Cointegration in Forex Pairs Trading.
Cointegration na troca de pares forex é uma ferramenta valiosa. Para mim, a cointegração é a base para uma excelente estratégia de negociação mecânica neutra do mercado que me permite lucrar em qualquer ambiente econômico. Se um mercado está em uma tendência de alta, tendência de baixa ou simplesmente se movendo de lado, a negociação de pares de divisas me permite colher ganhos durante todo o ano.
Uma estratégia de negociação de pares forex que utiliza cointegração é classificada como uma forma de negociação de convergência com base em arbitragem estatística e reversão para significar. Este tipo de estratégia foi popularizado por uma equipe de negociação quantitativa no Morgan Stanley na década de 1980, usando pares de ações, embora eu e outros comerciantes descobrirem que também funciona muito bem para negociação de pares de forex também.
Negociação de pares de Forex com base na cointegração.
O comércio de pares de Forex com base na cointegração é essencialmente uma estratégia de reversão para média. Declarado simplesmente, quando dois ou mais pares forex são cointegrados, significa que o spread de preços entre os pares de divisas separados tende a reverter ao seu valor médio consistentemente ao longo do tempo.
É importante entender que a cointegração não é correlação. A correlação é uma relação de curto prazo em relação a co-movimentos de preços. A correlação significa que os preços individuais se movem juntos. Embora a correlação seja dependente de alguns comerciantes, por si só é uma ferramenta não confiável.
Por outro lado, a cointegração é um relacionamento de longo prazo com co-movimentos de preços, nos quais os preços se movem juntos, mesmo dentro de certos intervalos ou spreads, como se estivessem amarrados. Descobri que a cointegração era uma ferramenta muito útil na troca de pares de forex.
Durante a minha troca de pares forex, quando o spread se alarga para um valor limiar calculado pelos meus algoritmos de negociação mecânica, eu "curto" o spread entre os preços dos pares. Em outras palavras, eu aposto que o spread reverterá em direção a zero devido à sua cointegração.
As estratégias básicas de negociação de pares de forex são muito simples, especialmente quando se utilizam sistemas de negociação mecânica: escolho dois pares de moedas diferentes que tendem a se mover de forma semelhante. Compre o par de moedas insuficientes e venda o par de desempenho. Quando a propagação entre os dois pares converge, eu fechar minha posição com lucro.
A troca de pares de Forex com base na co-integração é uma estratégia razoavelmente neutra para o mercado. Como exemplo, se um par de moedas cair, o comércio provavelmente resultará em uma perda no lado longo e um ganho compensatório no lado curto. Assim, a menos que todas as moedas e instrumentos subjacentes subitamente percam valor, o comércio líquido deve ser próximo de zero no pior cenário.
Do mesmo jeito, as negociações de pares em muitos mercados são uma estratégia de negociação de autofinanciamento, uma vez que o produto de vendas curtas às vezes pode ser usado para abrir a posição longa. Mesmo sem esse benefício, a troca de pares de divisas com cointegração ainda funciona muito bem.
Entendendo a co-integração para negociação de pares forex.
Cointegration é útil para mim na troca de pares forex porque me permite programar meu sistema de negociação mecânica com base em desvios de curto prazo dos preços de equilíbrio, bem como expectativas de preços a longo prazo, pelo que quero dizer correções e retorno ao equilíbrio.
Para entender como a negociação de negociação de pares de divisas orientadas pela cointegração, é importante primeiro definir a cointegração e depois descrever como ela funciona em sistemas de negociação mecânica.
Como eu disse acima, a cointegração refere-se à relação de equilíbrio entre conjuntos de séries temporais, como os preços de pares de divisas separados que, por si só, não estão em equilíbrio. Declarado no jargão matemático, a cointegração é uma técnica para medir a relação entre variáveis ​​não estacionárias em uma série temporal.
Se duas ou mais séries temporais tiverem um valor de raiz igual a 1, mas sua combinação linear é estacionária, então é dito que estão cointegradas.
Como um exemplo simples, considere os preços de um índice de bolsa e seu contrato de futuros relacionado: embora os preços de cada um desses dois instrumentos possam vagar aleatoriamente em breves períodos de tempo, eles retornarão ao equilíbrio e seus desvios serão estacionário.
Aqui está outra ilustração, declarada em termos do exemplo clássico de "caminhada aleatória": digamos que há dois bêbados individuais caminhando para casa depois de uma noite de carousing. Vamos continuar a assumir que esses dois bêbados não se conhecem, então não há uma relação previsível entre seus caminhos individuais. Portanto, não há cointegração entre seus movimentos.
Em contraste, considere a idéia de que um bêbado individual está vagando para casa enquanto acompanha seu cão em uma coleira. Neste caso, há uma conexão definitiva entre os caminhos dessas duas criaturas pobres.
Embora cada um dos dois ainda esteja em um percurso individual durante um curto período de tempo, e mesmo que um dos pares possa aleatoriamente levar ou atrasar o outro em qualquer ponto no tempo, ainda assim, eles sempre serão encontrados juntos. A distância entre eles é bastante previsível, pelo que o par é considerado cointegrado.
Voltando agora a termos técnicos, se houver duas séries temporais não estacionárias, como um conjunto hipotético de pares de moeda AB e XY, que se tornam estacionários quando a diferença entre eles é calculada, esses pares são chamados de série de primeira ordem integrada - também ligue para uma série I (1).
Mesmo que nenhuma dessas séries permaneça em um valor constante, se houver uma combinação linear de AB e XY estacionada (descrita como I (0)), então AB e XY são cointegradas.
O exemplo simples acima consiste em apenas duas séries temporais de pares de forex hipotéticos. No entanto, o conceito de cointegração também se aplica a séries temporais múltiplas, usando ordens de integração mais altas ... Pense em termos de um bêbado errante acompanhado por vários cães, cada um em uma coleira de comprimento diferente.
Na economia do mundo real, é fácil encontrar exemplos que mostrem cointegração de pares: renda e gastos, ou a dureza das leis criminais e o tamanho da população prisional. Na troca de pares forex, meu foco é capitalizar a relação quantitativa e previsível entre pares de moedas cointegradas.
Por exemplo, vamos assumir que estou assistindo esses dois pares de moeda hipotéticos cointegrados, AB e XY, e a relação cointegrada entre eles é AB & # 8211; XY = Z, onde Z é igual a uma série estacionária com uma média de zero, isto é, eu (0).
Isso parece sugerir uma estratégia de negociação simples: quando AB - XY & gt; V e V é o meu preço de gatilho limiar, então o sistema de negociação de pares forex venderia AB e compraria XY, uma vez que a expectativa seria AB para diminuir o preço e XY para aumentar. Ou, quando AB-XY & lt; - V, eu esperaria comprar AB e vender XY.
Evite a regressão espúria na troca de pares forex.
No entanto, não é tão simples como sugeriria o exemplo acima. Na prática, um sistema de negociação mecânica para troca de pares de forex precisa calcular a cointegração em vez de apenas confiar no valor R-quadrado entre AB e XY.
Isso ocorre porque a análise de regressão normal é baixa ao lidar com variáveis ​​não estacionárias. Provoca a chamada regressão espúria, o que sugere relacionamentos entre variáveis, mesmo quando não existe.
Suponhamos, por exemplo, que eu regredisse 2 séries temporais de "caminhada aleatória" separadas uma contra a outra. Quando eu teste para ver se há uma relação linear, muitas vezes eu vou encontrar valores altos para R-quadrado, bem como baixos valores de p. Ainda assim, não há relacionamento entre esses 2 passeios aleatórios.
Fórmulas e testes para cointegração na negociação de pares forex.
O teste mais simples para cointegração é o teste de Engle-Granger, que funciona assim:
Verifique que AB t e XY t sejam ambos I (1) Calcule a relação de cointegração [XY t = aAB t + et] usando o método de mínimos quadrados Verifique se os resíduos de cointegração e estão estacionários usando um teste de raiz de unidade como o Teste avaliado Dickey-Fuller (ADF).
Uma equação Granger detalhada:
I (0) descreve a relação de cointegração.
XY t-1 - βAB t-1 descreve a extensão do desequilíbrio longe do longo prazo, enquanto αi é tanto a velocidade como a direção em que a série temporal do par de moedas se corrige do desequilíbrio.
Ao usar o método Engle-Granger na negociação de pares forex, os valores beta da regressão são usados ​​para calcular os tamanhos comerciais para os pares.
Ao usar o método Engle-Granger na negociação de pares forex, os valores beta da regressão são usados ​​para calcular os tamanhos comerciais para os pares.
Correção de erros para cointegração em troca de pares forex:
Ao usar cointegração para negociação de pares de divisas, também é útil explicar como as variáveis ​​cointegradas se ajustam e retornam ao equilíbrio de longo prazo. Então, por exemplo, aqui estão as duas séries temporais de pares de forex mostrados de forma autoregressiva:
Negociação de pares de Forex com base na cointegração.
Quando uso o meu sistema de negociação mecânica para negociação de pares de divisas, a configuração e a execução são bastante simples. Primeiro, acho dois pares de moedas que parecem ser cointegradas, como EUR / USD e GBP / USD.
Então, eu calculo os spreads estimados entre os dois pares. Em seguida, eu verificar a estacionaridade usando um teste de raiz unitária ou outro método comum.
Tenho certeza de que meu feed de dados de entrada está funcionando adequadamente, e eu deixo meus algoritmos de negociação mecânica criar os sinais comerciais. Supondo que eu tenha executado back-tests adequados para confirmar os parâmetros, finalmente estou pronto para usar cointegração na minha troca de pares forex.
Encontrei um indicador MetaTrader que oferece um excelente ponto de partida para construir um sistema de negociação de pares de divisas de cointegração. Parece um indicador Bollinger Band, no entanto, o oscilador mostra o diferencial de preços entre os dois pares de moedas diferentes.
Quando este oscilador se move em direção ao extremo alto ou baixo, indica que os pares estão se desacoplando, o que sinaliza os negócios.
Ainda assim, para ter certeza de sucesso, confio no meu sistema de comércio mecânico bem construído para filtrar os sinais com o teste Augmented Dickey-Fuller antes de executar os negócios apropriados.
Claro, qualquer pessoa que queira usar cointegração para a negociação de pares forex, ainda que não tenha as necessárias habilidades de programação, pode contar com um programador experiente para criar um consultor especialista vencedor.
Através da magia da negociação algorítmica, programo meu sistema de negociação mecânica para definir os spreads de preços com base na análise de dados. Meu algoritmo monitora os desvios de preços, então compra e vende automaticamente pares de moedas para reduzir as ineficiências do mercado.
Riscos a ter em conta ao usar cointegração com troca de pares forex.
O comércio de pares de Forex não é totalmente livre de riscos. Acima de tudo, eu tenho em mente que a negociação de pares forex usando a cointegração é uma estratégia de reversão média, que se baseia no pressuposto de que os valores médios serão os mesmos no futuro como eram no passado.
Embora o teste Augmented Dickey-Fuller mencionado anteriormente seja útil na validação das relações cointegradas para o comércio de pares de forex, isso não significa que os spreads continuarão a ser cointegrados no futuro.
Confio em fortes regras de gerenciamento de risco, o que significa que meu sistema de negociação mecânica sai de negociações não lucrativas se ou quando a reversão-a-média calculada é invalidada.
Quando os valores médios mudam, é chamado de deriva. Eu tento detectar a deriva o mais rápido possível. Em outras palavras, se os preços dos pares Forex previamente cointegrados começam a se mover em uma tendência em vez de reverter para a média previamente calculada, é hora de os algoritmos do meu sistema de negociação mecânica recalcular os valores.
Quando uso o meu sistema de negociação mecânica para negociação de pares de divisas, uso a fórmula autorregressiva mencionada anteriormente neste artigo para calcular uma média móvel para prever o spread. Então, eu saio do comércio em meus limites de erro calculados.
Cointegration é uma ferramenta valiosa para minha troca de pares forex.
O uso da cointegração na negociação de pares forex é uma estratégia de negociação mecânica neutra do mercado que me permite negociar em qualquer ambiente de mercado. É uma estratégia inteligente que se baseia na reversão, mas isso me ajuda a evitar as armadilhas de algumas das outras estratégias de negociação forex de reversão para média.
Devido ao seu uso potencial em sistemas de negociação mecânica rentáveis, a cointegração para troca de pares de divisas atraiu o interesse tanto de comerciantes profissionais como de pesquisadores acadêmicos.
Há muitos artigos recentemente publicados, como esse artigo de blog focado em quantos, ou essa discussão acadêmica sobre o assunto, bem como uma grande discussão entre os comerciantes.
Cointegration é uma ferramenta valiosa no meu comércio de pares forex, e eu recomendo que você olhe para ele mesmo.
Diz Tommaso Sillian.
Muito bom artigo. É inspirador. Obrigado por escrevê-lo!
Harish Nachnani diz.
A correlação também é aplicada em ações (ações). Qual é a diferença? O processo acima pode ser aplicado às ações?
Eddie Flower diz.
Sim, o mesmo processo pode ser aplicado aos estoques, bem como aos derivados. Uma vez que existe um grande universo de estoques em comparação com os pares de divisas, deve haver uma maior quantidade de oportunidades potenciais para negociação. Com o poder de cruzamento dos sistemas comerciais de hoje, muitos conjuntos de relacionamentos podem ser examinados rapidamente, em tempo real. Cointegration também pode ser usado por comerciantes de opções; pode-se esperar que produza resultados como os populares spreads da Coca Cola-Pepsi, nos quais as relações de preços entre certos estoques / opções permitem que os comerciantes se envolvam em jogos de baixo risco com uma boa chance de ganhar.
Harish Nachnani diz.
Você troca intra dia ou durante semanas usando esta estratégia? Além disso, que linguagem de programação você recomendaria. R leva tempo para executar cálculos e se é comércio intra-dia, a latência entra em jogo.
A linguagem de programação não é importante para o comércio no final do dia. Qualquer linguagem importante como Perl, Python, C / C ++ e C # está bem. R pode ser extremamente rápido, mas retarda se for forçado a alocar dinamicamente a memória.
Eu troco usando gráficos diários, e eu permaneço na maioria dos negócios por alguns dias para algumas semanas. Shaun é um programador experiente, e sempre confio no seu julgamento para usar a melhor linguagem de programação para obter os melhores resultados para uma determinada estratégia de negociação. Na verdade, Shaun pode criar um programa bem equilibrado e vencedor para alavancar a co-integração e outros fatores também. Se você gostou de uma citação, entre em contato com ele diretamente em infoonestepremoved.
Chris Zimmer diz.
Existe algum interesse em uma implementação deste para o MT4. Se você pode fornecer algumas especificações sobre a implementação desta estratégia no código, envie para czimmeronestepremoved.
Estou fazendo um pequeno projeto sobre estratégias de co-integração no FX para meu mestrado. Eu acredito que você executou testes de cointegração em muitos pares de moedas. Quais as quais você achou ser estatisticamente significativamente cointegrado?
Eu não acho que Eddie realmente correu os números. O artigo pretende ser um guia geral para o conceito, mas não é o ponto de ser uma estratégia de boa-fé.
1) USD / JPY e EUR / CHF.
2) EUR / PLN e EUR / HUF.
3) USD / TRY e USD / ZAR.
4) AUD / USD e NZD / USD.
5) EUR / NOK e EUR / SEK.
Eu sei que estes estão bastante correlacionados, mas isso não significa cointegração.
Camilo Romero diz.
Existem bons pares de forex cointegrados:
Eu não acho que USDJPY / EURCHF seja um par cointegrado porque não haverá uma estratégia neutra do mercado.
Obrigado por compartilhar.
Camilo Romero diz.
Alguém implementou um código de retorno usando a estratégia de reversão média?
Eu deveria ajustar os valores do pip entre dois pares de divisas?
Alguém adicionou custo de comissão ao código de retorno e obteve resultados lucrativos?
Tenho certeza de que alguém tem, mas não é algo em que você encontrará uma resposta óbvia em gráficos de curto prazo. Você pode encontrar cointegrações de longo prazo, mas a pesquisa não foi feita pela I & # 8217;
A única cointegração é entre EUR e CHF e entre AUD e NZD, uma vez que o único comércio e economia íntima entre esses países e os bancos centrais estão criando essa cointegração.
Não EUR e GBP?
Robert J Armagost diz.
