Made available in DSpace on 2010-04-20T21:00:18Z (GMT). No. of bitstreams: 3 ernestokabashimaturma2003.pdf.jpg: 14228 bytes, checksum: dee04567d9b7d510262698cc8b1aac7a (MD5) ernestokabashimaturma2003.pdf: 322209 bytes, checksum: 07320e4df8ce4733adad8f20e464b5f9 (MD5) ernestokabashimaturma2003.pdf.txt: 96815 bytes, checksum: 7704291ee38c7a6004795b3faa07da1f (MD5) Previous issue date: 2006-02-01T00:00:00Z / Esta dissertação estuda a aplicação da estratégia Pairs Trading no mercado acionário brasileiro. Envolve basicamente a identificação de pares de ações que tenham movimentos de preço semelhantes e posteriormente a operação do diferencial entre seus preços. É possível observar no mercado a existência de um valor de equilíbrio de longo prazo para alguns pares de ações e quando o diferencial divergir de certa quantidade pré-definida opera-se o diferencial no intuito de que o mesmo retorne ao seu valor de equilíbrio de longo prazo, ou seja, espera-se que ocorra uma reversão à média do diferencial. A metodologia para a identificação desses pares de ações que descrevem movimentos semelhantes vem do conceito de cointegração. Essa metodologia é aplicada sobre as ações do índice Bovespa de 04-Jan-1993 a 30-Jun-2005. Inicialmente é feita uma pré-seleção dos pares de ações via correlação, ou medida de distância. Para a seleção final é feito o teste de cointegração, onde é utilizado o método de Dickey-Fuller aumentado (Augmented Dickey-Fuller test – ADF) para verificar a existência de raiz unitária da série de resíduo da combinação linear do logaritmo dos preços. Após a seleção, os pares são simulados historicamente (backtesting) para se analisar a performance dos retornos dos pares de ações, incluindo também os custos operacionais. / This dissertation addresses the application of Pairs Trading strategy in the Brazilian equity market. Basically it consists in the identification of the stock pairs, that have similar price movements, which can be subsequently traded based on their prices spread. It can be observed in the market that a long-term equilibrium value can be determined between some pairs of stocks and when this spread diverges to a certain predetermined value from the mean, it is traded in the expectation that it will return to the long term equilibrium value, i.e., the spread mean reversion. The methodology used to identify the pairs of stocks, which have similar movements, is derived from the concept of cointegration. This methodology was applied to all of the stocks that compose the Bovespa index from 04-Jan-1993 to 30-Jun-2005. Initially pairs of stocks were pre-selected using correlation, or distance measure. The Augmented Dickey-Fuller test (ADF) was also used in order to determine the cointegrated pairs. ADF is used to verify the existence of the unit root in the residual time series of the logarithm of prices. After the selection was completed the chosen pairs were backtested in order to analyze the performance of their returns, with the addition of the operational costs.

Made available in DSpace on 2010-04-20T21:00:53Z (GMT). No. of bitstreams: 4 Eduardo Menescal Lustosa Longo.pdf.jpg: 10145 bytes, checksum: b065ece0a6050c28545e0c2004a42402 (MD5) Eduardo Menescal Lustosa Longo.pdf.txt: 40329 bytes, checksum: 1026ba29309ee769eab96eae93bebd92 (MD5) Eduardo Menescal Lustosa Longo.pdf: 273765 bytes, checksum: c3f0204a9f073bb4276db2a68130c0cb (MD5) license.txt: 4886 bytes, checksum: a7c9cfe8632065c9656e1d827d849400 (MD5) Previous issue date: 2009-01-29T00:00:00Z / In this dissertation, we assess the application of pairs trading strategy in the Brazilian stock market. Differently from other papers about the same theme, we built synthetic asset from a linear relationship between stock prices. Accordingly to Burgeois and Minko (2005), we applied the Johansen methodology to identify stock pairs to be evaluated. After identifying cointegrated stock pairs, in order to filter out nonstationary synthetic assets, we did the DF-GLS and KPSS tests and removed those with unit root in the time series. Thereafter, we simulate the strategy (backtesting) in the selected pairs and in order to find the best results parameters, we optimized the results using different formation periods, trading periods and entry, exit and stop-loss parameters. To assure the most close to reality backtesting, we included in the results the brokerage, exchange and stock loan fees. In addition we added one day lag to trade after an order has triggered. / Neste trabalho, verificamos viabilidade de aplicação da estratégia de pairs trading no mercado acionário brasileiro. Diferentemente de outros estudos do mesmo tema, construímos ativos sintéticos a partir de uma combinação linear de preços de ações. Conforme Burgeois e Minko (2005), utilizamos a