التكامل المشترك في أزواج العملات الأجنبية.
التكامل المشترك في أزواج العملات الأجنبية هو أداة قيمة. بالنسبة لي، التكامل المشترك هو الأساس لاستراتيجية تجارية ميكانيكية محايدة السوق ممتازة التي تسمح لي للاستفادة في أي بيئة اقتصادية. سواء كان السوق في اتجاه صعودي، اتجاه هبوطي أو ببساطة تتحرك جانبية، وتداول أزواج الفوركس يسمح لي لحصاد المكاسب على مدار السنة.
يتم تصنيف إستراتيجية تداول أزواج العملات الأجنبية التي تستخدم التكامل المشترك كشكل من أشكال التداول المتقارب على أساس المراجحة الإحصائية والرجوع إلى المتوسط. هذا النوع من الاستراتيجية كان أول شعبية من قبل فريق التداول الكمي في مورغان ستانلي في 1980s باستخدام أزواج الأسهم، على الرغم من أنني والتجار الآخرين وجدوا أنه يعمل أيضا بشكل جيد جدا لتداول أزواج الفوركس، أيضا.
تداول أزواج الفوركس على أساس التكامل المشترك.
تداول أزواج الفوركس على أساس التكامل المشترك هو في الأساس استراتيجية عودة إلى متوسط. وباختصار، عندما يكون زوجين أو أكثر من أزواج الفوركس مدمجة، فإن ذلك يعني أن انتشار السعر بين أزواج الفوركس المنفصلة يميل إلى العودة إلى قيمته المتوسطة باستمرار مع مرور الوقت.
من المهم أن نفهم أن التكامل المشترك ليس ارتباطا. الترابط هو علاقة قصيرة الأجل فيما يتعلق بالتحركات المشتركة للأسعار. ويعني الترابط أن الأسعار الفردية تتحرك معا. على الرغم من الاعتماد على بعض الارتباط من قبل التجار، في حد ذاته انها أداة غير جديرة بالثقة.
ومن ناحية أخرى، فإن التكامل المشترك هو علاقة أطول أجلا مع التحركات المشتركة للأسعار، حيث تتحرك الأسعار معا في حدود أو فروق معينة، كما لو كانت مربوطة معا. لقد وجدت التكامل المشترك ليكون أداة مفيدة جدا في تداول أزواج الفوركس.
خلال تداول أزواج العملات الأجنبية، عندما ينتشر انتشار إلى قيمة عتبة يحسبها بلدي خوارزميات التداول الميكانيكية، وأنا "قصيرة" الفرق بين أسعار أزواج. وبعبارة أخرى، أنا أراهن على انتشار سوف يعود مرة أخرى نحو الصفر بسبب التكامل المشترك بينهما.
استراتيجيات التداول أزواج العملات الأساسية بسيطة جدا، وخصوصا عند استخدام أنظمة التداول الميكانيكية: اخترت اثنين من أزواج العملات المختلفة التي تميل إلى التحرك بالمثل. إنني أشتري زوج العملات الضعيفة وبيع الزوج المتداول. عندما يتقارب الفارق بين الزوجين، أغلق موقفي لتحقيق الربح.
تداول أزواج الفوركس على أساس التكامل المشترك هو استراتيجية محايدة السوق إلى حد ما. على سبيل المثال، إذا انخفض زوج العملات، فإن التداول من المحتمل أن يؤدي إلى خسارة على الجانب الطويل وكسب تعويض على الجانب القصير. لذلك، ما لم تفقد جميع العملات والأدوات الأساسية فجأة قيمة، يجب أن يكون صافي التجارة بالقرب من الصفر في أسوأ السيناريوهات.
وعلى نفس المنوال، فإن تداول الأزواج في العديد من الأسواق هو استراتيجية تداول ذاتي التمويل، حيث أن العائدات من المبيعات القصيرة يمكن أن تستخدم أحيانا لفتح الصفقة الطويلة. حتى من دون هذه الفائدة، لا يزال تداول أزواج العملات الأجنبية التي تعمل بالوقود المشترك يعمل بشكل جيد جدا.