Olá Eddie. Excelente artigo. Voltei a testar 10 anos de gráficos pensando e # 8221; Eu não posso ser a primeira pessoa a ter pensado nisso! & # 8221; quando encontrei este site. Muito obrigado por escrever isso. Eu não me sinto tão sozinho. 🙂 Apenas me perguntando qual corretor você usa ou você usa vários corretores. Obrigado pelo seu tempo.
Sinceramente Robert J. Armagost.
O corretor principal que eu uso é Pepperstone e STO (via TopTradr).
Olá Shaun eu tenho negociado esta estratégia manualmente. Tem software para automatizar isso? (Então, eu não tenho mais que acordar no meio da noite) Obrigado pelo seu tempo.
Não fora da prateleira, mas é algo que podemos construir. Me tire um email com suas regras de entrada e saída para obter uma estimativa. infoonestepremoved.
Robert & # 8212; Obrigado pelo seu bom feedback. Shaun tem as ferramentas certas para implementar este tipo de estratégia de negociação, e eu concordo inteiramente com as recomendações do corretor, Agradeço novamente por comentar! EF.

Análise da série de tempo Cointegrated para negociação de reversão média com R.
Análise da série de tempo Cointegrated para negociação de reversão média com R.
Um tempo atrás, consideramos um modelo de negociação baseado na aplicação dos modelos da série temporal ARIMA e GARCH aos dados diários S & amp; P500. Mencionamos nesse artigo, bem como em outros artigos anteriores de análises de séries temporais, que eventualmente considerariamos as estratégias de negociação de reversão e a forma de construí-los.
Neste artigo, eu quero discutir um tópico chamado cointegração, que é um conceito de séries temporais que nos permite determinar se conseguimos formar um meio de reversão de ativos. Vamos abordar a teoria das séries temporais relacionadas à cointegração aqui e no próximo artigo, vamos mostrar como aplicar isso às estratégias comerciais reais usando a nova estrutura de backtesting de código aberto: QSTrader.
Vamos prosseguir discutindo a reversão média na tradicional estrutura de "negociação de pares". Isso nos levará ao conceito de estacionariedade de uma combinação linear de ativos, levando-nos finalmente a cointegração e testes de raiz unitária. Uma vez que esboçamos esses testes, simularemos várias séries temporais no ambiente estatístico R e aplicaremos os testes para avaliar a cointegração.
Estratégias de negociação de reversão média.
A idéia tradicional de um "comércio de pares" de reversão média é simultaneamente curtos e curtos dois ativos separados compartilhando fatores subjacentes que afetam seus movimentos. Um exemplo do mundo das ações pode ser longo McDonald's (NYSE: MCD) e Short Burger King (NYSE: BKW - antes da fusão com Tim Horton).
A razão para isso é que os preços das ações a longo prazo provavelmente estarão em equilíbrio devido aos amplos fatores do mercado que afetam a produção e o consumo de hambúrgueres. Uma interrupção de curto prazo para um indivíduo no par, como uma interrupção da cadeia de suprimentos que afete apenas o McDonald's, levaria a uma deslocação temporária em seus preços relativos. Isso significa que um comércio longo-curto realizado neste ponto de interrupção deve se tornar rentável, pois os dois estoques retornam ao seu valor de equilíbrio uma vez que a interrupção é resolvida. Esta é a essência do clássico "comércio de pares".
Na medida em que estamos interessados ​​em realizar a negociação de reversão média não apenas em um par de ativos, mas também cestas de ativos que estão separadamente interligados.
Para conseguir isso, precisamos de uma estrutura matemática robusta para identificar pares ou cestas de ativos que significam reverter da maneira descrita acima. É aqui que surge o conceito de séries de tempo cointegradas.
A idéia é considerar um par de séries temporais não estacionárias, como os ativos de MCD e BKW de forma aleatória, e formar uma combinação linear de cada série para produzir uma série estacionária, que tem uma média e variância fixas.
Esta série estacionária pode ter interrupções de curto prazo onde o valor vagueia longe da média, mas devido à sua estacionaridade, este valor retornará eventualmente à média. As estratégias de negociação podem fazer uso disso aniquilando / diminuindo o par no ponto de interrupção apropriado e apostando em uma reversão de longo prazo da série para sua média.
As estratégias de reversão médias, como esta, permitem uma ampla gama de instrumentos para criar as séries de tempo estacionárias "sintéticas". Certamente, não estamos restritos a ações de "baunilha". Por exemplo, podemos fazer uso do Exchange Traded Funds (ETF) que acompanha os preços das commodities, como petróleo bruto e cestas de empresas produtoras de petróleo. Portanto, há muitos marcos para identificar tais sistemas de reversão significativos.
Antes de aprofundar a mecânica das estratégias de negociação reais, que serão objeto do próximo artigo, devemos primeiro entender como identificar estatisticamente tais séries cointegradas. Para isso, utilizaremos técnicas da análise de séries temporais, continuando o uso da linguagem estatística R como em artigos anteriores sobre o tema.
Cointegração.
Agora que motivamos a necessidade de um quadro quantitativo para realizar a negociação média de reversão, podemos definir o conceito de cointegração. Considere um par de séries temporais, ambas não-estacionárias. Se tomarmos uma combinação linear específica dessas séries, às vezes pode levar a uma série estacionária. Esse par de séries seria então denominado cointegrado.
A definição matemática é dada por:
Cointegração.
Deixe $ \ $ e $ \ $ ser duas séries temporais não estacionárias, com constantes $ a, b \ in \ mathbb $, constantes. Se a série combinada $ a x_t + b y_t $ estiver estacionada, dizemos que $ \ $ e $ \ $ são cointegrados.
Embora a definição seja útil, não nos fornece diretamente um mecanismo para determinar os valores de $ a $ e $ b $, nem se essa combinação é, de fato, estatisticamente estacionária. Para este último, precisamos utilizar testes para raízes unitárias.
Teste de raiz unitária.
Em nossa discussão anterior de modelos de AR (p) autorregressivos, explicamos o papel da equação característica. Observamos que era simplesmente um modelo autorregressivo, escrito em forma de mudança para trás, definido como igual a zero. Resolver esta equação nos deu um conjunto de raízes.
Para que o modelo seja considerado estacionário, todas as raízes da equação devem exceder a unidade. Um modelo AR (p) com uma raiz igual à unidade - uma unidade raiz - não é estacionário. Os passeios aleatórios são processos AR (1) com raízes unitárias e, portanto, também não são estacionários.
Assim, para detectar se uma série temporal é estacionária ou não, podemos construir um teste de hipóteses estatísticas para a presença de uma unidade de raiz em uma série de séries temporais.
Vamos considerar três testes separados para as raízes das unidades: Augmented Dickey-Fuller (AFD), Phillips-Perron e Phillips-Ouliaris. Veremos que eles são baseados em suposições diferentes, mas todos estão testando o mesmo problema, a saber, a estacionaria da amostra da série de tempo testada.
Vamos agora dar uma breve olhada nos três testes, por sua vez.
Teste Dickey-Fuller aumentado.
Dickey e Fuller [2] foram responsáveis ​​por apresentar o seguinte teste para a presença de uma unidade de raiz. O teste original considera uma série temporal $ z_t = \ alpha z_ + w_t $, em que $ w_t $ é ruído branco discreto. A hipótese nula é que $ \ alpha = 1 $, enquanto a hipótese alternativa é que $ \ alpha & lt; 1 $.
Disse e Dickey [6] melhoraram o teste Dickey-Fuller original levando ao teste Augmented Dickey-Fuller (ADF), no qual a série $ z_t $ é modificada para um modelo AR (p) de um modelo AR (1). Eu discuti o teste em um artigo anterior onde usamos o Python para calculá-lo. Neste artigo, realizaremos o mesmo teste usando R.
Teste Phillips-Perron.
O teste ADF assume um modelo AR (p) como uma aproximação para o exemplo da série temporal e usa isso para contabilizar as autocorrelações de ordem superior. O teste Phillips-Perron [5] não assume uma aproximação do modelo AR (p). Em vez disso, um método de suavização de kernel não paramétrico é utilizado no processo estacionário $ w_t $, o que permite que ele contabilize autocorrelação não especificada e heterocedasticidade.
Teste de Phillips-Ouliaris.
O teste Phillips-Ouliaris [4] é diferente dos dois testes anteriores, na medida em que está testando a evidência de cointegração entre os resíduos entre duas séries temporais. A principal idéia aqui é que testes como ADF, quando aplicados aos resíduos estimados de cointegração, não possuem as distribuições Dickey-Fuller sob a hipótese nula onde a cointegração não está presente. Em vez disso, essas distribuições são conhecidas como distribuições de Phillips-Ouliaris e, portanto, esse teste é mais apropriado.
Dificuldades com testes de raiz unitária.
Enquanto o teste ADF e Phillips-Perron são equivalentes assintóticamente, eles podem produzir respostas muito diferentes em amostras finitas [7]. Isso ocorre porque eles lidam com autocorrelação e heterocedasticidade de forma diferente. É necessário ter muito claro quais hipóteses estão sendo testadas para a aplicação desses testes e não para simplesmente aplicá-los cegamente a séries arbitrárias.
Além disso, os testes de raiz unitária não são excelentes para distinguir processos estacionários altamente persistentes de processos não estacionários. É preciso ter muito cuidado ao usá-los em determinadas formas de séries temporais financeiras. Isso pode ser especialmente problemático quando a relação subjacente que está sendo modelada (ou seja, a reversão média de dois pares similares), naturalmente, desmorona devido a mudanças de regime ou outras mudanças estruturais nos mercados financeiros.
Simulated Cointegrated Time Series com R.
Vamos agora aplicar os testes de raiz de unidades anteriores a alguns dados simulados que sabemos ser cointegrados. Podemos usar a definição de cointegração para criar artificialmente duas séries temporais não estacionárias que compartilham uma tendência estocástica subjacente, mas com uma combinação linear estacionada.
Nossa primeira tarefa é definir uma caminhada aleatória $ z_t = z_ + w_t $, onde $ w_t $ é ruído branco discreto. Dê uma olhada no artigo anterior sobre ruídos brancos e passeios aleatórios, se você precisar escovar esses conceitos.
Com a caminhada aleatória $ z_t $ vamos criar duas novas séries temporais $ x_t $ e $ y_t $ que ambos compartilham a tendência estocástica subjacente de $ z_t $, embora por diferentes montantes:
\ begin x_t & = & p z_t + w_ \\ y_t & = & q z_t + w_ \ end.
Se nós, então, tomamos uma combinação linear $ a x_t + b y_t $:
\ begin a x_t + b y_t & = & a (p z_t + w_) + b (q z_t + w_) \\ & = & (ap + bq) z_t + a w_ + b w_ \ end.
Vemos que só conseguimos uma série estacionária (que é uma combinação de termos de ruído branco) se $ ap + bq = 0 $. Podemos colocar alguns números para isso, para torná-lo mais concreto. Suponha $ p = 0,3 $ e $ q = 0,6 $. Depois de uma álgebra simples, vemos que se $ a = 2 $ e $ b = -1 $ nós possuímos $ ap + bq = 0 $, levando a uma combinação de séries estacionárias. Daí $ x_t $ e $ y_t $ são cointegrados quando $ a = 2 $ e $ b = -1 $.
Vamos simular isso em R para visualizar a combinação estacionária. Em primeiro lugar, desejamos criar e traçar a série de caminhada aleatória subjacente, $ z_t $:
Realização de uma caminhada aleatória, $ z_t $
Se traçamos o correlograma da série e suas diferenças, podemos ver poucas evidências de autocorrelação:
Correlogramas de $ z_t $ e a série diferida de $ z_t $
Portanto, esta realização de $ z_t $ claramente parece uma caminhada aleatória. O próximo passo é criar $ x_t $ e $ y_t $ a partir de $ z_t $, usando $ p = 0,3 $ e $ q = 0,6 $ e, em seguida, trace ambos:
Lote de $ x_t $ e $ y_t $ series, cada um baseado na caminhada aleatória subjacente $ z_t $
Como você pode ver, ambos parecem semelhantes. Claro que eles serão por definição - eles compartilham a mesma estrutura de caminhada aleatória subjacente de $ z_t $. Vamos agora formar a combinação linear, pentear, usando $ p = 2 $ e $ q = -1 $ e examinar a estrutura de autocorrelação:
Lote de pente - a série de combinações lineares - e seu correlograma.
É claro que o pente de série combinado se parece muito com uma série estacionária. Isto é esperado dada a sua definição.
Vamos tentar aplicar os testes de raiz de três unidades para a série de combinações lineares. Em primeiro lugar, o teste Augmented Dickey-Fuller:
O valor p é pequeno e, portanto, temos evidências para rejeitar a hipótese nula de que a série possui uma unidade de raiz. Agora, tentamos o teste Phillips-Perron:
Mais uma vez, temos um pequeno valor de p e, portanto, temos evidências para rejeitar a hipótese nula de uma unidade de raiz. Finalmente, tentamos o teste Phillips-Ouliaris (note que requer entrada de matriz dos constituintes da série subjacente):
Mais uma vez, vemos um pequeno valor p que indica evidências para rejeitar a hipótese nula. Por isso, é claro que estamos lidando com um par de séries que estão cointegradas.
O que acontece se criarmos uma combinação separada com, digamos $ p = -1 $ e $ q = 2 $?
Parcela de badcomb - a série de combinação linear "incorreta" - e seu correlograma.
Nesse caso, não temos provas suficientes para rejeitar a hipótese nula da presença de uma raiz unitária, conforme determinado pelo valor p do teste Dickey-Fuller aumentado. Isso faz sentido quando escolhemos arbitrariamente a combinação linear de $ a $ e $ b $ ao invés de configurá-los para os valores corretos de $ p = 2 $ e $ b = -1 $ para formar uma série estacionária.
Próximos passos.
Neste artigo, examinamos vários testes de raiz unitária para avaliar se uma combinação linear de séries temporais era estacionária, ou seja, se as duas séries estavam cointegradas.
Em futuros artigos, vamos considerar as implementações completas das estratégias de negociação de reversão média para as ações diárias e os dados dos ETF usando o QSTrader com base nestes testes de cointegração.
Além disso, expandiremos nossa análise para cointegração em mais de dois ativos, levando a estratégias de negociação que aproveitam as carteiras cointegradas.
Referências.
A Quantcademy.
Junte-se ao portal de adesão da Quantcademy que atende à comunidade de comerciantes de varejo de varejo em rápido crescimento e saiba como aumentar a rentabilidade da sua estratégia.
Comércio Algoritmo bem sucedido.
Como encontrar novas ideias de estratégia de negociação e avaliá-las objetivamente para seu portfólio usando um mecanismo de backtesting personalizado em Python.
Negociação Algorítmica Avançada.
Como implementar estratégias de negociação avançadas usando análise de séries temporais, aprendizado de máquinas e estatísticas bayesianas com R e Python.

Forex Mecânico.
Negociação no mercado FX usando estratégias mecânicas de negociação.
Cointegration no mercado Forex.
A partir dos diferentes tipos de arbitragem estatística disponível, o comércio de pares é talvez um dos mais populares. Em pares, a negociação de um comerciante tentará explorar a relação linear entre os valores de dois instrumentos, tentando comprá-los / vendê-los quando a relação entre seus valores aumentar / diminuir para valores que ofereçam potencial de lucro suficiente. No entanto, a negociação de pares não exige apenas uma correlação linear, mas também exige que os instrumentos sejam cointegrados, uma propriedade fundamental que assegura uma conexão fundamental entre os instrumentos que diminui a probabilidade de propagação entre os dois instrumentos # 8220; explodindo e # 8221; (ampliando muito além do que é esperado estatisticamente). Embora o comércio de pares seja geralmente descrito em ações / commodities, raramente vemos algum estudo de cointegração no mercado FX. Hoje, vamos analisar algumas cointegrações potenciais no mercado FX, por que elas existem e como elas podem ser exploradas.
