A performance analysis of conventional and fundamental exchange traded funds: ETFs and their risk-return characteristics in relation to building institutional investor’s passive portfolio

An exchange traded fund (ETF) is a financial instrument that tracks some predetermined index. Since their initial establishment in 1993, ETFs have grown in importance in the field of passive investing. The main reason for the growth of the ETF industry is that ETFs combine benefits of stock investing and mutual fund investing. Although ETFs resemble mutual funds in many ways, also many differences occur. In addition, ETFs not only differ from mutual funds but also differ among each other. ETFs can be divided into two categories, i.e. market capitalisation ETFs and fundamental (or strategic) ETFs, and further into subcategories depending on their fundament basis. ETFs are a useful tool for diversification especially for a long-term investor. Although the economic importance of ETFs has risen drastically during the past 25 years, the differences and risk-return characteristics of fundamental ETFs have yet been rather unstudied area. In effect, no previous research on market capitalisation and fundamental ETFs was found during the research process. For its part, this thesis seeks to fill this research gap. The studied data consist of 50 market capitalisation ETFs and 50 fundamental ETFs. The fundaments, on which the indices that the fundamental ETFs track, were not limited nor segregated into subsections. The two types of ETFs were studied at an aggregate level as two different research groups. The dataset ranges from June 2006 to December 2014 with 103 monthly observations. The data was gathered using Bloomberg Terminal. The analysis was conducted as an econometric performance analysis. In addition to other econometric measures, the methods that were used in the performance analysis included modified Value-at-Risk, modified Sharpe ratio and Treynor ratio. The results supported the hypothesis that passive market capitalisation ETFs outperform active fundamental ETFs in terms of risk-adjusted returns, though the difference is rather small. Nevertheless, when taking into account the higher overall trading costs of the fundamental ETFs, the underperformance gap widens. According to the research results, market capitalisation ETFs are a recommendable diversification instrument for a long-term investor. In addition to better risk-adjusted returns, passive ETFs are more transparent and the bases of their underlying indices are simpler than those of fundamental ETFs. ETFs are still a young financial innovation and hence data is scarcely available. On future research, it would be valuable to research the differences in risk-adjusted returns also between the subsections of fundamental ETFs.

Aktiivisten ja passiivisten osakerahastojen suoriutuminen Suomen ja Euroopan markkinoilla

The performance of active and passive fund management has been extensively studied especially in the US. This thesis is focused on the performance of active and passive fund management in the Finnish and European stock markets during a five-year time span from 3/2011 to 3/2016. The aim of this study is to find out which strategy will result in better returns for the small-scale investor. The thesis questions also which strategy leads to a better profit-risk rate and how well the fund managers perform in creating added value. The data of the study consists of 44 active Finnish funds and two passive exchange traded funds available for Finnish investors. Indexes of both Finnish and European markets and a risk-free rate are used to support the analysis. The data for the thesis is collected from the DataStream database. Performance indicators that are used in the study are: return, volatility, Sharpe ratio and Jensen’s alpha. Based on the results of this study it can be concluded that in the Finnish stock market the passive strategy yielded a little better profits than the average of active funds. In the European stock market, the profits for the passive fund were significantly better than the average of active funds. Considering the profit-risk rate, neither strategy out- performed. The results of this thesis are in line with the previous studies, that encourage to favor the passive strategy.

Evidence of portuguese stock market abnormal returns

According to the stock market efficiency theory, it is not possible to consistently beat the market. However, technical analysis is more and more spread as an efficient way to achieve abnormal returns. In fact there is evidence that momentum investing strategies provide abnormal returns in different stock markets, Jegadeesh, N. and Titman, S. (1993), George, T. and Hwang, C. (2004) and Du, D. (2009). In this work we study if like other markets, the Portuguese stock market also allows to obtain abnormal returns, using a strategy that consists in picking stocks according to their past performance. Our work confirms the results of Soares, J. and Serra, A. (2005) and Pereira, P. (2009), showing that an investor can get abnormal returns investing in momentum portfolios. The Portuguese stock market evidences momentum returns in short term, exhibiting reversal in long term.