metodologia de Johansen para a formação dos pares a serem testados. Após a identificação de pares cointegrados, para assegurar a estacionaridade do ativo sintético contruído a partir da relação linear de preços das ações, utilizamos os testes DF-GLS e KPSS e filtramos àqueles que apresentavam raiz unitária em sua série de tempo. A seguir, simulamos a estratégia (backtesting) com os pares selecionados e para encontrar os melhores parâmetros, testamos diferentes períodos de formação dos pares, de operação e de parâmetros de entrada, saída e stop-loss. A fim de realizarmos os testes de forma mais realista possível, incluímos os custos de corretagem, de emolumentos e de aluguel, além de adicionar um lag de um dia para a realização das operações

Esta tese é composta por três ensaios relacionados a macrofinanças e economia regional. O primeiro artigo analisa a lucratividade de portfólios de pairs trading auto-financiados para os mercados acionários Brasileiro, Europeu e Americano utilizando duas metodologias diferentes de seleção de pares: os métodos da distância e cointegração. Uma comparação ampla das metodologias de pairs trading, com uma base de dados grande de diferentes mercados é capaz de elucidar os principais benefícios e fragilidades de cada método. De modo geral, os resultados mostram que diferentes estruturas de mercado favorecem diferentes estratégias de pairs trading. Mais especificamente, a seleção via cointegração desempenha melhor nos mercados Brasileiro e Europeu, enquanto que o método da distância gera resultados melhores para os Estados Unidos. A melhor estratégia em cada mercado possui um alpha significante com um beta negligenciável. No segundo trabalho analisamos duas questões: (i) a capacidade do Brasil em adotar uma política monetária independente das influências dos juros americanos e (ii) os impactos da política monetária brasileira e dos juros americanos nas expectativas de inflação. Os resultados indicam que, para o período entre 1999 e 2007, existe uma reduzida independência da política monetária brasileira, e que o contágio do Fed Funds rate sobre a taxa Selic ocorre de modo completo. Para o período entre 2002 e 2007, também encontramos que os juros americanos são mais relevantes para a determinação das expectativas de inflação do que a taxa Selic, sendo auxiliado pelo câmbio para controlar as expectativas de inflação. Por outro lado, no período entre 2010 e início de 2015, com a ausência de mudanças no Fed Funds, a Selic se tornou mais independente e reativa, tanto às expectativas de inflação quanto ao hiato do produto. O terceiro artigo consiste em recalcular a MIP para o Rio Grande do Sul e para o Brasil a fim de incluir nas interligações setoriais os efeitos induzidos advindos da renda das famílias. Além disso, calculam-se os geradores de cinco variáveis (a saber: emprego, renda, tributos líquidos arrecadados, valor adicionado e produto), bem como são calculados os índices de Hirschmann-Rasmussen e os índices puros de ligação com o intuito de identificar os setores-chave das economias do Rio Grande do Sul e do Brasil. Posteriormente, utiliza-se dos geradores reestimados pela nova MIP fechada para estimar os impactos das quebras de safra de soja nos anos que ocorreram as maiores perdas tanto de valor quanto de volume na produção da oleaginosa (2004, 2005 e 2012). Os resultados indicam que os geradores do Rio Grande do Sul e do Brasil aumentam consideravelmente após a inclusão do efeito induzido, para todas as variáveis e setores analisados. Já as estimativas de impacto das quebras de safra indicam que as perdas podem chegar a até R$ 8,9 Bilhões para o RS e R$ 12,5 Bilhões para o Brasil em termos de queda na produção. / This thesis consists of three essays related to financial macroeconomics and regional economics. The first essay analyzes the profitability of self-financing portfolios using pairs trading for the Brazilian, European, and American stock markets using two different pairs selection methodologies: the distance and cointegration methods. A throughout comparison of pairs trading methodologies using large datasets from different markets uncovers the main benefits and drawbacks of each approach. Overall, the results show that different market structures favor different pairs trading strategies. More specifically, the cointegration approach performed better on the Brazilian and European markets, while the distance method delivered better results for the US. The best strategy in each market yields significant alpha with negligible beta. The ability of a country to use monetary policy in order to smooth economic fluctuations and keep inflation in check is crucial in an institutional framework of inflation targeting. Hence, in the second work, we examined two issues: (i) Brazil’s