Comecemos por definir o que queremos dizer por cointegração. Duas séries são cointegradas quando compartilham uma deriva estocástica comum. O exemplo típico para explicar a cointegração fala sobre um homem que vai a um bar com seu cachorro. Depois de ficar bêbado e deixar o bar, tanto o homem quanto o cão caminham pelo mesmo caminho para casa, embora sua deriva estocástica e # 8211; qual é o modo aleatório em que o homem caminha e o cachorro se pergunta ao longo do caminho; são diferentes. Quando isso acontece, seus caminhos estão de fato correlacionados, mas não estão cointegrados. If the man instead decides to put a leash on the dog their paths become cointegrated because they now share a common stochastic drift that is determined by the length of the leash. The man and the dog cannot be separated further than their leash allows, which makes any random movements they make beyond a certain length common to both (as they would pull on each other). In statistics we can evaluate for cointegration using several different tests from which theВ Augmented Dickey-Fuller (ADF) test is most popularly used. Note that this test evaluates only stationarity – not exactly cointegration – so another test such as a Johansen test is necessary to confirm cointegration.
When looking at classic examples of cointegration in financial time series you’ll notice that instruments that are cointegrated generally have some strong fundamental reasons to be cointegrated. The “leash” is a fundamental relationship between both instruments, their common stochastic drift. This relationship is usually very strong, for example two oil producing companies that share refineries in broadly the same countries and have the same clients, they are so tightly put together that it is very improbable for any random event to affect one without affecting the other. This is what makes deviations so tantalizing to exploit. В In Forex however, the story is a bit different because countries have a very hard time being so fundamentally similar.
You can actually see this easily when you look at the last year of data for several FX pairs that we usually view as correlated. For example the EUR/USD and GBP/USD traditionally have a large correlation. A normalized plot showing the last year of data shows you that both pairs indeed tend to move in the same direction but it is clear that this relationship does not follow the same stochastic drift. An ADF test using the last year of data for these two pairs will give you a value of 0.28 which is simply far too large to reject the null hypothesis. Looking at other similar pairs reveals very similar results, pairs like AUDUSD|NZDUSD – which are even more correlated than the EURUSD|GBPUSD turn out to also not be cointegrated.
So are there any cointegrations in the FX market? Actually the answer is yes. The Swiss National Bank’s decision to create a floor on the EURCHF at 1.20 generated a “leash” that made several pairs share a stochastic drift. For example the EURUSD and the CHFUSD are now cointegrated due to this fact. An ADF test will give you a value less than 0.01 for this pair, suggesting that they are indeed cointegrated (confirmed by the Johansen test as well). All similar CHF containing pairs also show cointegrations, such as the EURJPY|CHFJPY and the EURAUD|AUDCHF. This cointegrations all arise from the EURCHF peg, something which is evident when you look at the spread value as a function of time between any of these pairs. The third image shows you the spread of the EURUSD|CHFUSD pair as a function of time, it is no surprise that this is the exact same graph as the EURCHF for the past year. As the length of the “leash” varies, so does the value of the spread on the cointegrated pairs.
Could we take advantage of these cointegrations? Well, you certainly can. There are several ways in which cointegration can be traded but with a varying “leash” a good way is probably to trade the bollinger bands around the spread. You can trade on any timeframes but even when trading the daily timeframe you can make some money. The fourth image shows a very simple simulation in R where I traded the 3 pairs mentioned above, using 1:10 leverage, on a 10 period moving average using 1 standard deviation for band distances. The simulations show a 25% profit with a 10% drawdown within the past year, not too great but not too bad either. It is possible that further refinements and entries/exits on lower timeframes can indeed increase these margins.
One important thing to remember here is that the leash is a peg from a central bank. If this peg for some reason stops existing it is possible that this cointegration will simply vanish. It is therefore advisable to keep an eye on fundamental developments and stop trading the cointegration if this arises. It is also important to constantly repeat the statistical tests for cointegration as new data comes in so that you can stop trading any of these pairs as soon as the cointegration does show to break. If you would like to learn more about FX trading and how you too can design your own trading strategiesВ please consider joiningВ Asirikuy, a website filled with educational videos, trading systems, development and a sound, honest and transparent approach towards automated trading in general . Espero que tenha gostado deste artigo ! :o)
6 Responses to “Cointegration in the Forex market”
& # 8221; In statistics we can evaluate for cointegration using three different tests from which the Augmented Dickey-Fuller (ADF) test is the most popular.”
Yo, this is a stationarity check. it does not imply cointegration.
This is true, however when the result of this test is positive for financial series they are always cointegrated, this is why it is so popularly used for this purpose I believe. You can however perform a Johansen test as well or a Engle–Granger two step test. In the examples used on this article all series that pass the ADF test also pass the Johansen test, showing they are cointegrated.
i will be more than happy if you could share your r code in order to learn how to do this process.
Spread trading on EURUSD|CHFUSD sounds equivalent to trading EURCHF itself, which, as is actually directly possible at most brokers, should be preferred (pay only half the spread/commission costs). An EURUSD|CHFUSD spread is in fact a synthetic instrument for EURCHF.
So how is this spread trading any different (for the better)?
Thanks for commenting :o) You’re clearly right, it’s the same as trading a bollinger band strategy on the EUR/CHF. As mentioned on the article the spread is actually the same chart as the EUR/CHF. The cointegration of the EURUSD|CHFUSD is actually reflected as a tendency to return to the mean on the EUR/CHF. If you were going to trade this in practice you would indeed use the EUR/CHF to save trading costs instead of buying/selling EURUSD and USDCHF.
Great article overall but confusing in some places. As one comment’or has pointed out, ADF test is a unit root test. It is a formal test used to establish whether a price series is stationary or not. If you get a P value of more than 1%, 5% or 10% you can only fail to reject the null of unit root based on the significance level you are comfortable with. This does not infer the presence of co-integration.
The power of the ADF is also documented to be low so most researchers now go ahead to cross check with a complementary test such as KPSS.
It will be interesting to see the R code so we can also run it and see the results. You do mention that the Johansen test confirms the presence of co-integration, so all in all I believe your findings are on solid ground.
Some interesting questions that come up is how stable is the co-integration relationship? How frequently does the long run relationship estimate change and how big are these changes when they do occur.
Overall great article, keep them coming and do share some R code.

Cointegration trading forex

Pairs trading is a form of mean reversion that has a distinct advantage of always being hedged against market movements. It is generally a high alpha strategy when backed up by some rigorous statistics. This notebook runs through the following concepts.
The notebook is intended to be an introduction to the concept, and whereas this notebook only features one pair, you would probably want your algorithm to consider many pairs at once.
The notebook was originally created for a presentation at Harvard’s Applied CS department and has since been used at Stanford, Cornell, and several other venues. If you’re interested in learning more about how Quantopian is being used as a teaching tool at top universities, please contact me at [email protected] an.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Here’s a very simple algorithm based on the approach presented in the notebook.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Here’s a more sophisticated algorithm written by Ernie Chan. This algorithm computes a hedge ratio rather than just holding equal amounts of each security.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Very useful stuff.
What makes it lose systematically for nearly 3 months? Does Cointegration fail in that period?
Basically yes, they turned out not to be cointegrated in that time frame, but returned to being conitegrated in the long term.
I think the drawdown you point out is a strong case for why you would actually want many pairs trading at the same time. Pairs can be cointegrated over different time scales, and any given one will not always be in a tradable state (big spread, small spread). By increasing your sample size, you can make it far more likely that at least one pair will be strongly tradable state at a given time, and smooth out the weird bumps you see here.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Obrigado por isso. Muito útil. I noticed you used Augmented-Dickey Fuller test for the cointegration test. Do you have similar implementation using Johansen test? I'm not able to find the johansen test with python.
It appears that whereas there have been some attempts to add the Johansen test to the statsmodels library, currently there is no built-in implementation. Here, for instance, is a 3rd party implementation. I'm not sure when it will get added to the Python libraries, is there a way you can work around not having it?
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Obrigado. I did see that link. Pretty complicated to implement and to write it all in the IDE. In fact, Satya B attempted it here quantopian/posts/trading-baskets-co-integrated-with-spy.
The beauty of Johansen test is that it generates eigenvectors, which I think you can use other methods to calculate though I can't recall at the moment, for up to 12 assets and many other things, which can be used to create a basket. I was looking at one of the index arb strategy of Ernie and attempting to replicate it on Q's platform to assess the performance after fees/comm etc. I noticed fees seemed to chew up a lot of the performance. The ABGB & FSLR pair above has an sharpe ratio of 0.75 but ended with sharpe ratio of -0.29. A lot of seeming profitable pairs turned out to be non profitable after bid/ask spread, fees, commission etc. Hence, I am looking at 3 or more stocks pair trading, and index arb. johansen test will make this easier to implement.
I shall keep trying.
The notebook is an excellent statistical introduction to pairs trading, I recommend anyone interested in the topic also look into some of the financial research. Anatomy of Pairs Trading is a good start, and the references are helpful as well. Two more general papers on risk arbitrage strategies are Characteristics of Risk and Return in Risk Arbitrage and Limited Arbitrage in Equity Markets . There are some expensive lessons people have learned about running these kinds of strategies, and it's worth knowing the lessons in advance. Forewarned is forearmed.
Anthony, good to see you here! I have been looking for a good implementation of the Johansen test for a while but couldn't find one. There is a pretty long (but stale) discussion and pull request on github about including it in statsmodels: github/statsmodels/statsmodels/issues/448 and github/josef-pkt/statsmodels/commit/bf79e8ecb12d946f1113213692db6dac5df2b6e9 It's really too bad as definitely in quant finance this is pretty widely used.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Aaron. Thank you for the heads up. Appreciate it coming from your. I shall spend some time with those papers.
Thomas. Thanks for the link. As you said, it is a bit old. Better than naught I suppose.
Here is a python implementation for vector error correction models. You can also use it to find cointegration weights. econ. schreiberlin. de/software/vecmclass. py.
Here is a version of Ernie Chan's algorithm modified to trade multiple pairs. This is a good way to obtain multiple uncorrelated return streams and reduce the beta of the overall strategy.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Delany, Are there methods available to screen for pairs using stat tests? Or are those usually too computationally expensive?
We are working on a way to make the notebooks clone-able into one's own research environment. In the meantime those interested in playing around with the notebook from the original post can download it here. After downloading upload it into your research account. If you do not yet have a research account, enter an algorithm into the contest to receive access.
good trader, The method provided in the notebook will screen a given list of securities for cointegration, the underlying condition necessary for pairs trading. The problem is not as much the computational complexity as it is the loss of statistical power. The more comparisons you do, the less weight you must put on significant p-values. This phenomenon is described here. To be statistically rigorous, you must apply a Bonferroni correction to p-values obtained from a pairwise cointegration script. The reason being that the more p-values you generate, the more likely you are to encounter significant p-values which are spurious and do not reflect actual cointegration behavior in the underlying securities. Since the number of comparisons done when looking for pairwise cointegration in n securities grows at a rate of O(n^2), even looking at 20 securities would render most statistical tests useless. A better approach is to come up with a small set of candidate securities using analysis of the underlying economic links. A small number of statistical tests can then be done to determine which, if any, pairs are cointegrated. Let me know if this is what you meant.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
I disagree somewhat about the problem with too many comparisons. The Bonferroni correction is appropriate when you are looking for truth. For example, if you have a questionnaire with 1,000 items and you give it to people with and without cancer, you'll find on average 50 items that correlate with cancer at the 5% level of statistical significance, even if nothing on the questionnaire is related to cancer. If you consider combinations of two or more items, you can generate as many correlates are you like.
But when designing automated trading strategies, coincidental relations don't hurt you much. They add random noise and trading costs to your results. Since few results are 100% meaningless, most relations have at least some small degree of persistence, it's not critical to filter your strategy down to rigorously validated ones. Profits matter, not truth. Bonferroni and similar metrics push you to the most statistically reliable relations, which are not generally the most economically useful ones.
If by "analysis of the underlying economic links" you mean starting with natural pairs like two similar companies in the same industry, I have not found that useful. Basically people notice the obvious stuff. If you mean thinking about less obvious relations, especially things that are invisible in the usual data people use, then I agree. Ideally you want a validatable economic story for the pair relation, which explains both why it exists and why it is not arbitraged away. Not only does that guard against data mining, but it means you can measure whether the effect continues to work (without that, the only way you know the strategy isn't working is when you lose money).
Bom trabalho. I haven't read through your notebook line-by-line, but I can tell that it will be a great addition to the Quantopian example library. And following up with shared algos--good move.
You might have a look at the notebook I posted, quantopian/posts/analysis-of-minute-bar-trading-volumes-of-the-etfs-spy-and-sh. To visualize how a given pair goes in and out of cointegration, you could make a similar plot. Applying the statistical test 390 times per trading day over many years would require some patience, though.
Aaron Am I correct in reading your argument generally as follows?
- In the real world Bonferroni is too restrictive and the number of profitable pairs you lose via the correction outweighs the statistical certainty you gain.
I think we agree as to the final point you make. I think that many of the economic link analysis folks do are simplistic and ignore the potentially interesting relations that are more likely to contain non-arbitraged alpha.
Grant Thank you. We're actually planning to expand the example library to a full quant finance curriculum taught with notebooks and companion algorithms. We're going to have a series of summer lectures as we develop more topics, so keep an eye out for those. Your notebook is very cool and I do wonder how stable the cointegration scores are even for strongly cointegrated pairs. Unfortunately, I don't think I'll have time to look into that in the near future what with the production of our other curriculum notebooks. We are looking for guest contributors, however. If you have any notebooks you would like to be featured in our curriculum with full credit to the author(s), send them my way and I'll see if they would fit into our current content.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
In the real world Bonferroni is too restrictive and the number of profitable pairs you lose via the correction outweighs the statistical certainty you gain.
Não precisamente. Yes, Bonferroni is too restrictive in the sense that it gives you too few pairs, but Bonferroni also directs you to the wrong pairs.
In the example of a questionnaire with 1,000 items given to cancer patients and non-cancer patients, it's likely that most of the items have no effect on cancer, or at least such weak and complex effects that it's not worth using them for medical advice. So if you want 5% significance, you test each item at the 0.005% level (that is you want 3.9 standard deviations, not just 1.6). You don't mind that, because any real effect strong enough to matter will likely show up with strong significance. If you didn't do Bonferroni, you'd end up with 50 recommendations even when none of the items mattered, and a lot of useless advice.
Incidentally, Bonferroni is a very conservative correction, and there are more sophisticated ones that allow more items.
But if you have 1,000 pairs to test, it's likely that many of them have some degree of cointegral predictability. Even if there is no predictability, including the extra pair only adds a little noise to your strategy, which is not terrible. Also you don't believe that any of them have predictability so strong that anyone would have noticed it and arbitraged it away. So it's reasonable to consider all the pairs with 5% significance or less, and filter them out using economic or other criteria unrelated to the data. Selecting only the strongest statistical relations is not wise.
You can set this up in a Bayesian framework if you like consistency and precision; or you can just use ad hoc rules of thumb.
Just for the il-pair-literated who want to learn. must there be a story behind the pair? Should there be a logical explanation? I played around with pairs and found for example that MorganStanley and Expedia work. mas por que? Or doesn't one want to know why.
must there be a story behind the pair?
This is actually a semantic question rather than a financial one. If you adopted a pure statistical approach with no consideration of the actual pairs, you would end up with hundreds or thousands of pairs, including some overlapping ones. Then we wouldn't call it a pairs-trading strategy but a long-short equity strategy.
The idea of pairs trading is you can get additional insight by considering specific reasons for the dependence between the stocks; and that insight can result in more accurate positioning, and also avoidance of big losses when the relation breaks.
Obvious relations, like two large-cap stocks in the same industry, tend not to be useful. That's confusing sometimes, because some of the famous early pairs trades involved such pairs, and they're still used for examples in most texts. But too many people are watching those spreads too closely to get the high Sharpe ratios you need for undiversified strategies like pairs trading. Leave those marginal Sharpes to the long-short equity people who have a lot more positions.
Also, when we talk about a reason for the pairs relation, we're talking about both a positive--why is it hard to imagine a world in which the values of these companies diverge from their historical proportions--and a negative--why do these stocks respond to different economic news? So for two near-identical companies the first question is easy, but the second is hard. For two seemingly unrelated companies like MS and EXPE it's the reverse. You might say something like, "In a good economy Morgan Stanley gets a lot of business and people travel a lot," but that's basically true of almost any two companies.
The classic pairs reason was two companies that responded to the same basic economic factors, say oil prices or interest rates or US dollar strength, but at different points in the supply chain, say crude oil prices versus gas station revenues. A single link is not good enough, virtually all companies respond to these factors. But you can find pairs that are matched on narrower factors, say fracking activity in the Northeast US or precipitation in central California, or that match direction on a number of broad factors. Or you can find two companies that are actually in similar businesses today, but that for historical reasons are listed in different sectors. Another common situation is two companies involved at different points of the lifecycle of durable assets; homebuilders and furniture stores with similar geography for example.
