correctly compare the strategies’ performances, one needs to adjust them
by their risks. For this, we used the Sharpe Ratio, a standard measure in the literature
that was introduced by Sharpe (1966). It is generally defined as:
5
Skipping the most recent month is standard in the momentum literature, due to a contrarian effect
observed in the returns at the one month level. For further information see Lo and MacKinaly (1990).
16
where
is the return of the risky asset,
is the return of a risk-free asset, and
the volatility of this excess of return, i.e., the standard deviation of
is
.
Sharpe (1994) interprets the SR as an instrument to analyze the risk-adjusted
performance of a zero-investment (or zero-cost) portfolio, in the sense that one would
sell a risk-free asset to buy a risky asset.
In our case, we are already dealing with zero-investment portfolios, selling the
low-signal portfolios to buying the high-signal ones. So, the Sharpe Ratio used here is:
where
is the return of the strategy (value, momentum, or combo), and
volatility of the strategy. Note that
is the
already is, by definition, an excess of return (the
spread between the high-portfolio’s return and the low-portfolio’s return), and
is the
volatility of this excess of return.
No matter which frequency of data is used to compute the SR, it is standard in
the literature to annualize the SR, according to the simple methodology proposed by
Sharpe (1994), and then compare the SR from different portfolios to rank the
strategies. But this practice can lead to errors on the strategies ranking.
Levy (1972) shows that the SR tends to change with different investment
horizons. He also shows that as long as the intended investment horizon is different
from the horizon used to compute the ratio, the Sharpe ratio exhibits systematic
biases and any asset-allocation decisions based on it will be misleading.
Looking at our case, since in these strategies the investors always keep their
portfolios for at least six months6, there is no reason for us to calculate the SR using
daily or monthly data. So, we will only use data horizons equal or multiples of
6
Note that even though an investor changes his portfolio in every six months, according to the
previously presented methodology, his investment horizon can be bigger, because he can keep investing
on the strategy for other semesters.
17
semesters to compute it. Also, in order to check if the SR value changes over different
horizons, we will compute the SR using different horizons, and annualize them to
compare the results.
Following this idea, Lin and Chou (2003) argue that because investors differ in
their risk attitudes and in holding horizons, it is unreasonable to evaluate portfolio
performance based on one single investment horizon. So, as practical implementation
of the SR is reasonable only if the intended investment horizon equals the holding
period of the returns used to compute the ratio, they propose that plotting a graph of
Sharpe ratio against the investment horizon may be more appropriate for investors
with multiyear investment horizons.
Then, to conclude the evaluation of the risk-adjusted performance, after having
computed the SR for several investment horizons (all multiples of one semester), we
will plot a graph of SR against investment horizon, so that an investor could look at it
and rank the strategies according his investment horizon profile.
3.4. Correlations
In order to better understand the performances of the three strategies, we
analyze their relations with some financial variables, trying to obtain more information
about the behavior of the returns of the strategies.
So, after computing the performances of the value, momentum, and combo
strategies, we analyze the correlation between these performances and the three
other variables: (i) the Ibovespa, (ii) the correlation among the available stocks, and (iii)
the foreign net capital flow in the Brazilian stock market.
The Ibovespa series was also collected from the “Economatica” system, from
January of 2001 through December of 2010. It was used the daily quotation of the
index, so that it would be possible to compute de daily returns, and then calculate the
correlation between them and the returns of each one of the strategies presented
above.
18
To measure the correlation among the available stocks (i.e., the stocks that
“survived” the filters) we simply take the mean of the all the correlations between
pairs of stocks. Said in another way, this is the mean of all
elements that
are under (or above) the principal diagonal of the correlation matrix of the
stocks. From now on we use the letter
available
to represent this correlation measure.
For the foreign net capital flows in the Brazilian stock market, we used a daily
series from January of 2006 through December of 2009. The reason for the reduced
period of the database is simply the lack of additional available data, but at least this
window includes both pre- and post-crisis periods. The daily correlation between this
variable and the strategies’ returns over that period was computed.
19
4. RESULTS
Following the methodology illustrated on section 3, the MatLab software was
used to compute the returns of the value, momentum and combo strategies, their riskadjusted performances, the Sharpe ratios and the correlations between the
performance of the portfolios and the variables proposed on section 3.4. The results
are presented and analyzed in this section.
4.1. Performance
On figure 1 we can see the performance of the value, momentum and combo
strategies over the last decade, as well as the performance of the Ibovespa.