Stock and Bond Market Integration: Evidence from Russian Financial Markets

Minimizing the risks of an investment portfolio but not in the favour of expected returns is one of the key interests of an investor. Typically, portfolio diversification is achieved using two main strategies: investing in different classes of assets thought to have little or negative correlations or investing in similar classes of assets in multiple markets through international diversification. This study investigates integration of the Russian financial markets in the time period of January 1, 2003 to December 28, 2007 using daily data. The aim is to test the intra-country and cross-country integration of the Russian stock and bond markets between seven countries. Our test methodology for the short-run dynamics testing is the vector autoregressive model (VAR) and for the long-run cointegration testing we use the Johansen cointegration test which is an extension to VAR. The empirical results of this study show that the Russian stock and bond markets are not integrated in the long-run either at intra-country or cross-country level which means that the markets are relatively segmented. The short-run dynamics are also relatively low. This implies a presence of potential gains from diversification.

Performance persistence of equity funds in the Russian stock market

This thesis investigates performance persistence among the equity funds investing in Russia during 2003-2007. Fund performance is measured using several methods including the Jensen alpha, the Fama-French 3- factor alpha, the Sharpe ratio and two of its variations. Moreover, we apply the Bayesian shrinkage estimation in performance measurement and evaluate its usefulness compared with the OLS 3-factor alphas. The pattern of performance persistence is analyzed using the Spearman rank correlation test, cross-sectional regression analysis and stacked return time series. Empirical results indicate that the Bayesian shrinkage estimates may provide better and more accurate estimates of fund performance compared with the OLS 3-factor alphas. Secondly, based on the results it seems that the degree of performance persistence is strongly related to length of the observation period. For the full sample period the results show strong signs of performance reversal whereas for the subperiod analysis the results indicate performance persistence during the most recent years.