Anyway, when you have a reason, you have things to monitor to fine-tune your position; and to alert you if a big dislocation is a great trading opportunity or a sign than the historical relation has broken. If you don't have a reason, you'd better have a lot of diversification, meaning you can't afford the specific analysis work for each pair.
Wouldn't you admit though that if a pair has a story then that story is known and therefore unprofitable by the likes of slow to trade retail traders? And if one could mine the data and discover, through the data, stories that were unexpected that one could at least compete in the pairs trading space? I see your point on maintaining a large pool of pairs if the stories that connect the participants are weak or unexplored, but still, if we underlings wish to participate why wouldn't we use such a technique? Or do you maintain that retail traders can capture and profit from anomalous pair spreads of well known couples?
Wouldn't you admit though that if a pair has a story then that story is known and therefore unprofitable by the likes of slow to trade retail traders?
No, I wouldn't agree with that view. Pairs trading tends to be low capacity, especially in lower-cap stocks, and takes a lot of work. It's not attractive for asset managers because the investment amounts and risk characteristics are erratic. It's mostly pursued by individual full-time professional traders, who might follow a dozen pairs in addition to a few dozen other strategies, and semi-pro traders who are willing to take what the market gives them and stay in cash when none of their strategies are attractive. There are more good pairs than there are competent traders chasing them.
In principle, you could find good pairs using a clever automated filter, or by reading and thinking. My general feeling is the first is harder, and if you're going to do it, you'll want to do it to identify large numbers of pretty good pairs rather than two or three great pairs. In that case, I'd say just switch to long-short equity and forget pairs. The good thing about reading and thinking is most good quants are lazy, and would rather let the computer do the work. So you're competing with non-quants, some of whom are pretty good at reading and thinking, but are at a huge disadvantage to someone with a computer who knows a little math.
I don't want to come across as dogmatic, anyone who does what other people tell them is not likely to find great success in any sort of trading. If you think you can design an algorithm to identify good pairs, there's no harm in trying. It just doesn't strike me as the most promising approach.
. takes a lot of work.
Yeah. The easy pairs trade money was made long ago. Lucrative stories in lower-cap stocks though exposes a pair to the aberrations of smaller company volatility no? "Whoops, that solar stock just lost its major contract. Or, wow, that driller just got a windfall state contract." And then the story gets rewritten, or thee or four pages get torn out. One might catch such preludes to story changes if one only watches a dozen or so stories. But here, where we're looking to avoid story watching -- going fully automated, we would get nailed by such narrative breakdowns in just a few pair relationships.
When you say switch to long/short equities you would seem to advocate abandoning the statistical search for obscure (perhaps whimsical) stories in lieu of broader mean reversion -- is this true? But, if one has the tools, why not create dozens and dozens of strange storied pair trades. Sure the stories may not actually exist. But then again, maybe you discover 10 or 20 that are unique. And through a process of eliminating the poorly paired partners, you end up with a manageable set that are capable of dancing with the stars? This site is nothing if not a massive experiment in data mining no?
Again, I'm not trying to law down laws here, but the two straightforward approaches are (a) try to find a few pairs you can understand or (b) forget about pairs and just try to build a large portfolio of longs and shorts without worrying about pairing up stocks or doing unautomated research. In other words (a) niche clever research or (b) massive data mining.
Trying to split the difference by finding dozens of pairs but not doing the tailored research necessary to understand each one seems suboptimal.
try to find a few pairs you can understand.
If I'm reading things correctly, by "understand" you mean that there should be some underlying intuitive story behind the relationship, I suppose so that there is less risk that the relationship will suddenly disappear? Are you talking about a kind of narrative, "The reason we think this is happening, but can't really explain with a model, is. & quot; or an explanatory quantitative model that provides the story behind the relationship? Say I find a pairs trade based on the idea that when consumers buy lots of eggs, bacon sales drop off, and vice versa. I could make up a story that people can only eat so much for breakfast, and leave it at that. I have a warm, fuzzy feeling, and if I'm a professional trader, hopefully my management will feel warm and fuzzy, too. But is the risk really any different without the story? Unless I actually find a relevant study on breakfast eating, or conduct one myself, then I could just be deluded. And if the underlying cause can't be coded into a set of rules, then it is not really automated quantitative trading, right? As a Quantopian user who doesn't do this sort of thing for a living, I need to get an algo in the Quantopian hedge fund, let it run, and collect a check. No time for doing lots of offline analyses.
There are more good pairs than there are competent traders chasing them.
sounds like the land of milk and honey for us inhabitants of Quantopia. This would say that the Quantopian team should think about churning out candidate pairs for their 35,000+ users to examine like a bunch of ants, trying to come up with stories for a subset of them ("I'll take XYZ & PDQ, do some research, and see if I can find a 'story' to support the relationship.").
I'm just trying to sort out if any of this can be reduced to practice for Joe Schmo Quantopian user, or if it is a hopeless endeavor. Is there a path for Quantopian to get hundreds of lucrative, scalable pairs trading algos for their $10B hedge fund (keep in mind that by my estimation, they need several thousand distinct algos in the fund)? Or is this all a bunch of blah, blah, blah?
I've tried the automated searching of pairs/baskets, using the public knowledge techniques, and though I haven't gone through them all with my tick-level back-tester, the few that I did examine personally were largely worthless; the supposed spread mean-reversion that my grid search turned up was just spurious or due to bid-ask bounce.
However, I do know for a fact that people run decently profitable automated pairs trading portfolios. I take that to mean that it is possible, but the way that I approached it was naive. Perhaps the legwork method is the way to go, coming up with theses about drivers and then looking for portfolios that would express the theses, with the actual hedge ratio construction done "rigorously" using Kalman filters or whatever.
My take is that chatting about pairs trading is wonderful, but there should be a focus on reducing it to practice, with some sort of approachable workflow, so that a Quantopian user can sit down in his pajamas with a cup of coffee on a rainy day and actually come up with a halfway decent algo that would have a shot at getting into the crowd-sourced Q fund. For example, we have:
. try to find a few pairs you can understand.
Perhaps the legwork method is the way to go, coming up with theses about drivers.
ESTÁ BEM. So what's the workflow for your typical Q user? Keep in mind, this needs to be scalable. it won't do Q any good if only users with an advanced degree and 20 years of industry experience can be successful. If the answer is, "Well, there is no workflow. you just need to know" then pairs trading won't be approachable on Q. We have Aaron's "reading and thinking" recommendation above, but read what?
Also, I'd seen somewhere that there are techniques for synthesizing trading pairs, from baskets of securities. Does this work? Or does one effectively end up with the long-short equity portfolio referred to by Aaron Brown above?
The kind of warm-and-fuzzy story you mention is worthless for investing, although as you say it can reassure investors and regulators. What you're looking for is covariates to refine your strategy and, most important, warn you when it's not going to work. The quant trap is that when your relation breaks it simply looks more attractive to your model, and you spiral to doom.
The eggs-and-bacon story is actually the reverse of what you want. That says there is a fixed total consumption, so the total amount consumed of both products is fixed, meaning they are negatively cointegrated. If they were positively correlated, say because investors bid up or down all breakfast foods as a group, you would do anti-pairs trading. You're looking for things that have to be in some kind of long-term balance, but move is opposite directions in the short-term. A warm-and-fuzzy story might be residential construction and furniture sales, in the short run if people are saving for down payments they're not buying furniture, and newly house poor families are making due with old furniture and underfurnishing. But in the long run, houses will get furnished. This would never be a pairs trading story because it's relating entire sectors. To exploit this, you'd build a model tracing the full life cycle, and likely involving other factors like interest rates and family demographics and migration patterns, and trade large numbers of stocks.
To keep this practical, here is a Pairs Trading for Dummies recipe (I mean that respectfully, I'm a big fan for For Dummies books).
Run some kind of statistical screen to identify promising pairs trading targets. Don't look for extreme statistical significance, just some moderate level to screen out the noise like 5% or 1%. It can help to limit one member of each pair to companies or regions you know something about.
Clearly this is for someone who has quant skills, but also general research skills and business judgment.
Run some kind of statistical screen to identify promising pairs trading targets. Don't look for extreme statistical significance, just some moderate level to screen out the noise like 5% or 1%. It can help to limit one member of each pair to companies or regions you know something about.
it sounds like it could be productive for Quantopian to open-source some efficient tools for the screening (and maybe up their game in terms of computing resources). Let's say I'm an expert on company XYZ and maybe I could narrow down my field of candidate securities for comparison to NASDAQ-listed stocks, of which there are about 3,000. So, it is an O(N) computing problem, not O(N^2) as Delaney mentions above for the general screening problem. But, I'd like to compute the statistics on a rolling basis, every trading minute over 2 years. I'd have:
(3000 comparisons/minute)(390 minutes/day)(252 days/year)(2 years) = 589,680,000 comparisons.
Is something like this at all feasible on the Quantopian research platform? If not, how would I scale it back to something that would actually run in a reasonable amount of time (a few days at most) but still provide useful results?
I'm playing around with the algorithm by Ernie Chan that you posted.
Surprisingly, it fails entirely when I swap the pair, see the attached backtest (I've only changed the order).
Also, how to treat the negative hedge (beta from OLS). With the current implementation we go long (short) on both positions when the sign of the hedge is the same as the sign of the z-score, which you don't expect from pair trading. What economic reason can lead to such cointegrations?
Not sure exactly why it's failing when you swap the order. Seems like the math may not be robust to an 'upside-down' pair. The hedge ratio comes from the formal definition of cointegration, which is that for some b and u_t = y_t - b * x_t, u_t is stationary (the mean stays the same). Therefore we try to estimate the b parameter in each trade so that we can correctly produce a stationary drift between the two securities. It can be the case that the two are negatively cointegrated, whether there's a strong economic reason for this I'm not sure. You might try putting in place restrictions to not trade when you have double long or double short positions, or employing a better estimation method for b (more data points for example).
All of the issues you bring up are very sophisticated improvements, and making these improvements to the algorithm could result in something very good. I don't have cut and dried solutions for you, as you are now dancing around the edge of what is known about algorithmic trading. A lot of it comes down to rigorously testing different signal processing methods to see which yield the best out of sample performance. Also, like you said it's important to let the economic reasoning drive the creation of your model.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Thank you for your quick reply.
This is actually a very valuable response, as I was afraid I might have missed something obvious.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Here is a temp website which has similarity of movement information, which is about the same idea as pairs. StockA is the stock you are comparing to, row is how this pair ranks to all pairs, (its row count). It only contains information for the top 5000 or so pairs.
The data is pulled from the period of Aug 2014 to Feb 2015 and is an average of each day.
(Change IYR to symbol wanted)
The idea behind the algorithm is not actually for pairs trading, but is for similarity of how a pair moves. I will leave this test site up for a few weeks.
Thanks Delaney. It's a great starting step for pair trading technique.
I am working on the missing piece of this strategy which is how to use Quantopian Research environment to find statistical cointegration stock/ETF pairs from entire universe or from the same sectors. After I construct good pairs, then I can use the Notebook you provided for further analysis and backtest.
Does anyone have any suggestion for me?
I have a question for those trading pairs.
How do you deal with the large processing requirements?
I coded some tests for co-integration and results per combination take roughly 1 second.
I can get this down with parallel processing and by storing data locally but a universe of 2000 stocks will still have 4000000 potential combinations.
Perhaps pointing out the obvious, but .
A pre-screening tool, or pre-screening done for you for a fee .
When I was researching this sort of thing a couple of years ago, the baskets of 3 and 4 of only a few hundred ETFs took months on my MacBook. And they were all mostly garbage, though I never actually went through them all. I probably should.
If I remember correctly, that was 1.6T combinations, or something like that.
The formula is R to the Sterling S, divided by S!
so, for 4000 stocks, it would be.
(4000 x3999)/2! or, about 8 million pairs made from the 4000 typical stocks. for 3 stocks considered together, there would be 4000 x 3999 x 3998 /3!
You can prune the possible tree pretty easily though. I believe most stocks behave as if they really were ETFs (at the market neutral way of looking at it only) and can be represented by a group of other stocks, that move with their same fundamentals. You only have to know what sectors they move with, and then check for pairs against this.
So, for example, with HLF, it moves with consumer, several currencies, emerging markets, and a few others. It is hard to separate out exactly as emerging markets also move with currency, so which is which becomes the question.
For two typical tech stocks that appear to be very similar, it may well be the case that their main difference is which currencies they move with. So, for most of the time, they may appear co-integrated, but then, when there is a difference in currencies that affects one a lot, and not so much the other, they then move apart.
I was working on an algorithm to determine the underlying components, (so to speak) that collectively make each stock behave with the same logic as if it was a multi-sector ETF. (where the underlying stocks are a mystery to be solved) I have most of it done, and I believe I have enough done to prove it does work this way, but I lost my real time quote stream a few months ago, and so stopped working on it.
since my algorithm would need to consider up to 15 underlying components to solve this problem, it would be 4000 x 3999 x3998 . 3985/15! So, I have to trim it. The link I posted a few messages above shows some of the results of this work, where I first determine the possible stocks to consider, for each symbol.
It is my belief that the market is essentially swamped out with pairs trading, and this is why it works so mathematically perfect for each stock to behave as if it is an ETF.
There is certainly a high computational cost to looking at all possible pairs. However, there is a tradeoff to this approach, as you put yourself at a high risk for multiple comparisons bias. Please see earlier in this thread for a fairly complete discussion of this issue. Regardless of which method you use to select pairs, you'll want to do some additional validation using the notebook and then use the algorithms in this thread to try backtesting a strategy.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Indeed, Aaron Brown's advice is gold.
What is "multiple comparisons bias"? I'm lazy and don't feel like sifting through this rather extensive discussion thread.
I find it hard to believe that pairs trading would work as a scalable hedge fund strategy (be able to pour $10's of millions into a single pair). Is there any evidence? In other words, why is Quantopian promoting this?
This is one of the best threads on the site.
It scales; you can trade hundreds of pairs.
Multiple comparisons is a core problem in all of statistics, right up there with overfitting. The general idea is that if you run 100 statistical tests on random data, you should still expect to get 5 below a 5% cutoff and 1 below a 1% cutoff based on random chance. This is true when testing various iterations of a model, or many pairs. Because the number of pairs is O(n^2) you should expect to get a lot of spurious p-values when looking for pairs. A naive strategy of just looping through pairs won't work, you need to be a bit more sophisticated.
And yes you trade many pairs with low exposure to each. That said, I think that long-short equity strategies may be a better first bet to get into the fund at this point, just based on robustness and capacity.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
There is more electricity used in the state of New Jersey doing calculations on the market than there is electricity used in that state for manufacturing. Pairs strategy likely accounts for at least 50% of this usage as even HFT likely often uses some version of deviation from the mean. It is my opinion that the market is so saturated with pairs trading that given the price of any ten tickers that had no big news, one could deduce the price of the rest of the market and be within 0.7% of the actual price, 90% of the time for the top traded 4000 stocks. (and it could probably be done with less than ten tickers. ) So, for a 30 dollar stock, the margin of error would be about a quarter. This is how precisely, compared to each other, I think they move. Until there is news.
It sounds like a corollary to the reciprocal of the law of large numbers; given enough samples you will always find something to fit.
I would reintroduce the concept I proposed in an article in S&C last spring ; the directed acyclic graph or DAG. Using thousands of correlated or cointegrated pairs I built groups from them. Those groups were essentially social graphs of securities. You can search here for DAG, but briefly, you can use the concept of pair trading, that is, fade and favor the divergences, but with a correlated group. And such a group is assembled, dynamically, from a list of pairs that are "friends of friends". It's a pairs strategy, essentially, but with lower risk and less work managing hundreds of separate strategies.
That said, I think that long-short equity strategies may be a better first bet to get into the fund at this point, just based on robustness and capacity.
Have people been coming up with good ones? If so, what proportion are using the new data sets? If not, why not, do you think that is?
I haven't been focusing on them at all, mostly because there's a problem of opportunity cost; if I spend all my time looking for equity long-short algos, not only is there a chance I don't find anything, but if I do, there's still a chance that Quantopian doesn't select it, and since I cannot trade them myself, that time is wasted (unless I pitch it to other funds I suppose). If I look for algos that I personally can trade, and I find some, then I trade them.