ability to adopt a monetary policy independent from the contagion of the american interest rates and (ii) the impact of the brazilian monetary policy and of the american interest rate on inflation expectations. The results indicate that for the period between 1999 and 2007, there is a reduced independence of the brazilian monetary policy, and that the spillover of the Fed Funds rate over the Selic rate is comprehensive. For the period between 2002 and 2007, we also found that US interest rates are more relevant to the determination of inflation expectations than the Selic rate, being helped by the exchange rate to control inflation expectations. On the other hand, for the period between 2010 and early 2015, with no occurance of changes in the Fed Funds, the Selic became more independent and responsive to inflation expectations as well as to the output gap. The third paper consist of reestimating the Input-Output Matrix for Rio Grande do Sul and Brazil, in order to include in the sectoral linkages the induced effects arising from household income. Also, we estimate the multipliers for five variables (employment, income, net taxes collected, added value and gross product), as well as the Hirschmann-Rasmussen index and the Pure Linkages in order to identify the key-sectors of the Rio Grande do Sul and Brazil’s economy. We also use those multipliers to estimate the impacts of the soybean crop failure in Rio Grande do Sul, in the years with the biggest crop losses in terms of volume (2004, 2005 and 2012). The results indicate that the multipliers increase considerably after the inclusion of the induced effect, for all valiables and sectors. The crop failures indicate that the losses could reach up to R$ 8,9 Billions for RS and R$ 12,5 Billions for Brasil in terms of reduced economic activity.

In this thesis we study the utility maximization problem for assets whose prices are cointegrated, which arises from the investment practice of convergence trading and its special forms, pairs trading and spread trading. The major theme in the first two chapters of the thesis, is to investigate the assumption of market-neutrality of the optimal convergence trading strategies, which is a ubiquitous assumption taken by practitioners and academics alike. This assumption lacks a theoretical justification and, to the best of our knowledge, the only relevant study is Liu and Timmermann (2013) which implies that the optimal convergence strategies are, in general, not market-neutral. We start by considering a minimalistic pairs-trading scenario with two cointegrated stocks and solve the Merton investment problem with power and logarithmic utilities. We pay special attention to when/if the stochastic control problem is well-posed, which is overlooked in the study done by Liu and Timmermann (2013). In particular, we show that the problem is ill-posed if and only if the agent’s risk-aversion is less than a constant which is an explicit function of the market parameters. This condition, in turn, yields the necessary and sufficient condition for well-posedness of the Merton problem for all possible values of agent’s risk-aversion. The resulting well-posedness condition is surprisingly strict and, in particular, is equivalent to assuming the optimal investment strategy in the stocks to be market-neutral. Furthermore, it is shown that the well-posedness condition is equivalent to applying Novikov’s condition to the market-price of risk, which is a ubiquitous sufficient condition for imposing absence of arbitrage. To the best of our knowledge, these are the only theoretical results for supporting the assumption of market-neutrality of convergence trading strategies. We then generalise the results to the more realistic setting of multiple cointegrated assets, assuming risk factors that effects the asset returns, and general utility functions for investor’s preference. In the process of generalising the bivariate results, we also obtained some well-posedness conditions for matrix Riccati differential equations which are, to the best of our knowledge, new. In the last chapter, we set up and justify a Merton problem that is related to spread-trading with two futures assets and assuming proportional transaction costs. The model possesses three characteristics whose combination makes it different from the existing literature on proportional transaction costs: 1) finite time horizon, 2) Multiple risky assets 3) stochastic opportunity set. We introduce the HJB equation and provide rigorous arguments showing that the corresponding value function is the viscosity solution of the HJB equation. We end the chapter by devising a numerical scheme, based on the penalty method of Forsyth and Vetzal (2002), to approximate the viscosity solution of the HJB equation.