Essays on pricing of risk and international linkage of Russian stock market

Last two decades have seen a rapid change in the global economic and financial situation; the economic conditions in many small and large underdeveloped countries started to improve and they became recognized as emerging markets. This led to growth in the amounts of global investments in these countries, partly spurred by expectations of higher returns, favorable risk-return opportunities, and better diversification alternatives to global investors. This process, however, has not been without problems and it has emphasized the need for more information on these markets. In particular, the liberalization of financial markets around the world, globalization of trade and companies, recent formation of economic and regional blocks, and the rapid development of underdeveloped countries during the last two decades have brought a major challenge to the financial world and researchers alike. This doctoral dissertation studies one of the largest emerging markets, namely Russia. The motivation why the Russian equity market is worth investigating includes, among other factors, its sheer size, rapid and robust economic growth since the turn of the millennium, future prospect for international investors, and a number of important major financial reforms implemented since the early 1990s. Another interesting feature of the Russian economy, which gives motivation to study Russian market, is Russia’s 1998 financial crisis, considered as one of the worst crisis in recent times, affecting both developed and developing economies. Therefore, special attention has been paid to Russia’s 1998 financial crisis throughout this dissertation. This thesis covers the period from the birth of the modern Russian financial markets to the present day, Special attention is given to the international linkage and the 1998 financial crisis. This study first identifies the risks associated with Russian market and then deals with their pricing issues. Finally some insights about portfolio construction within Russian market are presented. The first research paper of this dissertation considers the linkage of the Russian equity market to the world equity market by examining the international transmission of the Russia’s 1998 financial crisis utilizing the GARCH-BEKK model proposed by Engle and Kroner. Empirical results shows evidence of direct linkage between the Russian equity market and the world market both in regards of returns and volatility. However, the weakness of the linkage suggests that the Russian equity market was only partially integrated into the world market, even though the contagion can be clearly seen during the time of the crisis period. The second and the third paper, co-authored with Mika Vaihekoski, investigate whether global, local and currency risks are priced in the Russian stock market from a US investors’ point of view. Furthermore, the dynamics of these sources of risk are studied, i.e., whether the prices of the global and local risk factors are constant or time-varying over time. We utilize the multivariate GARCH-M framework of De Santis and Gérard (1998). Similar to them we find price of global market risk to be time-varying. Currency risk also found to be priced and highly time varying in the Russian market. Moreover, our results suggest that the Russian market is partially segmented and local risk is also priced in the market. The model also implies that the biggest impact on the US market risk premium is coming from the world risk component whereas the Russian risk premium is on average caused mostly by the local and currency components. The purpose of the fourth paper is to look at the relationship between the stock and the bond market of Russia. The objective is to examine whether the correlations between two classes of assets are time varying by using multivariate conditional volatility models. The Constant Conditional Correlation model by Bollerslev (1990), the Dynamic Conditional Correlation model by Engle (2002), and an asymmetric version of the Dynamic Conditional Correlation model by Cappiello et al. (2006) are used in the analysis. The empirical results do not support the assumption of constant conditional correlation and there was clear evidence of time varying correlations between the Russian stocks and bond market and both asset markets exhibit positive asymmetries. The implications of the results in this dissertation are useful for both companies and international investors who are interested in investing in Russia. Our results give useful insights to those involved in minimising or managing financial risk exposures, such as, portfolio managers, international investors, risk analysts and financial researchers. When portfolio managers aim to optimize the risk-return relationship, the results indicate that at least in the case of Russia, one should account for the local market as well as currency risk when calculating the key inputs for the optimization. In addition, the pricing of exchange rate risk implies that exchange rate exposure is partly non-diversifiable and investors are compensated for bearing the risk. Likewise, international transmission of stock market volatility can profoundly influence corporate capital budgeting decisions, investors’ investment decisions, and other business cycle variables. Finally, the weak integration of the Russian market and low correlations between Russian stock and bond market offers good opportunities to the international investors to diversify their portfolios.

Performance Comparison of Behavioral Finance -based Investment Strategies in the Finnish Stock Market 1996-2010

In this thesis traditional investment strategies (value and growth) are compared to modern investment strategies (momentum, contrarian and GARP) in terms of risk, performance and cumulative returns. Strategies are compared during time period reaching from 1996 to 2010 in the Finnish stock market. Used data includes all listed main list stocks, dividends and is adjusted in case of splits, and mergers and acquisitions. Strategies are tested using different holding periods (6, 12 and 36 months) and data is divided into tercile portfolios based on different ranking criteria. Contrarian and growth strategies are the only strategies with improved cumulative returns when longer holding periods are used. Momentum (52-week high price1) and GARP strategies based on short holding period have the best performance and contrarian and growth strategies the worst. Momentum strategies (52-week high price) along with short holding period contrarian strategies (52-week low price2) have the lowest risk. Strategies with the highest risk are both growth strategies and two momentum strategies (52-week low price). The empirical results support the efficiency of momentum, GARP and value strategies. The least efficient strategies are contrarian and growth strategies in terms of risk, performance and cumulative returns. Most strategies outperform the market portfolio in all three measures. 1 Stock ranking criterion (current price/52-week highest price) 2 Stock ranking criterion (current price/52-week lowest price)