I realize there's an unfortunate schism wherein I am using your platform but not contributing to your business model, so if you have any ideas how I can help without wasting my time writing algos that only work high account levels, please let me know. Pairs trading/statistical arbitrage might be one solution, but I've found them very difficult to implement; anything that looks promising in Quantopian fails the backtest when using dividend-adjusted bid-ask tick data, so I might shift my focus back to building my own lower latency infrastructure for a while.
I would reintroduce the concept I proposed in an article in S&C last spring ; the directed acyclic graph or DAG. Using thousands of correlated or cointegrated pairs I built groups from them.
Legal. Yeah, pretty similar. The DAG though was used specifically to find the networked graph. Those trees might embody the same thing, not sure. But I'd guess the idea is approximate.
Why would anyone want to pairs trade when trading a Minimum Spanning Tree or correlated network graph of stocks is so much safer and easier? I've built dozens of pairs strategies and the directionality of the pair always broke the model. And all pairs I ever tested all went directional at some point -- beyond the account's ability to Martingale down.
Have people been coming up with good ones? If so, what proportion are using the new data sets? If not, why not, do you think that is?
I can't release any specific data on this. I can say that there's a lag between when we update product features/try to educate people about algorithm writing techniques (larger universe size, shorting), and when new strategies start appearing. We'd love more large universe strategies right now and I'm trying to figure out ways to make it easier for folks to develop large universe long-short strategies using pipeline.
I haven't been focusing on them at all, mostly because there's a problem of opportunity cost; if I spend all my time looking for equity long-short algos, not only is there a chance I don't find anything, but if I do, there's still a chance that Quantopian doesn't select it, and since I cannot trade them myself, that time is wasted (unless I pitch it to other funds I suppose). If I look for algos that I personally can trade, and I find some, then I trade them.
I realize there's an unfortunate schism wherein I am using your platform but not contributing to your business model, so if you have any ideas how I can help without wasting my time writing algos that only work high account levels, please let me know. Pairs trading/statistical arbitrage might be one solution, but I've found them very difficult to implement; anything that looks promising in Quantopian fails the backtest when using dividend-adjusted bid-ask tick data, so I might shift my focus back to building my own lower latency infrastructure for a while.
Totally reasonable. We don't release our product with the expectation that everybody will use it to develop strategies for the fund, we also want to support your use case of personal trading. We also understand there's a conflict between pushing people to write high capacity market neutral long-short strategies, when those will never work on their own money. What I'm trying to figure out is ways to make the workflow of producing and evaluating factors easier, because once you have a factor-based ranking system, it's pretty easy to slot that into an existing long-short algorithm using pipeline. I'm working on sharing a pipeline algorithm with the community and attaching it to the lectures page in an effort to get more cloning and tweaking going on.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
I share Simon's sentiment. I've continued to participate in the contests, but the idea of spending tens (hundreds?) of hours trying to come up with an uber algo that will compete with the big dogs sounds like a lot of work, with a very uncertain pay-off (it's not even clear that you are still working on the hedge fund. any substantive news?). The pipeline thingy has a bit of a learning curve, so I haven't taken that on yet (the fact that lots of obscure modules need to be imported is a red flag). That said, if there were good working examples that could be tweaked, I might give it a go.
What I'm trying to figure out is ways to make the workflow of producing and evaluating factors easier, because once you have a factor-based ranking system, it's pretty easy to slot that into an existing long-short algorithm using pipeline.
Why don't you get all of the Q eggheads together for 1 week and see if you can come up with a long-short algo that would be Q hedge-fundable, and publish it (and better yet, actually fund it). Not only would this provide an existence proof, but you should also gain some insight into the workflow and the person-hours to accomplish the task.
Here is a pipeline algorithm that I just published as the goto example of a long-short equity strategy. I'm sure it will go through many improvements as the public eye turns to it, but it should at least be a start. It's tricky because we do want to publish algorithms that are 95% of the way done, so that users can take the last 5% and improve the strategies in many different uncorrelated ways. With long-short equity most of the work is in choosing good factors and factor ranking techniques. Unfortunately those are the type of signals that will disappear when shared publicly, but the actual machinery to trade within the algorithm should stay pretty consistent. If you're maybe looking to learn pipeline a bit, I would recommend going through Lectures 17 and 18, then looking at the algorithm.
I can say for certain we are working on the hedge fund. Even if you have strategies that aren't consistently winning the contest, we may be interested in an algorithm that can consistently do ok. Ultimately, my job as the one overseeing the lectures is to keep trying to make it easier so people don't have to spend as much time working on algorithms that may never pay off for them, and so we get more algorithms that do pay off in the long run.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
I start to implement pair trading backtesting in research environment instead of IDE. The main reason is to automatic run multiple pairs performance analysis before I jump into IDE for full backtest. Another reason for this work is to do further analysis for returns from many pairs.
I am wondering where I can find the example of backtesting in research environment to start with. Any comment is very appreciated.
In your research environment there should be a 'Tutorials and Documentation' pasta. Inside the folder should be a notebook with the title 'Tutorial (Advanced) - Backtesting with Zipline'. Make a copy of that and let me know if that's enough to get you started.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
May 28 algo falls below benchmark if extended to date and -43% PvR with default slippage and commissions, tanking thru 2015.
Hope it can be rescued b/c it shows good potential.
The example strategies cheat and run on the same timeframe over which we did research and found the securities to be cointegrated. In a real strategy you'd want to find pairs that were cointegrated into the future and not just historically cointegrated. The template should stay largely the same, so it's an issue of swapping in new securities that you have statistical evidence will stay cointegrated.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Could you post a tutorial on calibrating an Ornstein Uhlenbeck process for mean reverting series residuals?
We've added a lecture on this to our queue. No idea when we might currently get to it, but it's on there.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Ages ago I posted, perhaps as anonymole, that a "pair" needn't be made of only two securities. In fact, the whole "we only allow low beta strats" mantra is pretty much an argument that all strategies should be a variation of a pairs strat. That is, over all, a market neutral position is best.
Taking this further however, and applying a more formal model to the pairs strategy (that the security set have a "story" attached to it) I wonder if the two halves of the pair would do better as independent baskets of securities. That if one approached a pairs strategy with the mind to match up two behaviorally opposed baskets of securities that instead of trying to search all pair combinations looking for all the super-great-marvelous attributes a pair should have, that instead, one determine the two sides of the pair coin and fill each side with the most appropriately identified securities -- for each side.
A simplistic model might be described thusly:
Equities which cycle up in the spring/summer and down in the fall/winter would be bundled together and set against equities which cycle oppositely (down in the summer, up in the winter).
No doubt there are more interesting or undiscovered cycles that exist. My point is that rather than identify securities that yin and yang, one discover technical, or macro, or fundamental classifications which zig when the other zags. Then find securities which fit each of those baskets of behavior.
This is a very interesting idea and definitely something that professional quants do. At the core we just want two assets on either side of a pair, and a portfolio of assets will do just as well as a single equity. There are probably pros and cons of each method, but the idea of using a basket of things rather than a single thing can greatly reduce your position concentration risk and lead to a better algorithm. I'd say it's worth research. You'd still likely want a few different pairs of baskets as each would smooth out the return curve of the other and produce a lower volatility algorithm.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
I have to run an errand, so I only have five minutes, but hopefully I can be clear in that time.
To demonstrate the chops of an AI system, I created an algorithm that can represent the small changes in stocks price, as the sum of a set of ETFs. For example, with MSFT one might have XLK, XLY, FXE, FXI, and some others.
I can show that the typical price movements during a day can be represented in this way. However, when there is specific news, then it is no longer true, if the news is strong.
What I believe this shows is that instead of things "returning to the mean" they are in fact not moving arbitrarily and so, if they return to the mean, it is because one of the underlying components in fact moved. (Of all the underlying components, usually only one or two have news, and the rest are balancing each other out, once the price has adjusted.)
How might one design a trading platform for this as even if you do know it is the sum of other waveforms that are causing one waveform, one still doesn't know what causes them to move until after the fact.
(the reduction in influence is 1/1.6 when looking at the components, so after a couple of feedback loops, the influence is not measurable. Thanks, and sorry for the hurried note,
Have you read Algorithmic Trading written by Ernie Chan? For sure you read it, I have a question: in fact I am not good in programming and working with Matlab, I am really interested in Currency cross rate part of the book and I want to implement the positions in live trading but I don't know how to do that in fact I can't understand what the numbers as positions mean! If somebody can guide me I'm really appreciated.
Not entirely sure I'm understanding your thesis but it seems that you've created an expression that models the returns of a specific stock from it's sector exposures. This is actually a common risk modeling tactic, check out my notebook here. To build a trading strategy off of this I would take your hypothesis about changing news and use that to alter the coefficients of your model. A cool place to start would be to check out the lectures on factor modeling and then maybe look at some news/sentiment data sets to see if you can find any anomalies.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
That is close. It models the returns to within a few cents usually, at any moment in time, depending on the stock and its volatility as a sum of its sectors. (except when it has specific news.) What I envision behind it is a large set of funds using NLP to invest by sector based on news. Because they are so large, then they tend to swamp out the market during normal times.
I can also show that stock prices changes are directly proportional to the sum of the underlying sectors information, for most time periods. For example, the price changes for three months show this and also for three weeks, which is a bit chaos like, as it would seem they wouldnt be so perfectly in tune. Anyway, with this I can sort stocks by their overall market efficiency (the more efficient you are, the more you sync with the relationship stated above).
I also believe that there are huge funds that are interested in doing nothing more than treading water (as one possible explanation) and they move their money around the world, just trying to stay even, and so the result is that at any given time, the sum of everything stays near zero. (when one thing goes up somewhere, something else somewhere else goes down.)
These relationships also break down during periods of very high volatility such as fall 2015.
There are other things I am able to quantify, but again have no idea how to use. When information about a specific stock or sector hits the market, it is my observation that the more objective the information, the faster the market responds, and the more subjective it is, the slower the market responds.
For example, when Ackman says that HLF is a pyramid scheme, then it can sometimes be hours, and sometimes even days before that news is no longer affecting the price of the stock, but when an analyst upgrades or downgrades a stock, that is more objective and the entire price adjustment is over in fifteen minutes. (If you subtract out market movements then an analysts announcement looks like a log curve, with most of the action in the beginning and a bit of a ringing at the last.)
Again, this all happens too fast to be of use, and it is after the fact that I can say, "That was subjective."
I don't think I am able to alter the coefficients as you suggest. I am using a hard coded take on a system of recursive polynomials for my modeling, so there are billions of coefficients.
Hi, I have a quick and possibly dumb question. Why did you use the ratio instead of the difference between S1 and S2 in the Quantopain pairs trading lecture? In the co-integration lecture, you use the difference instead. In other sources, they use the difference as well.
There's an updated notebook, algorithm, and video available on the lecture series page.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
And as a response to pandasaurus' question, which I unfortunately just saw, we have removed the ratio as it was a typo in the lecture.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Greetings Quantopian Community,
I was at the NYC Event on Pairs Trading, and the current example algorithm is deprecated, such that one cannot deploy it in live trading. With this fix, users can now deploy the algorithm in live trading. The fix is hosted as a pull request on github--thanks.
Muito obrigado. Could you please submit your PR to the following repo? It's where we store lectures and examples. Doesn't quite fit in the current form of zipline.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Thanks, Delaney. I submitted the PR to the specified branch.
Obrigado! Delaney. I am finishing my graduation thesis these days, Your work may help me a lot.
That's great to hear, Dzi. Hope it goes well!
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
I have question in regards to high frequency pairs trading using bid/ask price. One thing that I noticed is during an entry signal if I'm supposed to go long in one and short the other, the Long position that I enter would be using the ask price and this ask price normally is higher than the bid price, so when my exit signals to exit, my bid price that I close my position at will often cause me to loose than make money. What are some of the ways to prevent this from happening or what are some strategies that goes hand in hand with trading high frequently with pairs strategy. Further, how are limit orders used with the bid/ask price.
If you need to make the spread in order for the strategy to be profitable, then you are squarely competing with high-frequency market makers, and it's a whole different ball game. You are unlikely to win. If you have control over the specific order types you send, you could attempt to use mid-point pegs or something, but as soon as you admit any sort of limit orders where execution is not immediate, you now need to be concerned about being exposed unhedged, which is something that you'll need to backtest. (not easy either). What some people do is try and rest or peg an order for the less liquid leg, and attempt to save some of the cost of the wider spread (though again, these days, you'll probably just get adversely selected for no net gain), and then as soon as that fills, you aggressively execute the hedge leg across the narrower spread.
How does one use both bid and ask z score in high frequency trading? For simplicity, I can understand using z score, but when it comes to using both bid and ask price z score, I have trouble picturing how it is used.
Simon's right, mid-frequency strategies generally should be fairly robust to bid-ask spreads. If they're not the edge is probably too small to be consistently profitable. For high frequency trading you do have to consider the bid and ask in many different ways, as your trading will be very sensitive to movements in both. How exactly you use the data would depend on your model.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
You can imagine that the spread is a synthetic asset. For instance, X = 1L -1S so a single unit of X is long one unit of L and short one unit of S. If you need to buy one unit of X immediately, you will buy at the ask of L and sell at the bid of S. If you need to sell one unit of X, you will sell at the bid of L and buy at the ask of S.
You can then easily calculate the bid and ask for X, you have just two "z-scores" lidar com. Then, if you like, you can delay buying until the X_ask_zscore < threshold, and delay selling until the X_bid_zscore > exit_threshold.
Espero que isto ajude.
I had a chance to see this notebook before and I would recommend it to everyone here. Lots of amazing info can be found inside.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian. Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
Hey Simon. thanks for that last post. I've been thinking through the logic behind that, but I do have some questions. Hope you don't mind explaining or expanding on it a little. 1) If I understood you correctly you mean X being the spread between a pair? in other words one unit of X immediately to be traded immediately, I would think that you will buy at the ask of X rather than L to be immediate wouldn't you? One problem that I would encounter by buying one unit of X at the ask price of L would be that the ask price of L may not be the lowest ask price of X and therefore may cause me to still queue to purchase the unit of X or not even fill. Can you say a little more in regards to this?
2) Further, there is one concept that I'm having a hard time to understand. Let's say that my Z score > entry threshold of +2. I would short L by one unit by selling one unit of L at the bid price of L and go long one unit of Y at the ask price of Y. Assuming hedge ratio is 1 and all. When my Z score < exit threshold of say 0.2. I would then exit my short and long position of the pair. The issue that I would encounter assuming no fees and all is that I would loose money during these trades. I'm having a hard time understanding why that would be if my Z score returned to or close to mean. Is the reason behind this due to the fact that the volatility of the bid/ask price may not be high enough to allow the difference in the entry and exit bid/ask spread price at the start and end of the transaction to pull far enough to earn money?
Please take a look at the last part of the page for this link that shows the true correlations, which are arrived at by saying "from the point of view of a pairs trader, how correlated are these tickers."
If you know how to subtract out the part of the market that floats all boats, to be left only with the information pertaining to neutral, there are extreme correlations. XLK is the ticker used in the example, but there are a thousand I could have used. When you know how to subtract out all but the neutral information, the market becomes completely different in how it appears.
Scroll to the very bottom of the article and look at the two tables with correlation information. These numbers are this way because there is so much interest in pairs trading that it tends to swamp things out. It is even more pronounced in Europe.
1) I think you are getting a bit confused; X is not a real thing, it's a synthetic asset formed by the basket of L and S. X has a price to buy and a price to sell which you calculate from the bids and asks of the components. If you cross the spread, generally, you trade immediately in small enough size. You only have uncertainty about fills if you try to earn the spread. That gets much more difficult.
2) Maybe. If your trades are not making money, I mean, that's a big problem. I can't answer why they are not making money. It could be transaction costs like the bid/ask spreads, you should analyze the volatility of your baskets as a function of the bid/ask spreads you have to pay. If you have to cross four 5-cent spreads to try and capture a spread mean-reversion of 2 cents, well yeah you are going to have problems. A bigger problem I found was that mean reversion happens one of two ways; either the asset reverts to the mean, or the mean converges with the asset (assuming you are constantly recomputing the mean, which seems to be common practice). In both cases your z-score goes back to zero, but only in the first case do you make any money.
daniel I read your article, the correlations at the end, are those of prices, or returns ?