Figure 1: Cumulated performance of the portfolios
The cumulated return of the value strategy (541.97%) was much higher than
the return of the momentum strategy (75.38%), and consequently higher than the
combo’s return (308.18%), since it is a combination of those two. It was even much
20
higher than the Ibovespa’s cumulated return (349.30%), which is not a zeroinvestment portfolio7.
The analysis of the performance of the value strategy gets even more
interesting if we look just for the 2008-2010 period, the one of most economic
instability on the decade, comprehending the 2008 crisis and its recovery. On figure 2
it can be seen that during the peak of the crises, when the Ibovespa suffered a huge
devaluation, the value’s cumulated return not only didn’t decreased but even
increased a little bit. And during 2009, when the economy was recovering from the
crisis, the value strategy had a great performance, reaching a cumulated return of
about 80% on the second and third quarters of that year.
Figure 2: 2008-2010 performance
The reasons for this outstanding result can be noticed by analyzing the
separated performances of the value-high and value-low portfolios, which are shown
in figure 3. Studying the behavior of the semiannual performances of these portfolios,
we see that during the second semester of 2008 both portfolios had a great
depreciation, but the intensity was very similar, resulting in a stable performance of
7
One cannot directly compare the return of a zero-investment strategy with the gross return of
Ibovespa, since it is not a zero-cost portfolio. In order to do so, one should compute de difference
between the return of the Ibovespa and the return of a risk-free asset. In the Brazilian literature it is
common to use the CDI (Interbank Deposit Certificate) as a risk-free asset, whose return was 314.70%
on the period. So, the return of that zero-investment strategy would have been only 34.6%.
21
the value strategy, which is spread between those returns. In the following year, the
value-high portfolio had a much higher cumulated return than the low-value portfolio,
resulting on the great increase of the value strategy’s cumulated return, as we saw on
the last figure.
Figure 3: Semiannual performance of the value portfolios
The explanation for this behavior could be explained by the idea behind the
construction of the value portfolio. When one buys stocks with high BM, one expects
that the market value of these stocks will rise, and similarly, when one sell stocks with
low BM, one expects that the prices will be corrected by the market, decreasing. But
the 2008 crisis was characterized by a global loss of confidence on book information,
so the market failed on correcting the stocks mispricing, and both the high and low
portfolios had similar devaluation.
When the confidence crisis was gone, not only the BM information became
relevant again, but the value effect was amplified by the recovery of the economy,
resulting on the great performance of the value-high portfolio, and therefore, of the
value strategy. This value effect amplification could be explained by two factors: first,
the crisis make investors pay more attention to market mispricing, implying more
efficiency on its correction; second, due to the crisis, some prices were way too low
22
compared to the book information available, so that the correction of these mispricing
would imply in return much higher than usual.
Analyzing now the performance of momentum strategy on the same period,
figure 2 shows that it did well during the peak of the crisis (slightly better than the
value strategy indeed), but had a huge crash on the first semester of 2009, when the
economy was recovering from the crisis, and both value strategy and Ibovespa were
doing very well.
On figure 4, analyzing the semiannual performance of its high and low
portfolios, we can see why this happened. During the crisis, similarly to the value case,
both portfolios presented great devaluation, but the momentum-low had an even
worse performance, which resulted in a small increase of the momentum cumulated
return.
Figure 4: Semiannual performance of the momentum portfolios
In the following semester, on the other hand, the momentum-low portfolio had
a huge cumulated return, three times higher than the momentum-high portfolio,
leading to the worst semiannual performance of the momentum strategy on the entire
decade. The reason for this behavior may be at the huge devaluation of stocks on the
previous semester, followed by a reversal effect on the following period, when the
23
economy was recovering from the crisis. The market rapidly corrected the mispricing
on the economy, in a way that the stocks with lowest returns over the past six months
had the highest returns on the first semester of 2009. So, it was the arbitrage of the
market that corrected the mispricing and provoked this reversal effect, making the
momentum strategy to perform so badly.
When we turn our attention to the combo strategy, we can see on figure 2 that
it performed well during the crises, with a good stability, and even better after the
crises, with positive cumulative returns. That is, even though the momentum strategy
had a bad performance, the great performance of the value strategy more than
compensated it, making the combo strategy to perform well.
4.2. Risk-adjusted Performance
If an investor would look only to the past cumulated return of the strategies
when choosing an investment strategy, from figures 2 and 3 we can see that the value
strategy would be the chosen one, since it had the best performance either between
2001 and 2010 or from the 2008 crisis on. Moreover, by construction, the combo
strategy would never have the highest cumulated return, since it is the average of the
other two strategies, so the investor would never choose it.