فهم التكامل المشترك لتداول أزواج الفوركس.
التكامل المشترك مفيد بالنسبة لي في أزواج الفوركس التداول لأنه يتيح لي برنامج بلدي نظام التداول الميكانيكية على أساس كل من الانحرافات على المدى القصير من أسعار التوازن وكذلك توقعات السعر على المدى الطويل، والتي أعني التصحيحات والعودة إلى التوازن.
ولفهم كيفية عمل أزواج الفوركس التي يحركها التكامل المشترك، من المهم أولا تحديد التكامل المشترك، ثم وصف كيفية عمله في أنظمة التداول الميكانيكية.
كما قلت أعلاه، يشير التكامل المشترك إلى علاقة التوازن بين مجموعات من السلاسل الزمنية، مثل أسعار أزواج الفوركس المنفصلة التي هي في حد ذاتها ليست في حالة توازن. أما في المصطلحات الرياضية، فإن التكامل المشترك هو تقنية لقياس العلاقة بين المتغيرات غير الثابتة في سلسلة زمنية.
وإذا كان لكل سلسلتين زمنيتين أو أكثر قيمة جذر مساوية للقيمة 1، إلا أن تركيبة الخطية هي ثابتة، ثم يقال إنها مركبة كوينيغراتد.
وكمثال بسيط، يجب النظر في أسعار مؤشر سوق الأسهم والعقود الآجلة ذات الصلة: على الرغم من أن أسعار كل من هذين الصكين قد يهيمون على وجوههم بشكل عشوائي على فترات قصيرة من الزمن، في نهاية المطاف سيعودون إلى التوازن، وانحرافاتهم ستكون ثابت.
هنا مثال آخر، ذكر من حيث الكلاسيكية "المشي العشوائي" سبيل المثال: دعونا نقول هناك اثنين من سكران الفردية المشي هومويارد بعد ليلة من الكاروس. دعونا نفترض أيضا أن هذين السكرين لا يعرفون بعضهم البعض، لذلك ليس هناك علاقة يمكن التنبؤ بها بين مساراتهم الفردية. لذلك، ليس هناك تكامل بين تحركاتهم.
في المقابل، والنظر في فكرة أن الفرد في حالة سكر يتجول هوموارد في حين يرافقه كلبه على المقود. في هذه الحالة، هناك صلة محددة بين مسارات هذين المخلوقات الفقيرة.
على الرغم من أن كل من اثنين لا يزال على مسار فردي على مدى فترة قصيرة من الزمن، وعلى الرغم من أن أي واحد من الزوج قد يؤدي عشوائيا أو تأخر الآخر في أي نقطة معينة في الوقت المناسب، لا يزال، وسوف تكون دائما على مقربة من بعضها البعض. المسافة بينهما يمكن التنبؤ بها إلى حد ما، وبالتالي يقال أن الزوج أن يكون كوينيغراتد.
وبعد العودة الآن إلى المصطلحات التقنية، إذا كان هناك نوعان من السلاسل الزمنية غير الثابتة، مثل مجموعة افتراضية من أزواج العملات أب و زي، التي تصبح ثابتة عند حساب الفرق بينهما، وتسمى هذه الأزواج سلسلة متكاملة من الدرجة الأولى - أيضا استدعاء I (1) سلسلة.
على الرغم من أن أيا من هذه السلسلة يبقى في قيمة ثابتة، إذا كان هناك تركيبة خطية من أب و زي التي هي ثابتة (وصفها I (0))، ثم أب و زي هي كوينيغراتد.