Thanks for clearing that up for me. The idea of using synthetic assets is relatively new to me. I went and researched it a little and noticed that it is often used to capture streams of cash flow. I'm currently trying to perform residual pairs trading with Chinese Future Contracts. As I research it for the use of Futures, I don’t really find much articles or explanations. Is it applicable to Futures?
At the same time, I'm relatively new at this and trying to go through the lectures and stuff to learn. When you say I should analyze the volatility of my baskets as a function of the bid/ask spreads. Do you know where I can find a lecture that discuss this further? Sorry to ask some fundamental questions. One thing I notice in my data is that the bid/ask spread is really small and by small the it is just a spread of one tick of the futures contract; while the Volume for that tick is also small just around 80 or less contracts for either bid or ask.
The correlations are about prices, but just a subset.
(I have edited this down, as compared to what you probably have in email. Please don't copy anything from the email onto the board.)
James - maybe? You need pairs/baskets with enough variance to profitably trade the mean reversion. There tends to be a spectrum; structurally correlated assets (like ETF vs their component baskets) are perfect to trade, so perfect, that everyone does it and therefore the deviations are probably less than the spread. Then there's really shitty pairs which you find doing brute force analysis of the stock market. These have lots of variance, but they probably don't converge, and/or the relationship is totally spurious. Read closely Aaron Brown's posts on this thread. You want something in the middle.
Danial - I am not sure how useful correlations of prices of any kind are ? They are bound to be super high.
By itself I don't believe there is any one thing that is useful for a neutral strategy.
My approach is to look at the market as being represented by several hundred core waveform, and similar to the idea of Fourier Transform, you can use these fundamental waveform to create the 4000 heaviest played stocks. So, basically everything I believe about the market is based on the idea of correlations, as this is what I used as one of the first steps to find those wave forms. (which are not easy to find.)
Consider if you have Tickers AAA and BBB, and they are two similar stocks.
AAA might have as its composite the waves A, B, C, D, E, F, G, H, I, J, and BBB may have D, E, F, G, H, I, J, K, L.
During the times that there is little to no activity in the components A, B, C, K, L then the two tickers would be nearly perfectly correlated. But if suddenly component A had news (for example), then the perfect correlations would no longer hold, since stock BBB does not have an A component waveform..
If you apply the above to the idea of mean reversion, then you can see what I believe the mean reversion strategy is actually about.
In my opinion the best way to play a neutral strategy would be to devise a portfolio that is about the underlying fundamental wave components..
And in the interest of completeness, I will mention that in the above examples, waves A, B, C, etc are also made of composite waves, (and those composites . ) as the market is self referencing. The several hundred are at the bottom of the self referencing, and are something that exists in theory, that I believe I could "easily" find, but have not spent the time and energy to do so as of this date.
I also believe that if I had data for all the major markets of the world and was able to deduce the underlying component waves for those instruments that are heavily played by the collectively speaking, multi-trillion dollar funds, that the sum of these waves would (except for inflation) most of these times sum to be zero.
Some researchers generate the log price series of two equities with the daily close. Then the spread series is estimated using regression analysis based on log price series data. For equities X and Y, they run linear regression over the log price series and get the coefficient β.
Any reason they use log price series instead?
Desculpe, algo deu errado. Tente novamente ou contate-nos enviando comentários.
Você enviou um ticket de suporte com sucesso.
Nossa equipe de suporte estará em contato em breve.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian.
Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.
O material deste site é fornecido apenas para fins informativos e não constitui uma oferta de venda, uma solicitação de compra ou uma recomendação ou endosso para qualquer segurança ou estratégia, nem constitui uma oferta de prestação de serviços de consultoria de investimento pela Quantopian.
Além disso, o material não oferece nenhuma opinião em relação à adequação de qualquer segurança ou investimento específico. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. Se você é um aposentadorio individual ou outro investidor, entre em contato com seu consultor financeiro ou outro fiduciário não relacionado a Quantopian sobre se qualquer idéia, estratégia, produto ou serviço de investimento descrito aqui pode ser apropriado para suas circunstâncias. Todos os investimentos envolvem risco, incluindo perda de principal. A Quantopian não oferece garantias sobre a precisão ou integridade das opiniões expressas no site. Os pontos de vista estão sujeitos a alterações e podem ter se tornado pouco confiáveis ​​por vários motivos, incluindo mudanças nas condições do mercado ou nas circunstâncias econômicas.

Riqueza do robô.
Posted on January 2, 2016 by Kris Longmore.
In the first post in this series, I explored mean reversion of individual financial time series using techniques such as the Augmented Dickey-Fuller test, the Hurst exponent and the Ornstein-Uhlenbeck equation for a mean reverting stochastic process. I also presented a simple linear mean reversion strategy as a proof of concept. In this post, I’ll explore artificial stationary time series and will present a more practical trading strategy for exploiting mean reversion. Again this work is based on Ernie Chan’s Algorithmic Trading , which I highly recommend and have used as inspiration for a great deal of my own research.
In presenting my results, I have purposefully shown equity curves from mean reversion strategies that go through periods of stellar performance as well as periods so bad that they would send most traders broke. Rather than cherry pick the good performance, I want to demonstrate what I think is of utmost importance in this type of trading, namely that the nature of mean reversion for any financial time series is constantly changing. At times this dynamism can be accounted for by updating the hedge ratios or other strategy parameters. At other times, the only solution is to abandon the mean reversion approach altogether, perhaps in favour of a trend following approach. As this post will demonstrate, finding or constructing mean reverting price series is a relatively simple matter. The real key to profitably exploiting such series is the much more difficult matter of understanding, in real time, whether to continue a strategy as is, update its parameters or put it on ice temporarily or permanently.
Cointegration.
A collection of non-stationary time series variables are said to be cointegrated if there exists a linear combination of those variables that creates a stationary time series. This implies that we can artificially construct a mean reverting time series through the appropriate combination of non-stationary time series. For example, we can construct a portfolio of assets whose market value is a stationary time series and thus amenable to profitable exploitation through mean-reversion techniques, even through the price series of the constituent assets are not themselves mean reverting. A pairs trading strategy, where we buy one asset and short another with an appropriate allocation of capital to each, is an example of this method for exploiting the concept of cointegration, but we can also create more complex portfolios of three or more assets.
We can test whether a given combination of assets forms a stationary process using the stationarity tests described in the previous post. However, it is impossible to know a priori the coefficients (or hedge ratios) that form a stationary portfolio. How then does one test for cointegration? I’ll explore two approaches: the Cointegrated Augmented Dickey-Fuller test and the Johansen test.
Cointegrated Augmented Dickey-Fuller Test.
The Cointegrated Augmented Dickey-Fuller Test (CADF test) involves firstly performing a linear regression between two price series to determine the portfolio’s optimal hedge ratio and then conducting a stationarity test on the portfolio’s price series. The example below illustrates this concept using the currencies of Australia and New Zealand since they seem likely to cointegrate given that the economies of both countries are commodity-based and are affected by similar geopolitical forces. This extends the example in the first post, which explored the mean reverting tendencies of the foreign exchange pair AUD/NZD. In that example, the hedge ratio is always one since equal amounts of AUD and NZD are always being bought and sold. In this example, we allow for a flexible hedge ratio and attempt its optimization. In order to achieve this, we need to introduce a common quote currency, the more liquid the better. It makes sense to choose the US dollar. Therefore, the example below seeks to exploit a stationary portfolio of AUD/USD and NZD/USD.
Firstly, the price series of both exchange rates for the period 2009 to mid-2015, which look like they may cointegrate:
A scatter plot further suggests that the price series may cointegrate as the price pairs fall on a roughly straight line:
We can use least squares regression to find the optimal hedge ratio and plot the residual of AUD/USD-beta*NZD/USD, which admittedly does not look overly stationary:
NZDUSD . Close , data = closes )
Next we apply the ADF test to the spread (see the previous post for a brief description of the urca package, and why its implementation of the ADF test is suitable for this application):
z . lag . 1 + 1 + z . diff . lag )
In this case, the test statistic we are interested in is -0.94, which is greater than the 10% critical value of -2.57. Therefore, we unfortunately can’t reject the null hypothesis that the portfolio is not mean reverting. However, the negative value of the test statistic indicates that the portfolio is not trending.
One shortcoming of the ordinary least squares approach is that it is assymetrc: switching the dependent and independent variables in the regression results in a different hedge ratio. Good practice would dictate that both options be tested and the arrangement that results in the more negative test statistic be selected. Another approach is to use total least squares regression, which can be used to derive a symmetric hedge ratio. In a geometrical sense, total least squares minimizes the orthogonal distance to the regression line (as opposed to the vertical distance in the case of ordinary least squares) and thus takes into account variance of both the dependent and independent variables. The total least squares solution is easily computed in R using principal component analysis and is not limited to a two-asset portfolio:
AUDUSD . Close + NZDUSD . Close , data = closes )
z . lag . 1 + 1 + z . diff . lag )
This results in a more negative test statistic and a visually more stationary spread (at least for the period 2009 – 2012, see the figure below), but we are still unable to reject the null hypothesis that the spread obtained through total least squares regression is mean reverting.
Johansen test.
The Johansen test allows us to test for cointegration of more than two variables. Recall from the previous post, using a linear model of price changes:
Δy(t) = λy(t − 1) + β t + μ + α1Δy(t − 1) + … + αkΔy(t − k) + εt.
that if λ ≠ 0 , then Δy(t) depends on the current level y(t − 1) and therefore is not a random walk. We can generalize this equation for the multivariate case by using vectors of prices y(t) and coefficients λ and α, denoted Y(t), Λ and Α respectively. The Johansen test calculates the number of independent, stationary portfolios that can be formed by various linear combinations of the price series based on the eignevector decomposition of Λ. The urca package contains an implementation of the Johansen test that provides critical values that we can use to test whether we can reject the null hypothesis that there exist 0, 1, 2, …, n-1 cointegrating relationships, where n is the number of constituent time series. Conveniently, the eigenvectors can be used as the hedge ratios of individual price series to form a stationary portfolio. This process is illustrated below for the AUD/USD-NZD/USD portfolio. A third currency pair – USD / CAD & # 8211; is added in the next section to attempt to create a stationary portfolio of three currencies.
In this case, we can’t reject either null hypothesis that r (the number of cointegrating portfolios) is zero or one, since the test statistic in both cases is less than even the 10% critical value. That is, it is unlikely that we can form a stationary portfolio from the price history used in this example. However, it may still be worth pursuing a mean reverting strategy if the half-life of mean reversion is sufficiently low (see the previous post for more details).
As stated above, the eignevectors form the optimal hedge ratio. They are conveniently ordered by maximum likelihood, so in this case we would select a portfolio of 1 lot of AUD/USD long or short and 3.41 lots of NZD/USD in the opposite direction. In this case, unfortunately, the resulting portfolio does not look any more stationary than that constructed using the ordinary least squares and total least squares regression approaches:
Mean reversion of a portfolio of more than two instruments.
We can add a third asset and use the Johansen test to determine the probability that there exists a mean reverting portfolio along with the hedge ratios of such a portfolio. In this case, I will add USD/CAD and take the reciprocal of price so that the quote currencies are consistent (note that when building a trading strategy from this triplet, that the directions signalled for USD/CAD would need to be reversed):
Again, we unfortunately find no significant cointegrating relationship. However, as discussed in the first post, we sometimes don’t need to hold our results to scientifically stringent statistical significance in order to make money, particularly if the half life of mean reversion is sufficiently short. Therefore, we will retain the first eigenvector to form a portfolio of the three instruments for further investigation. First, lets take a look at a time series plot of the portfolio’s value:
The half life of mean reversion of the portfolio is 53.2 days. This is calculated in the same manner as for a single mean reverting time series in the previous post, namely by regressing the value of the portfolio against its value lagged by one time period:
y. lag , data = df )
Recall that in the previous post, we were able to construct a theoretically profitable linear mean reverting strategy from a single time series with a half life of mean reversion of over 300 days, so at first glance, this results holds some promise.
Linear mean reversion on a cointegrated time series.
Below is the equity curve of the linear mean reversion strategy from the previous post on the three-instrument portfolio with the value of the portfolio overlaid on the equity curve:
The strategy suffers significant drawdown and only returns a profit factor of 1.04 and a Sharpe ratio of 0.29.
Obviously, the linear mean reversion strategy presented above and detailed in the previous post would not be suitable for live trading even if the example shown here had generated an impressive backtest. Applied to equities, it would require buying and selling an infinitesimal number of shares when price moves an infinitesimal amount. This is less of a problem when applied to currencies since we can buy and sell in units as small as one-hundredth of a lot. However, the real killer for such a strategy is the trading costs associated with bar-by-bar portfolio rebalancing, as well as the fact that we can’t know the capital required at the outset. Having said that, there is still much value in testing a mean reversion idea with this linear strategy as it shows whether we can extract profits without any data snooping bias as there are no parameters to optimize. Also, a consequence of the bar-by-bar portfolio rebalancing is that the results of the linear strategy backtest are likely to have more statistical significance than other backtests that incorporate more complex entry and exit rules. Essentially, the simple linear strategy presented here can be used as a proof of concept to quickly determine whether a portfolio is able to be exploited using mean reversion techniques.
Practical approach to linear mean reversion.
If the simple linear strategy is not practical for trading, how can we exploit mean reverting portfolios? In Algorithmic Trading , Ernie Chan suggests a Bollinger band approach where trades are entered when price deviates by more than x standard deviations from the mean, where x is a parameter to be optimized. The lookback period for the rolling mean and standard deviation can be optimized or set to the half life of mean reversion. The trade would be exited when price reverts to y standard deviations from the mean where again y is an optimization parameter. For y = 0 the trade is exited when price reverts to the mean. For y = - x the trade is reversed at x standard deviations from the mean. The obvious advantage of this approach is that we can easily control capital allocation and risk. We can also control the holding period and trade frequency. For example, setting x and y to smaller values will result in shorter holding periods and more round-trip trades.
Exploiting the AUD-NZD-CAD portfolio using this simple implementation with x = 2 and y = 1 returns the following equity curve, with transaction costs included:
The equity curve of the Bollinger strategy is of similar shape to the linear mean reversion strategy, but it trades much less and allows for simpler control of risk and exposure.
Pensamentos finais.
This post extended the previous article on the exploitation of individual mean reverting time series by exploring the construction of portfolios whose market value is mean reverting. In addition to the simple linear mean reversion strategy I also presented a more practical approach that could form the basis of an actual trading strategy.
As stated in the introductory paragraphs, I wanted to show the good and the bad of mean reversion trading. The equity curves presented show periods of outstanding performance as well as periods of the polar opposite. Clearly, there are times when mean reversion is highly profitable, and other times when it just doesn’t work (perhaps trend following is more suitable at these times). But how does one determine, in real time, which regime to follow? How does one determine when to switch? I’ve explored several options, including a simple filter based on a trend indicator and a filter based on the actual performance of the strategy in real time. However, due to the lag associated with the filter values, these approaches are of little if any value. Diversification is another option, that is, continuously trade both mean reversion and trend following strategies at the same time in the belief that the profit from the dominant regime will more than make up for the losses of the other.
If you have an idea about how to address this issue, please let me know in the comments. I’d love to hear from you.
Download files and data used in this analysis.
Here you can download the price data and scripts (Zorro and R) used in this post: Mean reversion 2.
Ilya Kipnis.
Knowing when to revert and when to trend follow without the signal lagging is the gazillion dollar question. From my conversations with my mentor, you want a regime changing model for that.
After all, if you have a rangebound instrument, pick your favorite mean reversion indicator and go nuts. If you have a trending market, just buy and hold the trend. But to know which is which? I’d love to see some ideas posted elsewhere. I’ve tried depmix’s default settings and it just gave me garbage.
Kris Longmore.
Regime switching models are a whole new area of research for me. Something I’ve been meaning to tackle for a while now, but haven’t yet gotten around to. This is good motivation to bump it up the to do list. I’ll spend some time learning the first principles and then take a look at the depmix package you mentioned. Although from your experience it sounds like the solution is not a simple one.
Your last suggestion should work fine. Trade a basket of uncorrelated systems with a range of parameters. You’ll get the sum of returns with reduced drawdowns. Some Zorro code is here: financial-hacker/build-better-strategies-part-2-model-based-systems/
Kris Longmore.