However, the investor is not interested in the past return, but in the future
return, which is uncertain, and a higher volatility will certainly make it more uncertain.
So, when choosing the best investment strategy, the agent should also analyze the
volatility of the past returns, and that’s when the combo strategy becomes more
attractive.
Figure 5 shows the semiannual returns of the value and momentum strategies,
and we can clearly see that they are negatively correlated8 (-0.23). This negative
correlation is responsible for a smaller volatility of the combo strategy, if compared to
value and momentum strategies, making its portfolio less risky than the other two.
8
The correlation between the daily returns of the value and momentum strategies is also negative and
very similar to that (-0.22).
24
Figure 5: Correlation between value and momentum semiannual returns
This way, since the value strategy has the highest past cumulated returns, and
the combo strategy has the smallest risk, we need to adjust the performance of the
portfolios by their risk to rank the strategies. Asness, Moskowitz and Pedersen (2009)
adjusted the cumulative returns of value, momentum and combo strategies for four
markets (US, UK, continental Europe, and Japan) by their monthly volatility. The results
can be seen in the figures of the appendix.
Following this idea, we did a similar exercise, but instead of using the monthly
volatility, it was used the semiannual volatility to adjust our series of cumulative
return, due to the argumentation presented in section 3.3. The results can be seen in
figure 6.
Comparing the risk-adjusted performance of the portfolios with the nonadjusted performance on figure 2, we can see that the combo strategy has a relatively
better result, but still worse than the value strategy one. This result is different from
the results of Asness, Moskowitz and Pedersen (2009)9, where the combo strategy riskadjusted performance surpasses the performances of both the value and momentum
strategies. One possible reason for this result is that, while on those cases the negative
9
See the graphs on the appendix.
25
correlation between value and momentum is very strong (-0.63, -0.59, -0.50, and -0.52,
respectively), in the Brazilian market it is -0.23. This way, the decrease on the volatility
of the combo strategy on the Brazilian market wouldn’t be as large as it appears to be
on the cases analyzed by those authors, which made this strategy less powerful here.
Figure 6: Performance adjusted by semiannual volatility.
Comparing these four markets with the Brazilian market, it can also be noticed
that the Brazilian market is more similar to the Japanese market than the others, in
which the value strategy has better results than the momentum strategy. Another
similarity is that for some periods the combo is better than the value, and sometimes it
is worse. This can be evidence that the period of analysis can interfere on the ranking
of the strategies, and to explore it in a deeper dimension, we also analyze the
performance of the strategies before and after the crisis, splitting the database in
before and after January 1st, 2008.
Figure 7 shows the performances from January of 2001 to December of 2007,
adjusted by the semiannual volatility of the period. Notice that the pattern of the
performances is very similar to the one we observe for the entire period.
On the other hand, figure 8 shows the performances from January of 2008 to
December of 2010, adjusted by the semiannual volatility of the period. In this case, the
performance of the combo strategy is strictly better than the others.
26
Figure 7: 2001-2007 performance adjusted by semiannual volatility
This difference of results can be explained by the fact that from 2001 to 2007
the correlation between value and momentum is weak and positive (0.07), which takes
off the power of the combo portfolio, while from 2008 to 2010 the correlation
between value and momentum is negative and very strong (-0.74), which reduces the
combo volatility and consequently improves its risk-adjusted performance.
Figure 8: 2008-2010 Performance adjusted by semiannual volatility
27
These results of the performances before and after the 2008 crisis indicate that
the combo strategy in the Brazilian market was more efficient during the most instable
period, as it was expected.
However, although the analysis of these last two figures is important to see
what happened before and after the 2008 crisis, the results should not be generalized
for all crises, since there is only one great crisis in this sample. Moreover, we are
looking only for past results, comparing pre- and post-crisis results, and it is hard for an
investor to predict exactly when a crisis will begin.
Also, according to what was argued on section 3.3, this analysis can change
according to the chosen investment horizon, since it will change the volatility of the
returns. So, the previous results of this subsection are only completely valid for an
investor that has an investment horizon of six months.
So, the analysis of the performance’s graphs can be useful on explaining some
events, or to capture some details, but it is not the best way to rank the strategies,
since it is not completely objective and would require redoing all these analyses when
changing the investment horizon.