المثال البسيط أعلاه يتكون من سلسلتين زمنيتين فقط من أزواج الفوركس الافتراضية. ومع ذلك، فإن مفهوم التكامل المشترك ينطبق أيضا على سلسلة زمنية متعددة، وذلك باستخدام أوامر التكامل أعلى ... فكر من حيث سكر يتجول يرافقه العديد من الكلاب، كل على المقود مختلفة طول.
في اقتصاديات العالم الحقيقي، فإنه من السهل العثور على أمثلة تظهر التكامل بين الأزواج: الدخل والإنفاق، أو قسوة القوانين الجنائية وحجم السجناء. في تداول أزواج العملات الأجنبية، ينصب تركيزي على الاستفادة من العلاقة الكمية التي يمكن التنبؤ بها بين أزواج العملات المتراكمة.
على سبيل المثال، لنفترض أنني أشاهد هذين الزوجين المفترسين للعملة الافتراضية، أب و زي، والعلاقة المشتركة بينهما هي أب & # 8211؛ زي = Z، حيث يساوي Z سلسلة ثابتة بمتوسط صفر، وهذا هو I (0).
ويبدو أن هذا يشير إلى استراتيجية تداول بسيطة: عندما أب - زي & غ؛ V، و V هو بلدي عتبة سعر الزناد، ثم نظام تداول أزواج الفوركس سوف تبيع أب وشراء زي، لأن التوقعات ستكون ل أب لتقليل في الأسعار و زي لزيادة. أو، عندما أب - زي & لوت؛ - V، وأتوقع لشراء أب وبيع زي.
تجنب الانحدار الهامشي في تداول أزواج الفوركس.
ومع ذلك، فإنه ليس بسيطا كما يقترح المثال أعلاه. في الممارسة العملية، يحتاج نظام التداول الميكانيكي لتداول أزواج الفوركس إلى حساب التكامل المشترك بدلا من الاعتماد على قيمة R-سكارد بين أب و زي.
وذلك لأن تحليل الانحدار العادي يقصر عند التعامل مع المتغيرات غير ثابتة. ويسبب ذلك ما يسمى الانحدار الهامشي، مما يوحي العلاقات بين المتغيرات حتى عندما لا يكون هناك أي.
لنفترض، على سبيل المثال، أنني أترتب على مسلسل زمني واحد منفصل "المشي العشوائي" ضد بعضها البعض. عندما اختبر لمعرفة ما إذا كان هناك علاقة خطية، في كثير من الأحيان سوف تجد قيم عالية ل R - التربيع وكذلك القيم P المنخفضة. ومع ذلك، لا توجد علاقة بين هذين المشيين العشوائيين.
الصيغ واختبار التكامل المشترك في تداول أزواج الفوركس.
وأبسط اختبار للتكامل المشترك هو اختبار إنغل-غرانجر الذي يعمل على النحو التالي:
التحقق من أن أب t و زي t هما على حد سواء I (1) حساب العلاقة التكامل المشترك [زي t = أب t + إت] باستخدام طريقة المربعات الصغرى تحقق من أن بقايا التكامل المشترك وثابتة باستخدام اختبار وحدة الجذر مثل المعزز ديكي فولر (أدف) الاختبار.
معادلة غرانجر مفصلة:
I (0) يصف علاقة التكامل المشترك.
ويصف زي T-1 - βAB t-1 مدى الاختلال بعيدا عن المدى الطويل، في حين أن αi هي السرعة والاتجاه الذي تصحح فيه السلاسل الزمنية لزوج العملات نفسها من الاختلال.
عند استخدام طريقة إنغل-غرانجر في تداول أزواج الفوركس، يتم استخدام قيم بيتا للانحدار لحساب أحجام التداول للأزواج.
عند استخدام طريقة إنغل-غرانجر في تداول أزواج الفوركس، يتم استخدام قيم بيتا للانحدار لحساب أحجام التداول للأزواج.