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Atenciosamente, Secretaria de Registro, Suzi on 2011-09-16T18:56:44Z (GMT) / Submitted by Sheyla Brito (sheyla.brito@yahoo.com) on 2011-09-19T15:05:46Z No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T15:12:27Z (GMT) No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T15:12:47Z (GMT) No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) / Made available in DSpace on 2011-09-19T15:15:25Z (GMT). No. of bitstreams: 1 Dissertacao_Sheyla-Brito_versao-final_2011-09.pdf: 903173 bytes, checksum: 2e19043be0af3ce4c63641a374093018 (MD5) Previous issue date: 2011-08-19 / This dissertation is focused on studying the Brazilian stock market behavior, more specifically related to a pair trading strategy. The assets included in here come from listed stocks of Brazilian Stock Exchange Index (Ibovespa) and the pair selection is exclusively based on a statistic characteristics, known as cointegration, without fundamentalist analysis. The applied theory treats similar movement of stock prices between pairs which tends to revert to an equilibrium mean of price differences. The strategy will present positive returns when reversion occurs in a pre-defined time. Back-testing data comprises intraday prices from 2006 until 2010 of Ibovespa stocks. The tools in which pair selection and trading rules are coded are MATLAB (selection) and Streambase (trading). Selection is processed through Dickey-Fuller augmented test into MATLAB to check the existence of a unit root on an error time series of a linear combination of stock prices, for each pair. Operation is simulated through intraday back-testing data as mentioned, input into Streambase tool. Within back-testing period, the strategy results are profitable in 2006, 2007 and 2010. Parameters, to enter and stop the operation, were adjusted for the first month of 2006 and could be successfully applied for the whole year of 2006 (yield of Selic + 5.8% for 2006), for 2007, where yield were close to Selic and for 2010, with yield of Selic + 10.8%. In periods of high volatility (2008 and 2009), tests with the same parameters of the ones adjusted for 2006 generated losses, showing the strategy is highly impacted per volatility returns of stock prices. This behavior suggests that, in actual operations, parameters should be constantly reevaluated in order to adapt them to volatile scenarios. / Esta dissertação estuda o movimento do mercado acionário brasileiro com o objetivo de testar a trajetória de preços de pares de ações, aplicada à estratégia de pair trading. Os ativos estudados compreendem as ações que compõem o Ibovespa e a seleção dos pares é feita de forma unicamente estatística através da característica de cointegração entre ativos, sem análise fundamentalista na escolha. A teoria aqui aplicada trata do movimento similar de preços de pares de ações que evoluem de forma a retornar para o equilíbrio. Esta evolução é medida pela diferença instantânea dos preços comparada à média histórica. A estratégia apresenta resultados positivos quando a reversão à média se efetiva, num intervalo de tempo pré-determinado. Os dados utilizados englobam os anos de 2006 a 2010, com preços intra-diários para as ações do Ibovespa. As ferramentas utilizadas para seleção dos pares e simulação de operação no mercado foram MATLAB (seleção) e Streambase (operação). A seleção foi feita através do Teste de Dickey-Fuller aumentado aplicado no MATLAB para verificar a existência da raiz unitária dos resíduos da combinação linear entre os preços das ações que compõem cada par. A operação foi feita através de back-testing com os dados intra-diários mencionados. Dentro do intervalo testado, a estratégia mostrou-se rentável para os anos de 2006, 2007 e 2010 (com retornos acima da Selic). Os parâmetros calibrados para o primeiro mês de 2006 puderam ser aplicados com sucesso para o restante do intervalo (retorno de Selic + 5,8% no ano de 2006), para 2007, onde o retorno foi bastante próximo da Selic e para 2010, com retorno de Selic + 10,8%. Nos anos de maior volatilidade (2008 e 2009), os testes com os mesmos parâmetros de 2006 apresentaram perdas, mostrando que a estratégia é fortemente impactada pela volatilidade dos retornos dos preços das ações. Este comportamento sugere que, numa operação real, os parâmetros devem ser calibrados periodicamente, com o objetivo de adaptá-los aos cenários mais voláteis.