Hence, for this purpose we will compute and compare the Sharpe ratios (SR),
which is an objective way to rank zero-investment strategies. As we explained on
section 3.3, the SR also suffers from the “investment horizon dilemma”, and in order to
show it is true, table 1 presents the annualized10 SR of the three strategies for different
investment horizons.
Table 1: Annualized Sharpe Ratios x Investment Horizons
1 semester
Annualized Sharpe ratio
Value
Momentum
Combo
1,26
0,38
1,20
2 semesters
1,20
0,31
1,06
4 semesters
1,31
0,25
0,93
6 semesters
1,13
0,28
1,16
8 semesters
1,34
0,39
2,22
Horizon
10
The Sharpe ratios were annualized according to the methodology of Sharpe (1994).
28
Note that with a horizon of one semester, the value strategy has the highest SR,
but with a horizon of 6 or 8 semesters the combo strategy has the highest SR, which is
an evidence of the existence of that dilemma.
However, differently from what happens on the graphs’ analysis, this problem
is simpler to be solved when we are dealing with the SR. All we need to do is to
compute the SR for different horizons (which is much simpler than plotting all those
graphs for each different horizon) and rank the strategies for each horizon. Then, all an
investor needs to do is to choose his investment horizon, and the strategy’s choice will
be made. Plotting a graph of the annualized SR over different horizon, as Lin and Chou
(2003) suggested, makes the visualization easier, as showed in figure 9.
Figure 9: Annualized Sharpe Ratio x Investment Horizons
So, after ranking the strategies over different horizons in the Brazilian stock
market, we can see that the value strategy is the best option if the investor wants to
invest for up to five semesters, and from six to ten semesters of investment horizon
the combo strategy is more attractive. The momentum strategy alone seems to never
be the best option.
29
It is valid to mention that, due to the small size of the used sample, as the
chosen investment horizon gets bigger, the computed SR becomes less robust, since
the number of observations gets smaller. For example, using six-month overlapping
data, for an investment horizon of one semester we have 20 observations to compute
the SR, while for a six semesters horizon we have only 15 observations, and for a ten
semesters horizon we have only 11 observations.
And if we consider that when we use overlapping data we use repeated
information, the results for big investment horizons get even less trustful, since for a
six semesters horizon we have less than 4 “real” observations, and for a ten semesters
horizon we have only two “real” observations. So, for the sample size we have, it may
not be prudent to make statements about long investment horizons decisions.
Then, our results show that for investment horizon of one to five semesters the
value strategy should be the best option for the investor, while for investment
horizons of six to ten semesters the combo strategies seems to be better, although this
last result may not be very robust.
4.3. Correlations
In this section we compute the correlations between the performance of the
strategies and the three variables suggested on section 3.4.
4.3.1. Ibovespa
Here we present the correlations between the semiannual returns of the
Ibovespa and the value, momentum and combo strategies. The correlations are
calculated over the entire period, as well as for the pre-crisis and post-crisis period,
and can be seen on table 2.
Analyzing the entire period, the correlation between the semiannual returns of
the Ibovespa and the value strategy was positive, but when we split the period in
30
before and after 2008 we see that this positive correlation is due to the post-crisis
period high correlation, since the correlation of the pre-crisis period was near to zero.
Table 2: Correlation between the Ibovespa and the strategies
Period
2001-2010
Correlation (Ibovespa, X)
X = Value
X = Momentum
X = Combo
0.28
-0.31
-0.09
2001-2007
0.04
-0.29
-0.19
2008-2010
0.62
-0.41
0.01
When we look to the correlation with the momentum strategy, it is quite the
opposite of the previous one, as expected, since value and momentum are negatively
correlated. Comparing the values of the correlations on pre- and post-crisis periods,
we can see that both value and momentum strategies were more correlated
(positively or negatively) to the Ibovespa during the instable period (this was especially
true to the value strategy), which made the combo strategy practically uncorrelated
with the Ibovespa during the crisis.
4.3.2. Stocks Correlation
On figure 10 we plotted the correlation among the available stocks
over
time. This is actually the correlation among the prices of the stocks that could be used
on the construction of the portfolios, which change every six months.
We can see that for most of the period the value of
stood between 0.12 and
0.17, but during the peak of the crisis it reached 0.20, getting ever higher on the
following semester (0.23), while the economy was already recovering from the crisis,
as showed on figure 1.
The correlations between
and the semiannual returns of the value,
momentum and combo strategies were 0.18, -0.57, and -0.39, respectively. Since value
and momentum are negatively correlated, these opposite results between them were
expected. We can also notice that the impact of
on the momentum strategy was
31
more intense than its impact on the value strategy, leading also to a negative
correlation between
and the combo strategy.