Pricing anomalies in the Finnish stock market

The aim of this thesis is to examine whether the pricing anomalies exists in the Finnish stock markets by comparing the performance of quantile portfolios that are formed on the basis of either individual valuation ratios, composite value measures or combined value and momentum indicators. All the research papers included in the thesis show evidence of value anomalies in the Finnish stock markets. In the first paper, the sample of stocks over the 1991-2006 period is divided into quintile portfolios based on four individual valuation ratios (i.e., E/P, EBITDA/EV, B/P, and S/P) and three hybrids of them (i.e. composite value measures). The results show the superiority of composite value measures as selection criterion for value stocks, particularly when EBITDA/EV is employed as earnings multiple. The main focus of the second paper is on the impact of the holding period length on performance of value strategies. As an extension to the first paper, two more individual ratios (i.e. CF/P and D/P) are included in the comparative analysis. The sample of stocks over 1993- 2008 period is divided into tercile portfolios based on six individual valuation ratios and three hybrids of them. The use of either dividend yield criterion or one of three composite value measures being examined results in best value portfolio performance according to all performance metrics used. Parallel to the findings of many international studies, our results from performance comparisons indicate that for the sample data employed, the yearly reformation of portfolios is not necessarily optimal in order to maximally gain from the value premium. Instead, the value investor may extend his holding period up to 5 years without any decrease in long-term portfolio performance. The same holds also for the results of the third paper that examines the applicability of data envelopment analysis (DEA) method in discriminating the undervalued stocks from overvalued ones. The fourth paper examines the added value of combining price momentum with various value strategies. Taking account of the price momentum improves the performance of value portfolios in most cases. The performance improvement is greatest for value portfolios that are formed on the basis of the 3-composite value measure which consists of D/P, B/P and EBITDA/EV ratios. The risk-adjusted performance can be enhanced further by following 130/30 long-short strategy in which the long position of value winner stocks is leveraged by 30 percentages while simultaneously selling short glamour loser stocks by the same amount. Average return of the long-short position proved to be more than double stock market average coupled with the volatility decrease. The fifth paper offers a new approach to combine value and momentum indicators into a single portfolio-formation criterion using different variants of DEA models. The results throughout the 1994-2010 sample period shows that the top-tercile portfolios outperform both the market portfolio and the corresponding bottom-tercile portfolios. In addition, the middle-tercile portfolios also outperform the comparable bottom-tercile portfolios when DEA models are used as a basis for stock classification criteria. To my knowledge, such strong performance differences have not been reported in earlier peer-reviewed studies that have employed the comparable quantile approach of dividing stocks into portfolios. Consistently with the previous literature, the division of the full sample period into bullish and bearish periods reveals that the top-quantile DEA portfolios lose far less of their value during the bearish conditions than do the corresponding bottom portfolios. The sixth paper extends the sample period employed in the fourth paper by one year (i.e. 1993- 2009) covering also the first years of the recent financial crisis. It contributes to the fourth paper by examining the impact of the stock market conditions on the main results. Consistently with the fifth paper, value portfolios lose much less of their value during bearish conditions than do stocks on average. The inclusion of a momentum criterion somewhat adds value to an investor during bullish conditions, but this added value turns to negative during bearish conditions. During bear market periods some of the value loser portfolios perform even better than their value winner counterparts. Furthermore, the results show that the recent financial crisis has reduced the added value of using combinations of momentum and value indicators as portfolio formation criteria. However, since the stock markets have historically been bullish more often than bearish, the combination of the value and momentum criteria has paid off to the investor despite the fact that its added value during bearish periods is negative, on an average.

The us subprime crisis and stock market integration: evidence from the BRICS

The aim of this study is to examine the level of stock market co-movement in the BRICS countries and three major industrialized countries (Japan, UK and USA). While analyzing the interdependence and integration of markets, two subsets are examined: before (2000 – 2007) and during the global financial crisis (2007-2011). Generally, interdependence across markets is likely to increase during a highly volatile period. This is problematic because if it were true, the main benefit of international diversification would be reduced at times when it is most needed. The results reveal the dominant role of the US financial markets over the examined time period. Empirical studies of this research paper indicate that cross-market linkages have become slightly stronger during the ongoing subprime crisis than before crisis. However, results also show that an investor may obtain some international diversification benefits by investing especially in the BRICS countries despite the fact of unstable economic condition and growing globalization.