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Qualquer dúvida, não hesite em nos contatar. (11) 3799-7732. Atenciosamente, Isabele Garcia on 2018-07-11T20:16:39Z (GMT) / Submitted by Brendan Anson Pritchard (bpanson@gmail.com) on 2018-07-11T20:55:03Z No. of bitstreams: 1 Dissertation-BrendanAnsonV9-1.pdf: 1286517 bytes, checksum: bfafb586060f6c84a656ffa94abe7cae (MD5) / Approved for entry into archive by Simone de Andrade Lopes Pires (simone.lopes@fgv.br) on 2018-07-11T21:06:20Z (GMT) No. of bitstreams: 1 Dissertation-BrendanAnsonV9-1.pdf: 1286517 bytes, checksum: bfafb586060f6c84a656ffa94abe7cae (MD5) / Approved for entry into archive by Isabele Garcia (isabele.garcia@fgv.br) on 2018-07-11T21:20:32Z (GMT) No. of bitstreams: 1 Dissertation-BrendanAnsonV9-1.pdf: 1286517 bytes, checksum: bfafb586060f6c84a656ffa94abe7cae (MD5) / Made available in DSpace on 2018-07-11T21:20:32Z (GMT). No. of bitstreams: 1 Dissertation-BrendanAnsonV9-1.pdf: 1286517 bytes, checksum: bfafb586060f6c84a656ffa94abe7cae (MD5) Previous issue date: 2018-05-29 / The study examines the risk and reward potential of arbitrage in the digital asset market. Specifically, it looks at exchange to exchange and statistical arbitrage, or pairs trading, for the cryptocurrencies, Bitcoin (BTC) and Litecoin (LTC). In this instance they are traded on the LTC/BTC pair. The LTC/BTC is examined with pairs trading by performing statistical tests and implementing automated trading strategy to determine potential profit levels. Subsequently, additional trading strategies are examined based on the concepts of the statistical results in this study and other technical analysis indicators. The study outlines the profit potential of exchange to exchange arbitrage but also shows how this type of arbitrage is in fact quite risky and not as simple as the large spreads would suggest. Pairs trading strategies are instead put forward as a method of profiting on the price movement disparities in the digital asset market without running the same risks as exchange to exchange arbitrage. The strategies proposed are based on statistical tests as well as technical analysis indicators that both aim at predicting price trend and direction and try to profit off abnormal price movements and subsequent normalization. It turns out that a range of profit levels can be achieved. All though the strategies proposed are too rudimentary to consider for live trading, they do prove the basic proof of concept that there are ways to profit from pairs trading in the digital asset market. Trading strategies can be formed that provide considerable returns while reducing risk that would otherwise be encountered with long term investment positions and/or exchange to exchange arbitrage in the digital asset market. / O seguinte estudo examina o potencial de risco e recompensa de arbitragem no mercado de ativos digitais. Especificamente, analisa a arbitragem entre bolsas de cryptomoeda e arbitragem estatística, ou pairs trading, para as cryptomoedas, Bitcoin (BTC) e Litecoin (LTC). Neste caso, elas são negociadas no par LTC/BTC. O LTC/BTC é examinado em pares e negociadas por meio da realização de testes estatísticos e implementando a estratégia de negociação automatizada para determinar os níveis potenciais de lucro. Subsequentemente, estratégias adicionais de negociação são examinadas com base nos conceitos dos resultados estatísticos deste estudo e outros indicadores de análise técnica. O estudo delineia o potencial de lucro de arbitragem entre bolsas, mas também mostra como esse tipo de arbitragem é, na verdade, bastante arriscado e não tão simples quanto as grandes margens sugeririam. Estratégias de negociação em pares são apresentadas como um método de lucrar com as disparidades de movimento de preços no mercado de ativos digitais, sem correr os mesmos riscos que a troca por arbitragem de câmbio. As estratégias propostas baseiam-se em testes estatísticos, assim como em indicadores de análise técnica que visam prever a direção e a tendência do preço e tentar lucrar com movimentos ou tempos anormais de preços e normalização subsequente. Ficou comprovado que diferentes de níveis de lucro podem ser alcançados. Embora as estratégias propostas sejam rudimentares demais para serem consideradas para negociação com dinheiro vivo, elas provam o conceito básico de que existem maneiras de lucrar com a negociação de pares no mercado de ativos digitais. Estratégias de negociação podem ser formadas, proporcionando retornos consideráveis e, ao mesmo tempo, reduzindo o risco de que outra forma seja encontrada em posições de investimento de longo prazo e / ou em troca de arbitragem de câmbio no mercado de ativos digitais.