Figure 10: Correlation among available stocks
over time
We should be careful not to generalize these results by simply saying that “the
most correlated the available stocks, the higher the return of the value strategy, and
that the more diversified the portfolio, the higher the returns of the momentum and
combo strategies”, since significant changes on
only happened during the 2008
crisis/recovery, a single event in our sample.
In fact, the analysis made in section 4.1 shows that the performances of both
value and momentum strategies stood practically stable during the second semester of
2008, when
was very high, and had very extreme (and opposite) results on the first
semester of 2009, when
behavior” of
achieved its highest value. So, due to the relatively “good
and the performances of the strategies for the rest of the period in
comparison to the first semester of 2009, we may suspect that the correlation
between
and the performances was strongly affected by this extreme observation.
Then, we can’t use these results in order to make statements about how
portfolio diversification affects the performances of those strategies in general. Maybe
we could try doing that if we had a larger sample, with more crises, but even then it
32
would not be very useful information for the investor, since the strategies by
construction don’t allow the investor to try to diversify the portfolios.
Therefore, because of the observed pattern of
and the small sample we have,
the results of this sub-section are only valid to show how the correlation among the
stocks was affected by the 2008 crisis, which helps illustrating the affect of the crisis on
the performances of the strategies.
So, we can say that the 2008 crisis increased the correlation among the stocks,
and in that scenario (of global crisis of confidence followed by recovery) the value
strategy had a great performance, while the momentum strategy had a bad
performance.
4.3.3. Foreign Capital Flow
Finally, we examined the correlation between the daily foreign capital flow into
the Brazilian market and the daily returns of the value, momentum, and combo
strategies, which were all very close to zero (-0.05, 0.02, and -0.02, respectively),
suggesting that this variable does not have significant impact on the performance of
these strategies.
33
5. CONCLUSIONS
In this work we analyzed the performance of value, momentum and combo
strategies on the Brazilian stock market over the past decade. The value strategy had
the higher cumulated return over the past ten years, compared to the momentum and
the combo strategies, and even after adjusting the returns of the portfolios by their
risks.
This result is different from the results of Asness, Moskowitz and Pedersen
(2009), where the combo strategy had the best risk-adjusted performance in the US,
UK, Continental Europe and Japan. This finding could be explained by the weaker
negative correlation between value and momentum strategies on the Brazilian market
(-0.23), if compared this correlation on those markets (always stronger than -0.5),
which would lead to a less powerful combo strategy.
Splitting the period of analysis in pre-crisis (2001-2007) and post-crisis (20082010), we found that the value strategy still had the best performance one the first
period, but on the second period (the one of most instability), as the correlation
between the value and momentum strategies became considerably more negative (0.74), the combo strategy had the best risk-adjusted performance.
After computing the Sharpe ratio of the strategies for different investment
horizons, we found that the strategies’ ranking could change with the chosen horizons.
The SR analysis showed that the value strategy is the best option for horizons of 1 to 5
semesters, but the combo strategy may be better for horizons of 6 to 10 semesters,
although this last result is not as robust as the first one.
We also found that the momentum strategy on the Brazilian market doesn’t
appear to be a good option for the investor, if compared to the other two strategies.
This result is coherent with Bonomo and Dall'Agnol (2003), who did not find a
momentum effect on the Brazilian market, but instead found a reversal effect.
Regarding the correlations, we found that the correlation between the
Ibovespa and the performance of the value strategy was positive, but mostly during
34
the post-crisis period, while for the momentum strategy this correlation was
consistently negative, also with a stronger relation on the post-crisis period. The
momentum strategy correlated very poorly with the Ibovespa in the entire period.
About the correlation among the stocks, its correlation with the performance of
the value (momentum) strategy was positive (negative), but probably due to the
period of recovery from the crisis.
Finally, we found that the daily foreign capital flow into the Brazilian market
has no impact on the performance of the value, momentum or combo strategies.
35
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37
APPENDIX
Here are presented some graphs from Asness, Moskowitz and Pedersen (2009).
The graphs show the cumulative returns to value, momentum, and a 50/50
combination of value and momentum strategies among individual stocks in four
markets: U.S., U.K., Japan, and Continental Europe. In the last graph we have an equalweighted combination of all stock selection strategies. Also reported on each figure are
the annualized Sharpe ratios of each strategy and the correlation between value and
momentum in each market. They used monthly returns to compute both the Sharpe
ratios and the correlations.
38