تصحيح الخطأ للتكامل المشترك في أزواج العملات الأجنبية:
عند استخدام التكامل المشترك لتداول أزواج الفوركس، من المفيد أيضا حساب كيفية ضبط المتغيرات المركزة والعودة إلى التوازن على المدى الطويل. لذلك، على سبيل المثال، وهنا هما عينة الوقت أزواج الفوركس سلسلة أظهرت أوتورجريسيفيلي:
تداول أزواج الفوركس على أساس التكامل المشترك.
عندما أستخدم نظام التداول الآلي الخاص بي لتداول أزواج الفوركس، فإن الإعداد والتنفيذ بسيطان إلى حد ما. أولا، أجد أزواج العملات التي تبدو وكأنها قد تكون مشتركة، مثل ور / أوسد و غبب / أوسد.
ثم، أحسب فروق السعر المقدرة بين الزوجين. بعد ذلك، تحقق من وجود استبانة باستخدام اختبار جذر الوحدة أو طريقة شائعة أخرى.
أتأكد من أن خلاصة البيانات الواردة تعمل بشكل مناسب، وأسمح لخوارزميات التداول الميكانيكية بإنشاء إشارات التداول. على افتراض لقد قمت بتشغيل الاختبارات الخلفية كافية لتأكيد المعلمات، وأنا أخيرا على استعداد لاستخدام التكامل المشترك في بلدي أزواج الفوركس التداول.
لقد وجدت مؤشر ميتاتريدر الذي يوفر نقطة انطلاق ممتازة لبناء نظام تداول أزواج الفوركس المشترك. يبدو وكأنه مؤشر بولينجر باند، ولكن في الواقع يظهر مذبذب الفرق السعر بين اثنين من أزواج العملات المختلفة.
عندما يتحرك هذا المذبذب نحو أعلى أو منخفض للغاية، فإنه يشير إلى أن أزواج هي فصل، مما يشير إلى الصفقات.
ومع ذلك، للتأكد من النجاح أعتمد على بلدي نظام البناء الميكانيكية بنيت بشكل جيد لتصفية الإشارات مع اختبار ديكي فولر المعزز قبل تنفيذ الصفقات المناسبة.
وبطبيعة الحال، أي شخص يريد استخدام التكامل المشترك له أو لها أزواج الفوركس التداول، ولكن يفتقر إلى المهارات المطلوبة ألغو البرمجة، ويمكن الاعتماد على مبرمج من ذوي الخبرة لخلق مستشار خبير الفوز.
من خلال سحر التداول الخوارزمي، وأنا برنامج بلدي نظام التداول الميكانيكية لتحديد ينتشر السعر على أساس تحليل البيانات. خوارزميات بلدي خوارزمية لانحرافات الأسعار، ثم تلقائيا يشتري ويبيع أزواج العملات من أجل حصاد أوجه القصور في السوق.
المخاطر التي يجب أن تكون على دراية عند استخدام التكامل المشترك مع تداول أزواج الفوركس.
تداول أزواج العملات الأجنبية ليس خاليا تماما من المخاطر. قبل كل شيء، أنا أضع في اعتبارنا أن أزواج العملات الأجنبية التداول باستخدام التكامل هو استراتيجية انعكاس المتوسط، الذي يقوم على افتراض أن القيم المتوسطة سوف تكون هي نفسها في المستقبل كما كانت في الماضي.
على الرغم من أن اختبار ديكي-فولر المعزز المذكور سابقا مفيد في التحقق من العلاقات المتآزرة لتداول أزواج الفوركس، إلا أنه لا يعني أن فروق الأسعار ستستمر في أن تكون مشتركة في المستقبل.
أنا أعتمد على قواعد قوية لإدارة المخاطر، مما يعني أن نظام التداول الآلي الخاص بي يخرج من الصفقات غير المربحة إذا أو عندما يتم إبطال العائد المحسوب إلى المتوسط.