配對交易策略為一被廣為使用的交易策略，其特性為使用數個關聯性高的資產同時建立多空部位，藉此消除大部分的市場風險，賺取與市場趨勢無關聯性的報酬；本研究欲探討共整合法配對交易策略應用於兩類標的資產上之可行性及其功效:台灣證券交易所掛牌的6檔陸股ETF、以及COMEX黃金期貨與CME日幣期貨之組合。本研究使用之配對交易策略應用於6檔陸股ETF大部分參數設定下可獲得正報酬，獲利性卻不如預期，且共整合性質較佳之配對無法保證其交易績效亦較佳；COMEX黃金期貨及CME日幣期貨雖相對共整合性質不佳，仍以原策略測試可獲得較優秀的績效，此結果顯示共整合法配對交易策略於兩類資產上可行性皆不高，而配對交易策略於黃金、日幣組合上可能仍有其功效，尚須以不同方法進行驗證。 / Pairs trading strategy is one kind of market neutral strategy which take both long and short positions in two or more highly correlated assets. By doing this pairs trading strategy can eliminate market risk and make profits which are not correlated with market trends. This paper aims to figure out if pairs trading strategy work well on China ETFs listed in TWSE and the COMEX gold-CME yen future pair. We use the cointegration approach to test and simulate trading performance on the securities mentioned. The result shows that pairs trading strategy profit on China ETFs under most of the parameters, but the returns are insufficient. Furthermore, good cointegration property in the input periods can’t guarantee better performances in the outputs periods. For COMEX gold future and CME yen future, cointegration property in the input periods are worse than China ETFs, but using the same strategy we find a more profitable outcome. The empirical result indicate that pairs trading strategy might still work on gold and yen, but the cointegration approach is not suitable for these two groups of assets.

<p dir="ltr">Statistical arbitrage is a prevalent trading strategy which takes advantage of mean reverse property of spreads constructed from pairs or portfolios of assets. Utilizing statistical models and algorithms, statistical arbitrage exploits and capitalizes on the pricing inefficiencies between securities or within asset portfolios. </p><p dir="ltr">In chapter 2, We propose a framework for constructing diversified portfolios with multiple pairs trading strategies. In our approach, several pairs of co-moving assets are traded simultaneously, and capital is dynamically allocated among different pairs based on the statistical characteristics of the historical spreads. This allows us to further consider various portfolio designs and rebalancing strategies. Working with empirical data, our experiments suggest the significant benefits of diversification within our proposed framework.</p><p dir="ltr">In chapter 3, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and subsequently liquidating positions, all while considering the impact of transaction costs. Then we leverages a refined signature optimal stopping method to resolve this sequential optimal stopping problem, thereby unveiling the precise entry and exit timings that maximize gains. Our framework operates without any predefined assumptions regarding the dynamics of the underlying mean-reverting spreads, offering adaptability to diverse scenarios. Numerical results are provided to demonstrate its superior performance when comparing with conventional mean reversion trading rules.</p><p dir="ltr">In chapter 4, we introduce an innovative model-free and reinforcement learning based framework for statistical arbitrage. For the construction of mean reversion spreads, we establish an empirical reversion time metric and optimize asset coefficients by minimizing this empirical mean reversion time. In the trading phase, we employ a reinforcement learning framework to identify the optimal mean reversion strategy. Diverging from traditional mean reversion strategies that primarily focus on price deviations from a long-term mean, our methodology creatively constructs the state space to encapsulate the recent trends in price movements. Additionally, the reward function is carefully tailored to reflect the unique characteristics of mean reversion trading.</p>