Thanks for the suggestion Kevin. I think the key term in your comment is ‘uncorrelated’. I’ve had mixed success with strategy diversification in the past thanks mainly to the correlation between strategies changing over time. But that’s not really a failure of diversification, rather a failure of the trader to properly manage it.
great analysis. I did a lot of stuff there and traded (my website is down) so here are some things I found out.
No need to diversify mean reverting and trading, just find 5-10 cointegrating relationship and your Sharpe ratio will be 2+ as residuals are all uncorrelated. You’ll also need to do a WFO or IS/OOS test as no one will take seriously if you have a look-ahead bias. (there is a 50% performance degradation in out of sample testing from my own experience after doing in sample optimization) I strongly suggest WFO for every parameter as it will adapt to changing market modes. Also try other loading from PCA as the first one has the most variance but also the most likely to contain trends.
As for regime switching some filter to filter out trends is an option if you can find one. No need to waste time as regime switching field is huge.
Additional an execution algo that uses EMA vs SMA was better option for me (probably due to large funds using it also and size moves markets), plus you can use 2 st dev to enter but exit after n days could be a better one as a rule.
Anyhow hope it helps. If you want to talk more feel free to contact me.
Kris Longmore.
Hi D, thanks for sharing your findings! Some great stuff there that hadn’t occurred to me. I’ll definitely be pursuing them. Totally agree regarding walk forward testing; it is an essential part of the evaluation phase of strategy development in my opinion.
I hadn’t considered using the other loadings from the principal components analysis, but I will look into that too. I also like the n-day exit idea. It is appealing in its simplicity and I have found it useful in the past.
Eduardo Gonzatti.
Have you tried to use some kind of dominantPhase analysis from Zorro in the cointegrated spread and then trading it (spread) when the phase indicated so?
Ps: I’ve traded cointegrated equity pairs for some 4 yrs, and have no clue about cointegrated fx pairs =) but they do look way better and more robust for doing such.
Kris Longmore.
Hi Eduardo, no I hadn’t considered extracting phase information from the cointegrated spread. My first reaction to the idea is that this approach would be applicable if some sort of cyclical behaviour was present in the spread. I don’t presently know if that is the case or not, but I will certainly look into it. In your experience, have you found exploitable cycles in the spreads you have traded?
Eduardo Gonzatti.
Actually, I had this idea when fiddling with the Zorro manual a couple days ago.. I was studying about spectral analysis of financial time series returns and stumble upon Zorro’s cycle/phase indicators based in Hilbert Transforms, so it just occurred to me that, IF you assume that a spread (say, a cointegrated ols residue of two equities) is mean reverting (cointegrated and low enough half life with OU equation), you could probably use the same kind of transformation / cycle analysis that Zorro does (i thinks it’s based in John Ehlers books) in those spreads, in order to get “optimized” entry points, assuming those would predict turning points in the spread itself.
Don’t know if my assumption is mathematically sound, but it’s a hunch..
Personally, I never tried something aside from N*sigmas deviations for trading cointegrated spreads, because of the assumption that they are stochastic.
Sorry for any misspellings,
Hi Robot Master,
Thank you for the analysis. One question, is keeping the quote currency constant also necessary for CADF and OU, or it is only for required for Johansen?
Kris Longmore.
If you think about what the tests are doing, the answer to this becomes fairly obvious. The tests mentioned look for a unit root and/or stationarity of the time series in question. In this case, the time series is a spread created by the linear combination of the constituent currency pairs. Would it make much sense to test a spread that consists of, for example:
What would the units of the spread be?
Thank you for answering.
With two pairs with same quote currency, one unit moves have the same dollar values. So what you say is, unless we have this, the tests will not make any sense. Then for example for sgdchf vs zarjpy the pairs to test are sgdusd and zarusd, inverting the quotes or trading signals when necessary.
Am i correct with my interpretation.
Kris Longmore.
Assuming you want to trade a mean reverting spread that consists of SGD and ZAR, yes what you described is how I would approach it.
What about using 10 assets and combining them in groups of 3 with a loop and then calculate the eigenvalues of all those combinantions to get as an output the best cointegration portfolio?
Just a heads up:
You’re missing a negative here:
It should be, '-log(2) / lambda'
And caution to the lag function; I'm unsure which package was used, but you might be erroneously shifting the lag forward to y(t+1) by using '-1' if you're using the base. lag function. I like quantmod. Lag(y, k = 1).
Kris Longmore.
Thanks for pointing that out – you are absolutely correct on both counts. I’ve updated the code accordingly and found that the actual half life should be roughly 53 days, an increase over the 40 days calculated erroneously. I will some day get around to updating the affected results (ie the equity curves of the trading strategies that used the erroneous half life)!
Can you enlighten me as to the meaning, when both eigenvalues for a pair are the same sign? They are normally opposite… so I’m selling one and buying the other. The same sign seems to imply go long (or short) on both… which seems at odds with the pair trading methodology.
Riskmaverick.
Just came across your blog post while searching for the concept around half-life in mean reversion. I would be keen to know your thoughts around using Kalman filter to estimate hedge ratio. Would be even better if you have an example implementation in R.
Kris Longmore.
I think Kalman filtering is a great way to estimate hedge ratios. The optimal hedge ratio is rarely static, and Kalman filtering provides a sensible way to update it in real time taking into account the inherent uncertainty in its calculation.
Is there a easy way to ensure that the cointegration relationship is about to expire?
Kris Longmore.
I’m not sure of any easy way, but one reason these relationships break down is a structural change in the underlying relationship, for example following an earnings announcement that causes a sudden revaluation in one security. In that case, a different cointegrating relationship would probably emerge, once the jump or decline in price settled down to its new level. Another example that relates to the cointegration of ETFs that track the economies of two countries: a relationship could break down when one country’s economy shifts in some fundamental way, for example from a manufacturing to a service base. The two ETFs end up being exposed to different factors and so the cointegration relationship breaks down. In this case, it would happen more slowly.

Cointegration trading forex

Cointegration in forex pairs trading is a valuable tool. For me, cointegration is the foundation for an excellent market-neutral mechanical trading strategy that allows me to profit in any economic environment. Whether a market is in an uptrend, downtrend or simply moving sideways, forex pairs trading allows me to harvest gains year-round.
A forex pairs trading strategy that utilizes cointegration is classified as a form of convergence trading based on statistical arbitrage and reversion to mean. This type of strategy was first popularized by a quantitative trading team at Morgan Stanley in the 1980s using stock pairs, although I and other traders have found it also works very well for forex pairs trading, too.
Forex pairs trading based on cointegration.
Forex pairs trading based on cointegration is essentially a reversion-to-mean strategy. Stated simply, when two or more forex pairs are cointegrated, it means the price spread between the separate forex pairs tends to revert to its mean value consistently over time.
It’s important to understand that cointegration is not correlation. Correlation is a short-term relationship regarding co-movements of prices. Correlation means that individual prices move together. Although correlation is relied upon by some traders, by itself it’s an untrustworthy tool.
On the other hand, cointegration is a longer-term relationship with co-movements of prices, in which the prices move together yet within certain ranges or spreads, as if tethered together. I’ve found cointegration to be a very useful tool in forex pairs trading.
During my forex pairs trading, when the spread widens to a threshold value calculated by my mechanical trading algorithms, I “short” the spread between the pairs’ prices. In other words, I’m betting the spread will revert back toward zero due to their cointegration.
Basic forex pairs trading strategies are very simple, especially when using mechanical trading systems: I choose two different currency pairs which tend to move similarly. I buy the under-performing currency pair and sell the out-performing pair. When the spread between the two pairs converges, I close my position for a profit.
Forex pairs trading based on cointegration is a fairly market-neutral strategy. As an example, if a currency pair plummets, then the trade will probably result in a loss on the long side and an offsetting gain on the short side. So, unless all currencies and underlying instruments suddenly lose value, the net trade should be near zero in a worst-case scenario.
By the same token, pairs trading in many markets is a self-funding trading strategy, since the proceeds from short sales can sometimes be used to open the long position. Even without this benefit, cointegration-fueled forex pairs trading still works very well.
Understanding cointegration for forex pairs trading.
Cointegration is helpful for me in forex pairs trading because it lets me program my mechanical trading system based on both short-term deviations from equilibrium prices as well as long-term price expectations, by which I mean corrections and returning to equilibrium.
To understand how cointegration-driven forex pairs trading works, it’s important to first define cointegration then describe how it functions in mechanical trading systems.
As I’ve said above, cointegration refers to the equilibrium relationship between sets of time series, such as prices of separate forex pairs that by themselves aren’t in equilibrium. Stated in mathematical jargon, cointegration is a technique for measuring the relationship between non-stationary variables in a time series.
If any two or more time series each have a root value equal to 1, but their linear combination is stationary, then they are said to be cointegrated.
As a simple example, consider the prices of a stock-market index and its related futures contract: Although the prices of each of these two instruments may wander randomly over brief periods of time, ultimately they will return to equilibrium, and their deviations will be stationary.
Here’s another illustration, stated in terms of the classic “random walk” example: Let’s say there are two individual drunks walking homeward after a night of carousing. Let’s further assume these two drunks don’t know each other, so there’s no predictable relationship between their individual pathways. Therefore, there is no cointegration between their movements.
In contrast, consider the idea that an individual drunk is wandering homeward while accompanied by his dog on a leash. In this case, there is a definite connection between the pathways of these two poor creatures.
Although each of the two is still on an individual pathway over a short period of time, and even though either one of the pair may randomly lead or lag the other at any given point in time, still, they will always be found close together. The distance between them is fairly predictable, thus the pair are said to be cointegrated.
Returning now to technical terms, if there are two non-stationary time series, such as a hypothetical set of currency pairs AB and XY, that become stationary when the difference between them is calculated, these pairs are called an integrated first-order series – also call an I(1) series.
Even though neither of these series stays at a constant value, if there is a linear combination of AB and XY that is stationary (described as I(0)), then AB and XY are cointegrated.
The above simple example consists of only two time series of hypothetical forex pairs. Yet, the concept of cointegration also applies to multiple time series, using higher integration orders… Think in terms of a wandering drunk accompanied by several dogs, each on a different-length leash.
In real-world economics, it’s easy to find examples showing cointegration of pairs: Income and spending, or harshness of criminal laws and size of prison population. In forex pairs trading, my focus is on capitalizing on the quantitative and predictable relationship between cointegrated pairs of currencies.
For example, let’s assume that I’m watching those two cointegrated hypothetical currency pairs, AB and XY, and the cointegrated relationship between them is AB – XY = Z, where Z equals a stationary series with a mean of zero, that is I(0).
This would seem to suggest a simple trading strategy: When AB – XY > V, and V is my threshold trigger price, then the forex pairs trading system would sell AB and buy XY, since the expectation would be for AB to decrease in price and XY to increase. Or, when AB – XY < - V, I would expect to buy AB and sell XY.
Avoid spurious regression in forex pairs trading.
Yet, it’s not as simple as the above example would suggest. In practice, a mechanical trading system for forex pairs trading needs to calculate cointegration instead of just relying on the R-squared value between AB and XY.
That’s because ordinary regression analysis falls short when dealing with non-stationary variables. It causes so-called spurious regression, which suggests relationships between variables even when there aren’t any.
Suppose, for example, that I regress 2 separate “random walk” time series against each other. When I test to see if there’s a linear relationship, very often I will find high values for R-squared as well as low p-values. Still, there’s no relationship between these 2 random walks.
Formulas and testing for cointegration in forex pairs trading.
The simplest test for cointegration is the Engle-Granger test, which works like this:
Verify that AB t and XY t are both I(1) Calculate the cointegration relationship [XY t = aAB t + e t ] by using the least-squares method Verify that the cointegration residuals e t are stationary by using a unit-root test like the Augmented Dickey-Fuller (ADF) test.
A detailed Granger equation:
I(0) describes the cointegration relationship.
XY t-1 − βAB t-1 describes the extent of the disequilibrium away from the long-run, while αi is both the speed and direction at which the currency pair’s time series corrects itself from the disequilibrium.
When using the Engle-Granger method in forex pairs trading, the beta values of the regression are used to calculate the trade sizes for the pairs.
When using the Engle-Granger method in forex pairs trading, the beta values of the regression are used to calculate the trade sizes for the pairs.
Error correction for cointegration in forex pairs trading:
When using cointegration for forex pairs trading, it’s also helpful to account for how cointegrated variables adjust and return to the long-run equilibrium. So, for example, here are the two sample forex pairs’ time series shown autoregressively:
Forex pairs trading based on cointegration.
When I use my mechanical trading system for forex pairs trading, the setup and execution are fairly simple. First, I find two currency pairs which seem like they may be cointegrated, such as EUR/USD and GBP/USD.
Then, I calculate the estimated spreads between the two pairs. Next, I check for stationarity using a unit-root test or another common method.
I make sure that my inbound data feed is working appropriately, and I let my mechanical trading algorithms create the trading signals. Assuming I’ve run adequate back-tests to confirm the parameters, I’m finally ready to use cointegration in my forex pairs trading.
I’ve found a MetaTrader indicator which offers an excellent starting point to build a cointegration forex pairs trading system. It looks like a Bollinger Band indicator, yet in fact the oscillator shows the price differential between the two different currency pairs.
When this oscillator moves toward either the high or low extreme, it indicates that the pairs are decoupling, which signals the trades.
Still, to be sure of success I rely on my well-built mechanical trading system to filter the signals with the Augmented Dickey-Fuller test before executing the appropriate trades.
Of course, anyone who wants to use cointegration for his or her forex pairs trading, yet lacks the requisite algo programming skills, can rely on an experienced programmer to create a winning expert advisor.
Through the magic of algorithmic trading, I program my mechanical trading system to define the price spreads based on data analysis. My algorithm monitors for price deviations, then automatically buys and sells currency pairs in order to harvest market inefficiencies.
Risks to be aware of when using cointegration with forex pairs trading.
Forex pairs trading is not entirely risk-free. Above all, I keep in mind that forex pairs trading using cointegration is a mean-reversion strategy, which is based on the assumption that the mean values will be the same in the future as they were in the past.
Although the Augmented Dickey-Fuller test mentioned previously is helpful in validating the cointegrated relationships for forex pairs trading, it doesn’t mean that the spreads will continue to be cointegrated in the future.
I rely on strong risk management rules, which means that my mechanical trading system exits from unprofitable trades if or when the calculated reversion-to-mean is invalidated.
When the mean values change, it’s called drift. I try to detect drift as soon as possible. In other words, if the prices of previously-cointegrated forex pairs begin to move in a trend instead of reverting to the previously-calculated mean, it’s time for the algorithms of my mechanical trading system to recalculate the values.
When I use my mechanical trading system for forex pairs trading, I use the autoregressive formula mentioned earlier in this article in order to calculate a moving average to forecast the spread. Then, I exit the trade at my calculated error bounds.
Cointegration is a valuable tool for my forex pairs trading.
Using cointegration in forex pairs trading is a market-neutral mechanical trading strategy that lets me trade in any market environment. It’s a smart strategy that’s based on reversion to mean, yet it helps me avoid the pitfalls of some of the other reversion-to-mean forex trading strategies.
Because of its potential use in profitable mechanical trading systems, cointegration for forex pairs trading has attracted interest from both professional traders as well as academic researchers.
There are plenty of recently-published articles, such as this quant-focused blog article, or this scholarly discussion of the subject, as well as plenty of discussion among traders.
Cointegration is a valuable tool in my forex pairs trading, and I highly recommend that you look into it for yourself.
Pairs Trading – Entry Point Confirmation Using Technical Indicators.
Trading pairs without adequate confirmation is like building a house without a structural engineer. In the short term the design may be stable and safe, however over a longer period of time, the sensitivity to weather conditions and other factors could be hazardous.
Systems that are based on one factor alone will invariably have a shelf life and will need to be retrained to accommodate shifts in market conditions. As discussed in our previous article on cointegration, the degree to which a trader does not adhere to these strict guidelines, can greatly affect his/her profitability.
Technical indicators for entry signals on a pairs trade.
Some of the key technical indicators and patterns that can work well for confirming entry signals include the Relative Strength Index (RSI), Market Facilitation Index (MFI) and Candlestick charting. Each has a unique attribute, and can assist in defining key entry and exit points.
Índice de Força Relativa (RSI)
Although this is a relatively common indicator that does not stand the test of time by itself, the RSI can be an effective tool in pairs trading. Defined as the change in momentum, this technical indicator will range from 100 (extremely overbought) to 0 (extremely oversold). Traditionally the trigger points are 70 for a short and 30 for a long. With respect to pairs trading, this strength index allows the trader to confirm overbought and oversold scenarios.