عندما تتغير القيم المتوسطة، انها تسمى الانجراف. أحاول الكشف عن الانجراف في أقرب وقت ممكن. وبعبارة أخرى، إذا بدأت أسعار أزواج الفوركس التي تم تجميعها سابقا في التحرك في اتجاه بدلا من العودة إلى المتوسط المحسوب سابقا، فقد حان الوقت لخوارزميات نظام التداول الآلي الخاص بي لإعادة حساب القيم.
عندما أستخدم نظام التداول الميكانيكي الخاص بي لتداول أزواج الفوركس، أستخدم صيغة الانحدار الذاتي المذكورة سابقا في هذه المقالة من أجل حساب المتوسط المتحرك للتنبؤ بالانتشار. ثم، أنا الخروج من التجارة في بلدي حدود الخطأ المحسوبة.
التكامل المشترك هو أداة قيمة لأزواج الفوركس بلدي التداول.
استخدام التكامل في أزواج الفوركس التداول هو استراتيجية التداول الميكانيكية محايدة السوق التي تسمح لي التجارة في أي بيئة السوق. انها استراتيجية ذكية تقوم على العودة إلى يعني، ومع ذلك فإنه يساعدني على تجنب المزالق لبعض استراتيجيات العودة إلى المتوسط يعني تداول العملات الأجنبية.
ونظرا لاستخدامه المحتمل في أنظمة التداول الميكانيكية المربحة، فقد اجتذب التكامل المشترك لتداول أزواج الفوركس الاهتمام من التجار المحترفين وكذلك الباحثين الأكاديميين.
هناك الكثير من المقالات التي نشرت مؤخرا، مثل هذه المادة بلوق تركز على بلوق، أو هذه المناقشة العلمية للموضوع، فضلا عن الكثير من النقاش بين التجار.
التكامل المشترك هو أداة قيمة في بلدي أزواج الفوركس التداول، وأنا أوصي أن ننظر في الأمر لنفسك.
يقول توماسو سيليان.
مادة جيدة جدا. هو ملهم. شكرا لكتابة ذلك!
يقول هاريش ناتشناني.
كما يتم تطبيق الارتباط في الأسهم (الأسهم). ماهو الفرق؟ هل يمكن تطبيق العملية المذكورة أعلاه على الأسهم؟
يقول إدي زهرة.
نعم، يمكن تطبيق نفس العملية على الأسهم وكذلك على المشتقات. ونظرا لوجود مثل هذا الكون الكبير من الأسهم عند مقارنته بأزواج الفوركس، ينبغي أن يكون هناك عدد أكبر من الفرص المحتملة للتداول. مع عدد من الطحن قوة اليوم & # 8217؛ s نظم التداول، العديد من مجموعات من العلاقات يمكن فحصها بسرعة، في الوقت الحقيقي. ويمكن أيضا استخدام التكامل المشترك من قبل التجار الخيارات؛ فإنه من المتوقع أن تنتج نتائج مثل انتشار كوكا كولا-بيبسي الشعبي الذي تسمح فيه العلاقات السعرية بين بعض الأسهم / الخيارات للمتداولين بالاشتراك في مسرحيات منخفضة المخاطر إلى حد ما مع فرصة جيدة إلى حد ما للفوز.
يقول هاريش ناتشناني.
هل تتداول في غضون يوم أو أكثر من أسابيع باستخدام هذه الاستراتيجية؟ أيضا، ما لغة البرمجة التي تنصح بها. R يستغرق وقتا طويلا لتشغيل الحسابات وإذا كان في غضون التجارة اليوم، الكمون يأتي في اللعب.
لغة البرمجة لا تهم التداول في نهاية اليوم. أي لغة رئيسية مثل بيرل، بايثون، C / C ++ و C # على ما يرام. R يمكن أن يكون سريع للغاية لكنه يبطئ إذا كان & # 8217؛ s اضطر إلى تخصيص حيوي الذاكرة.