Interdependence of Emerging Eastern European stock markets

One of the main developments in the global economy during the past decades has been the growth of emerging economies. Projections for their long-term growth, changes in the investment climate, corporate transparency and demography point to an increasing role for these emerging economies in the global economy. Today, emerging economies are usually considered as financial markets offering opportunities for high returns, good risk diversification and improved return-to-risk ratios. However, researchers have noted that these advantages may be in decline because of the increasing market integration. Nevertheless, it is likely that certain financial markets and specific sectors will remain partially segmented and somewhat insulated from the global economy for the year to come. This doctoral dissertation investigates several stock markets in Emerging Eastern Europe (EEE), including the ones in Russia, Poland, Hungary, the Czech Republic, Bulgaria and Slovenia. The objective is to analyze the returns and financial risks in these emerging markets from international investor’s point of view. This study also examines the segmentation/integration of these financial markets and the possibilities to diversify and hedge financial risk. The dissertation is divided into two parts. The first includes a review of the theoretical background for the articles and a review of the literature on EEE stock markets. It includes an overview of the methodology and research design applied in the analysis and a summary of articles from the second part of this dissertation and their main findings. The second part consists of four research publications. This work contributes to studies on emerging stock markets in four ways. First, it adds to the body of research on the pricing of risk, providing new empirical evidence about partial stock market segmentation in EEE. The results suggest that the aggregate emerging market risk is a relevant driver for stock market returns and that this market risk can be used to price financial instruments and forecast their performance. Second, it contributes to the empirical research on the integration of stock markets, asset prices and exchange rates by identifying the relationships between these markets through volatility and asset pricing. The results show that certain sectors of stock markets in EEE are not as integrated as others. For example, the Polish consumer goods sector, the Hungarian telecommunications sector, and the Czech financial sector are somewhat isolated from their counterparts elsewhere in Europe. Nevertheless, an analysis of the impact of EU accession in 2004 on stock markets suggests that most of the EEE markets are becoming increasingly integrated with the global markets. Third, this thesis complements the scientific literature in the field of shock and volatility spillovers by examining the mechanism of spillover distribution among the EU and EEE countries. The results illustrate that spillovers in emerging markets are mostly from a foreign exchange to the stock markets. Moreover, the results show that the effects of external shocks on stock markets have increased after the enlargement of the EU in 2004. Finally, this study is unique because it analyzes the effects of foreign macroeconomic news on geographically closely related countries. The results suggest that the effects of macroeconomic announcements on volatility are significant and have effect that varies across markets and their sectors. Moreover, the results show that the foreign macroeconomic news releases, somewhat surprisingly, have a greater effect on the EEE markets than the local macroeconomic news. This dissertation has a number of implications for the industry and for practitioners. It analyses financial risk associated with investing in Emerging Eastern Europe. Investors may use this information to construct and optimize investment portfolios. Moreover, this dissertation provides insights for investors and portfolio managers considering asset allocation to protect value or obtain higher returns. The results have also implications for asset pricing and portfolio selection in light of macroeconomic news releases.

The Impact of European Macroeconomic News Announcements on CIVETS Stock Markets

The purpose of this research is to investigate how CIVETS (Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa) stock markets are integrated with Europe as measured by the impact of euro area (EA) scheduled macroeconomic news announcements, which are related to macroeconomic indicators that are commonly used to indicate the direction of the economy. Macroeconomic announcements used in this study can be divided into four categories; (1) prices, (2) real economy, (3) money supply and (4) business climate and consumer confidence. The data set consists of daily market data from CIVETS and scheduled macroeconomic announcements from the EA for the years 2007-2012. The econometric model used in this research is Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). Empirical results show diverse impacts of macroeconomic news releases and surprises for different categories of news supporting the perception of heterogeneity among CIVETS. The analyses revealed that in general EA macroeconomic news releases and surprises affect stock market volatility in CIVETS and only in some cases asset pricing. In conclusion, all CIVETS stock markets reacted to the incoming EA macroeconomic news suggesting market integration to some extent. Thus, EA should be considered as a possible risk factor when investing in CIVETS.