RSI shows how a technical indicator can be used to spot entry opportunities.
The sppread between Gold and Silver is considerable, with the cointegration still above the required 80 mark (according to catalyst corner). The relative strength index has confirmed that silver is trading in the oversold bracket (at 75), providing the trader with a valid entry for a short position .
Market Facilitation Index (MFI)
Invented by technical analyst Bill Williams, the MFI identifies the momentum of a movement based on the volume. Depending on the strength of the buying and selling pressure, the indicator will price in an estimate of whether the trend is strong or weak.
Commonly used with longer time frames, the Market Facilitation Index is calculated by using the high, low and volume bars. Unlike RSI, the indicator is represented by a bar graph with coloration. Green highlights strong volume and momentum, whilst blue, brown and light brown indicate indecisive volume reactions. In pairs trading, the MFI can identify long term momentum patterns and which cross to buy or short.
Included below is a table from Wikipedia, which visually highlights the degree to which an adjust in volume can influence the market facilitation index.
The money flow index uses basic bar information to create a colored graph.
Gold has crossed below silver on a linear regression basis. The Market Facilitation Index however has indicated that volume and momentum are rising, and there will be a rebound in the price. The trader would look at going long gold and short silver.
Castiçais.
Candlesticks are an extremely efficient way of determining the trend of a price. Different patterns defined by the open high low and close price can supply the trader with efficient entry and exit points. From a pairs trading point of view, it is important to only open a position based on a strong buy or sell pattern. Bullish signals include a piercing pattern, inverted hammer, morning star and abandoned baby. For more information on each of these patterns it is recommended to visit stockcharts.
During the month of April, the spread between Gold and Silver is relatively tight. A morning star formation appears on the Gold price, indicating a potential bullish reversal. The trader in this case, would open a Long Gold, Short Silver to capitalize on a sudden breakout in the price.
Pairs Trading Case Study: Gold / Silver.
Finding a pair of currencies or commodities that can stand up to the cointegration test on both a short term and long term basis can be quite difficult. It is common for pairings to have some degree of distance or long term deviation away from the linear regression and this can greatly affect performance.
Several high profile market neutral hedge funds have been victim to this regression breakout. Long Term Capital Management (LTCM) is the most famous example. The fund lost several billion dollars in 1998 during the Russian financial crisis. Nearly every position in its bonds and derivative pairings went off the rails all at the same time.
Trading pairs is not full proof and strict risk management and cointegration retraining must be implemented. As discussed in our previous posts on correlation and cointegration, we are looking for the degree to which two variables will return to their common mean. This will determine our entry and exit strategy, and where we will place our stops.
In one of our previous articles – ‘Analysing Pairs with Correlation and Cointegration’, we identified Gold and Silver as a good potential trading pair due to its statistically high long term percentage levels. We calculated the cointegration using a free tool from the website – Catalyst Corner catalystcorner.
30 Day Correlation: 94.98%
2 Year Correlation: 26.99%
13 Year Correlation: 95.3%
2 Year Cointegration: 85%
Silver (Black) Gold (Orange Green) 30 Minute Chart.
Setting up Charts.
Setting up a pairs template in MetaTrader is relatively simple and requires two free indicators (these have been included with the tutorial). The first indicator is that of the FX Correlator and the second is the overlay chart. Highlighted below are the step by step instructions on adding each to your chart.
1. Open Metatrader and Choose Chart.
2. Drag the Overlay Chart onto the open chart window, and specify default settings. Clique OK.
3. Attach the FX Correlator to the chart, click INPUTS and change all currencies to FALSE except for USD and AUD. The reason why we are keeping these two as TRUE is outlined in the trade setup section. Clique OK.
Trade Setup.
You will now see two indicators positioned on the chart window. The top overlay chart will highlight the price of silver in comparison to gold. You will notice that the general trend direction is quite similar (correlation), however there are points along the timeline where the prices widen and then regress (cointegration). These are the points that we are looking to profit from.
The FX correlator is a unique indicator that calculates a spread between the main chart window and specified other crosses. When we added the indicator to the chart, we only specified the AUD and USD currencies. Hence we can only see two coloured linear regression points along the time line. The reason we chose the Aussie dollar, was because of its susceptibility to commodity prices movements and the US dollar is the natural base cross with Gold and Silver.
• Long Gold and Short Silver when the USD crosses above the AUD on the FX Correlator.
• Short Gold and Long Silver when the USD crosses below the AUD on the FX Correlator.
In the diagram above, we have circled a number of trade setups. On the 14th of May at 4:00, the USD crossed higher than the AUD, triggering a potential Short Silver/Long Gold scenario. According to the chart, Silver regressed back to the mean and overlapped Gold at 12:00. The second possible trade scenario occured on the 15th of May at 20:00. As the AUD crossed above the USD, a Long Silver / Short Gold trade was triggered with the spread widening.
Gerenciamento de riscos.
• Tight Stops on both crosses.
• Calculate the correlation and cointegration of Gold and Silver regularly (daily basis). If the cointegration breaks down (below 80%) do not trade.
• Position size should be based on underlying value and may not be equal.
Charting a Linear Regression.
Linear Regression can be an effective tool when defining the overall momentum or trend of a series of prices. It can be adapted to all data. Fields outside of trading, including risk management and statistics, use the same statistical technique. Insurance providers will commonly plot the relationship between claims and age groups to determine premium levels.
To put it into perspective, if there were five people in a group who each owned two television sets, one person who owned no tv and two people that owned four tv sets, then the linear regression on a rough basis would indicate the trend is just slightly above the two sets. The standard error or deviation in this case would be the two outside samples of no tv and four televisions.
Can regression be an effective tool for trading on a longer term basis or is it too susceptible to market volatility and future pricing? To understand how linear regression really works, we need to chart the channel and its standard deviation levels.
The first tutorial below looks at a scatter graph in excel and how to plot a linear regression. Please note that it does not include the standard deviation channels.
Charting a Simple Regression in Excel.
Open your Metatrader platform and click on TOOLS, HISTORY CENTER. Choose the relevant pair for your regression analysis. Once you have chosen the time frame, click on EXPORT and SAVE the spread sheet. Open the spread sheet and highlight the two relevant columns you would like to use in the scatter chart. In the diagram above we used time (minutes) and price. Click INSERT and choose SCATTER. A drop down menu will appear. To get a true reflection, click on SCATTER WITH ONLY MARKERS. A chart will appear with dots representing the distribution of pricing data. To decipher the linear regression, highlight the chart and click on LAYOUT in the excel menu. Navigate to TREND LINE. A drop down menu will appear with several options. Choose LINEAR TREND LINE. The regression line will now appear.
Excel draws a linear regression of the EURSUD prices using data from MetaTrader M5 charts.
As discussed previously, the excel chart will only give a basic trend and will not supply the user with detailed standard deviations. It is also recommended that you do not highlight too much data for a realistic short term interpretation.
We specified eight hours of five minute data on the EURUSD cross in the above diagram.
Charting Linear Regression in Metatrader.
Open the desired chart and time frame in Metatrader Click on INSERT and CHANNELS. You will then be provided with a list. Choose LINEAR REGRESSION. Hold down your left mouse button and drag the linear regression over the desired time period. In the above diagram, we chose a linear regression with a starting date of the 13th May at 10:30. You will notice that the regression line will appear and adjust according to the data. One standard deviation will also appear. If you would like a second deviation channel on your chart, navigate back to the top of the terminal menu and click on INSERT – CHANNELS and choose Standard Deviation. You will then need to drag the standard deviation channel using your left mouse button and specify the same time period.
MetaTrader interprets the price movements and draws a liner regression.
Recomendação.
It is recommended when trading using regression, that you specify a shorter range so as to manage the volatility. As prices shift, so will the channel, and profit potentials could quickly turn to losses.
It is important to always keep stops tight in case of violent swing backs in the price.
Correlation vs. Cointegration.
Correlation and cointegration are two regression based concepts that are commonly misused by the trading community. Complex in their formulation, both are inter related and are used to calculate the relationships between two or more products (ie commodities, forex, stock prices) over a specific time period.
Correlation.
A value of +1 (positive correlation) or -1 (negative correlation) is assigned based on the how efficiently the two prices react to each other. Correlation identifies pairs that move in either tandem or opposing directions .
A good example of a long term correlation pairing is that of the EURUSD and the USDCHF crosses, which trade in a similar direction. On the other side of the coin, the EURGBP and the AUDNZD trade in opposing directions. They show a negative correlation of -0.81.
Although this figure indicates that the crosses moved against each other, there is a slight degree of uncertainty over the long term sustainability of this negative result. Professional traders commonly set the entry benchmark for pairs above or below 0.9 or -0.9.
Correlation does have a significant drawback, which can greatly affect profitability. Although two pairs may be correlated, they are still not in complete unison, which can cause a slight drift in the prices. In the case of the EURGBP and the AUDNZD, it is a drift -0.19.
Read the post on forex correlation for more details on the topic.
Image credit: Vassia Atanassova.
The left box shows a strong correlation. The middle shows a weak correlation. The far right shows an image with no correlation.
Cointegration.
Cointegration analyses the movements in prices and identifies the degree to which two values are sensitive to the same mean or average price over a given time period. It doesn’t say anything about the direction that the pairs will move. Cointegration only measures whether or not the distance between them remains stable over time.
If we look at gold and silver, for example, we may find that they track a common average value. They may trade in opposite directions from day to day. At some unknown point in the future, they should revert back towards that average and hence they are cointegrated. Hedge funds commonly use this formula to program statistical arbitrage models to identify pairs to trade.
Another important factor to keep in mind is the look back period of the mean and standard deviation. In essence, if you make the look back value 700, then the regression channel will calculate what the average price is over 700 periods. This can be too inefficient and will limit the sensitivity to changes in the market dynamic.
On the other hand, if you set a short look back period, then it will cause a whipsaw effect and will be far too sensitive. It is important to get a balanced look back within the range of 200-350.
Gold / Silver Example.
• Top Section: Standard Deviation and Linear Regression.
• Middle Section: Relative Performance Gold (dark blue) and Silver (light/ turquoise blue)
• Bottom Section: Gold Daily Chart and Time Line.
The above chart highlights the overall correlation of Gold and Silver and the degree to which breakouts could trigger trade opportunities. I have circled a number of different cointegration scenarios and referenced these on the second section with P1, P2, P3 and P4 labels.
Silver Spike – Marcha.
A significant spike in the price of Silver in March sent the linear regression value below the lower standard deviation channel of -2.0. To capitalize on the significant discrepancy in prices, the trader would have looked at shorting silver and going long gold. Performance wise, this would have resulted in an overall profit as silver weakened heavily, crossing below gold in May.
Silver Oversold – July.
The silver price continues to weaken on a relative level to gold. In June and July, the regression value passes above the top standard deviation channel, indicating that silver is oversold and the price will have to revert back to its mean. The trader decides to open a long position in silver and short gold. As forecast, it returns to its mean and the gap between both spot prices closes quickly.
Silver Overshoots – December.
Once again the silver price overshoots gold. This sets up a long gold, short silver opportunity. On a performance level, the trader would capitalize on.
the spread and profit from the position.
Silver Selloff – April.
Puncturing the second standard deviation channel, the gold price stabilises whilst silver weakens heavily. This has now supplied the trader with a long.
silver, short gold opportunity.
Forex Correlation.
Correlation strategies appeal to forex traders because it removes the stress associated with picking market direction. When two correlated pairs diverge from one another, the idea is to simply buy one pair and sell the other.
What are correlated currency pairs?
Correlation offers a mathematical probability of two “time series” moving in the same direction. Applying the idea to forex, it means that we need to pick two currency pairs. EURUSD and USDCHF are two popular choices due to their extremely high correlation, so we’ll use those.
Now we ask a simple question: “If the EURUSD rises, what is the probability of that the USDCHF will also rise”? Our calculations will pump out a simple a number between -1 and +1. +1 means that that if Currency A rose in value, then it is 100% certain that Currency B rose in value. -1 means that if Currency A increased in value, then it is 100% certain that Currency B decreased in value. A value of 0 means that the movement of Currency A exercises no effect at all on Currency B.
Traders generally consider a correlation significant whenever the number is greater than 70%. EURUSD and USDCHF are so popular because they hold the strongest correlation among the major currency pairs. When market volatility was very low a few years ago, it was around -93%. Today, the correlation tends to hang around -80%. The European debt problems and Swiss National Bank’s intervention have a lot to do with the decrease in this number. Their trading relationships are far less stable.
Risks of correlation strategies.
Let’s move back into familiar territory with my favorite example, the moving average. If you take the average over the past 20 bars, you know from experience that the average will differ if you study a 50 period versus a 200 period average. If you look at the average on a 5 minute chart versus an hourly chart, the number will vary yet again.
The take-away here is that the correlations work the same way. The correlation between EURUSD and USDCHF might even be positive if you look at a short enough time scale. As you back away in time, you will notice that the further out you go, the more steady the correlation numbers look. If the weekly correlation of the EURUSD and USDCHF is -80%, you would expect the numbers to get more wild and erratic as you scale all the way down to a tick chart.
The same problem with the moving average also appears. Studying the correlation over 50 periods provides a responsive number, but it is also far less consistent than the 200 period correlation. What a short period gains in responsiveness, it loses in stability.
You should also consider whether the correlation that you’re studying makes fundamental sense. Just because the temperature change in Mongolia predicted the direction of USDJPY for the past week does not make it a good idea to use in the future. The same goes with pair trading.
EURUSD and USDCHF should be highly correlated for two reasons. They both contain the same currency in the pair (USD), which half weights them with the same instrument. Additionally, the EUR and CHF both have strong trading relationships with the US. You would expect both the Euro Zone and Switzerland to share a need for buying and selling US dollars. They need them for buying oil, importing and exporting to the US, etc. Anyone with a cursory understanding of macroeconomics could explain why this relationship makes sense.
Correlation traders typically settle on pairs that share a common currency. The EURUSD and USDCHF trade both share the US dollar. When you buy EURUSD and buy USDCHF, you are really:
Buying EUR and selling USD.
Buying USD and selling CHF.
Notice that the USD cancels itself out. What you are really doing is buying EUR and selling CHF. This is commonly known as the EURCHF pair. Assuming that the spread is not outrageous, it makes more sense to simply buy or sell EURCHF directly rather than going through the convoluted process of managing two open trades.
If you decide to pursue the two pair approach, you must consider the need to balance the trade sizes against each other. Using standard lots as the example, 100,000 EUR is 137,500 USD. 100,000 USD is 90,900 CHF. If you buy one standard lot of EURUSD, you are buying $137,500 of it. When you buy a standard lot of USDCHF, you are only buying $100,000.
$137,500 obviously does not equal $100,000. Unless you intentionally decided to trade different sizes, you may want to consider equalizing them.
€100,000 / $137,500 = x * (₣90,900/$100,000)
x = €100,000 / ₣90,00 * $100,000 / $137,500 = 0.803.
You would need your EURUSD trade to be 80% of the size of the USDCHF trade.
What correlation is not.
Correlation only provides insight into the probability of direction. It says absolutely nothing about the strength of a particular move. A few months ago the USDCHF climbed 1,000 points in value within a single day. The EURUSD only moved a few hundred pips. The USDCHF moved dramatically further than the EURUSD both in terms of pips, but more importantly, as a percentage of price.
Consider if you were short EURUSD that day and short USDCHF. You lost a ton of money. On the flip side, if you were long EURUSD and long USDCHF, then you got lucky and earned the move. Regardless of what happened, correlation told you nothing about the outcome when they move in the same direction. For that reason, I prefer looking at a less intuitive method called cointegration.
Cointegration.
Conintegration turns the problem on its head. Rather than asking whether or not two pairs move in the same direction, it asks how likely are they to remain a certain distance apart. Naturally, that distance tends to vary with time. What you want the cointegration formula to tell you is how likely two pairs are to come back to a standard distance. If you see two pairs spread unusually far apart and the numbers tell you that they usually come back together, then it makes sense to consider a pair trade.
Ernest Chan has a friendly introduction to cointegration that I highly recommend. A much uglier, math intensive introduction to the subject, albeit one that is also far more thorough, is in the book Pairs Trading by Ganapathy Vidyamurthy.