The Anchoring Bias of Investors and the 52-Week High Momentum Strategy in the OMX Helsinki Stock Exchange: Psychological Approach to Market Efficiency

The behavioural finance literature expects systematic and significant deviations from efficiency to persist in securities markets due to behavioural and cognitive biases of investors. These behavioural models attempt to explain the coexistence of intermediate-term momentum and long-term reversals in stock returns based on the systematic violations of rational behaviour of investors. The study investigates the anchoring bias of investors and the profitability of the 52-week momentum strategy (GH henceforward). The relatively highly volatile OMX Helsinki stock exchange is a suitable market for examining the momentum effect, since international investors tend to realise their positions first from the furthest security markets by the time of market turbulence. Empirical data is collected from Thomson Reuters Datastream and the OMX Nordic website. The objective of the study is to provide a throughout research by formulating a self-financing GH momentum portfolio. First, the seasonality of the strategy is examined by taking the January effect into account and researching abnormal returns in long-term. The results indicate that the GH strategy is subject to significantly negative revenues in January, but the strategy is not prone to reversals in long-term. Then the predictive proxies of momentum returns are investigated in terms of acquisition prices and 52-week high statistics as anchors. The results show that the acquisition prices do not have explanatory power over the GH strategy’s abnormal returns. Finally, the efficacy of the GH strategy is examined after taking transaction costs into account, finding that the robust abnormal returns remain statistically significant despite the transaction costs. As a conclusion, the relative distance between a stock’s current price and its 52-week high statistic explains the profits of momentum investing to a high degree. The results indicate that intermediateterm momentum and long-term reversals are separate phenomena. This presents a challenge to current behavioural theories, which model these aspects of stock returns as subsequent components of how securities markets respond to relevant information.

Dynamic linkages of real estate and stock markets in Finland

Traditionally real estate has been seen as a good diversification tool for a stock portfolio due to the lower return and volatility characteristics of real estate investments. However, the diversification benefits of a multi-asset portfolio depend on how the different asset classes co-move in the short- and long-run. As the asset classes are affected by the same macroeconomic factors, interrelationships limiting the diversification benefits could exist. This master’s thesis aims to identify such dynamic linkages in the Finnish real estate and stock markets. The results are beneficial for portfolio optimization tasks as well as for policy-making. The real estate industry can be divided into direct and securitized markets. In this thesis the direct market is depicted by the Finnish housing market index. The securitized market is proxied by the Finnish all-sectors securitized real estate index and by a European residential Real Estate Investment Trust index. The stock market is depicted by OMX Helsinki Cap index. Several macroeconomic variables are incorporated as well. The methodology of this thesis is based on the Vector Autoregressive (VAR) models. The long-run dynamic linkages are studied with Johansen’s cointegration tests and the short-run interrelationships are examined with Granger-causality tests. In addition, impulse response functions and forecast error variance decomposition analyses are used for robustness checks. The results show that long-run co-movement, or cointegration, did not exist between the housing and stock markets during the sample period. This indicates diversification benefits in the long-run. However, cointegration between the stock and securitized real estate markets was identified. This indicates limited diversification benefits and shows that the listed real estate market in Finland is not matured enough to be considered a separate market from the general stock market. Moreover, while securitized real estate was shown to cointegrate with the housing market in the long-run, the two markets are still too different in their characteristics to be used as substitutes in a multi-asset portfolio. This implies that the capital intensiveness of housing investments cannot be circumvented by investing in securitized real estate.

The impact of companies’ demergers to the stock prices: a Finnish perspective

Tässä kauppatieteiden kandidaatintyössä tutkittiin millaisia vaikutuksia julkisesti noteerattujen yhtiöiden osakekurssissa tapahtuu, kun jo valmiiksi Helsingin pörssissä listattu yritys jakautuu kahdeksi uudeksi pörssiyritykseksi. Molempien yrityksien osakkeita voi tämän jakautumisen jälkeen vapaasti ostaa tai myydä. Aikaisempi tutkimus on pääsääntöisesti keskittynyt Yhdysvaltojen markkinoille ja näiden tutkimusten tuloksien perusteella on monessa tapauksessa havautta, että on mahdollista saavuttaa ylinormaaleja tuottoja, kun pörssiyritys jakautuu kahdeksi uudeksi pörssiyritykseksi. Tässä analyysissä jakautumiset ajallisesti tapahtuivat vuosien 1994 ja 2013 välisenä aikana Suomessa ja näitä jakautumia oli yhteensä 16 kappaletta. Tutkimuksessa on hyödynnetty tilastollisten menetelmien analyysiä sekä CAP-mallia, jotta voitaisiin löytää vastauksia seuraaviin kysymyksiin: Vaikuttaako pörssiyrityksen jakautuminen kahdeksi pörssiyritykseksi alkuperäisen yhtiön ja uuden yhtiön osakekursseihin? Onko vaikutus positiivinen, negatiivinen vai onko jakautumisella mitään havaittavaa vaikutusta? Tämän tutkimuksen tulokset antavat uutta tietoa tutkijoille, analyytikoille, opettajille, opiskelijoille, yrityksille ja yritysten johdolle sekä erityisesti sijoittajille. Tulosten mukaan on nähtävissä monia vaikutuksia osakekursseissa, kun pörssiyritys jakautuu. Vaikutus näyttää kuitenkin olevan jossain määrin yritys-riippuvainen. Kun sijoitetaan oikeaan aikaan, on monia jakautuvia yrityksiä, jotka antavat hyvän tuoton keskimäärin, mutta kuten tavallista ja tyypillistä osakemarkkinoille, on myös jakautuvia yhtiöitä, jotka antavat negatiivisia tuottoja tai tuotot ovat nollassa

Eficiência da magic formula de value investing no mercado brasileiro

O objetivo deste trabalho é realizar procedimento de back-test da Magic Formula na Bovespa, reunindo evidências sobre violações da Hipótese do Mercado Eficiente no mercado brasileiro. Desenvolvida por Joel Greenblatt, a Magic Formula é uma metodologia de formação de carteiras que consiste em escolher ações com altos ROICs e Earnings Yields, seguindo a filosofia de Value Investing. Diversas carteiras foram montadas no período de dezembro de 2002 a maio de 2014 utilizando diferentes combinações de número de ativos por carteira e períodos de permanência. Todas as carteiras, independentemente do número de ativos ou período de permanência, apresentaram retornos superiores ao Ibovespa. As diferenças entre os CAGRs das carteiras e o do Ibovespa foram significativas, sendo que a carteira com pior desempenho apresentou CAGR de 27,7% contra 14,1% do Ibovespa. As carteiras também obtiveram resultados positivos após serem ajustadas pelo risco. A pior razão retorno-volatilidade foi de 1,2, comparado a 0,6 do Ibovespa. As carteiras com pior pontuação também apresentaram bons resultados na maioria dos cenários, contrariando as expectativas iniciais e os resultados observados em outros trabalhos. Adicionalmente foram realizadas simulações para diversos períodos de 5 anos com objetivo de analisar a robustez dos resultados. Todas as carteiras apresentaram CAGR maior que o do Ibovespa em todos os períodos simulados, independentemente do número de ativos incluídos ou dos períodos de permanência. Estes resultados indicam ser possível alcançar retornos acima do mercado no Brasil utilizando apenas dados públicos históricos. Esta é uma violação da forma fraca da Hipótese do Mercado Eficiente.