أنا التجارة باستخدام الرسوم البيانية اليومية، وأنا البقاء في معظم الصفقات لبضعة أيام لبضعة أسابيع. شون هو مبرمج خبير، وأنا أثق دائما حكمه لاستخدام أفضل لغة البرمجة للحصول على أفضل النتائج لاستراتيجية التداول معين. في الواقع، يمكن لشون خلق برنامج متوازن، الفوز لتحقيق الاستفادة من التكامل المشترك وعوامل أخرى كذلك. إذا كنت & # 8217؛ د مثل الاقتباس، يرجى الاتصال به مباشرة في معلومات @ أونيستيبريموفيد.
يقول كريس زيمر.
وهناك بعض االهتمام بتنفيذ هذا البرنامج ل MT4. إذا كنت تستطيع تقديم بعض التفاصيل على تنفيذ هذه الاستراتيجية في التعليمات البرمجية، يرجى إرسالها إلى زيمر @ أونيستيبريموفد.
أنا أفعل مشروع صغير على استراتيجيات التكامل المشترك في فكس لبلدي ماجستير. أعتقد أنك ركض اختبارات التكامل المشترك على الكثير من أزواج العملات. ما هي تلك التي وجدت أنها ذات دلالة إحصائية مركزة بشكل كبير؟
أنا لا & # 8217؛ ر أعتقد إدي ركض في الواقع الأرقام. والمقصود من هذه المادة أن تكون دليلا شاملا لهذا المفهوم، ولكن ليس تماما لدرجة كونه استراتيجية حسن النية.
1) أوسد / جبي و ور / تشف.
2) ور / بلن و ور / هف.
3) أوسد / تري و أوسد / زار.
4) أود / أوسد و نزد / أوسد.
5) ور / نوك ور / سيك.
وأنا أعلم أن هذه ترتبط ارتباطا وثيقا للغاية، ولكن هذا لا يعني التكامل المشترك.
يقول كاميلو روميرو.
هناك أزواج الفوركس جيدة سوينغاتراتد:
لن يكون الدولار أوسجبي / ورشف زوجا متآلفا لأنه لن يكون هناك استراتيجية محايدة للسوق.
شكرا للمشاركة.
يقول كاميلو روميرو.
هل نفذ أي شخص شفرة باكتست باستخدام إستراتيجية الإرجاع المتوسط؟
هل يجب أن أقيم القيم بين أزواج الفوركس؟
هل أضاف أي شخص تكلفة العمولة إلى باكتست كود وحصلت على نتائج مربحة؟
I & # 8217؛ m متأكد من شخص ما لديه، لكنه & # 8217؛ s ليس شيئا حيث أنت & # 8217؛ سوف تجد لإجابة واضحة على الرسوم البيانية على المدى القصير. قد تجد كوانتيغراتيونس على المدى الطويل، ولكن هذا & # 8217؛ s لا البحوث أنا & # 8217؛ القيام به.
ويتمثل التكامل المشترك الوحيد بين اليورو والفرنك السويسري وبين الدولار الأسترالي والدولار النيوزيلندي حيث أن التجارة والاقتصاد الحميمين الوحيدين بين هذه البلدان والمصارف المركزية يخلقان هذا التكامل المشترك.
ليس اليورو و الجنيه الإسترليني؟
يقول روبرت J أرماغوست.
مرحبا إدي. مقال ممتاز. لقد تم اختبار مرة أخرى 10 سنوات من الرسوم البيانية التفكير & # 8221؛ لا أستطيع أن أكون أول شخص فكر في هذا! & # 8221؛ عندما وجدت هذا الموقع. شكرا جزيلا لكتابة هذا. أنا لا & # 8217؛ ر يشعر تماما حتى وحده بعد الآن. 🙂 فقط أتساءل أي وسيط كنت تستخدم أو هل تستخدم وسطاء متعددة. شكرا على وقتك.
مع خالص التقدير روبرت J. أرماغوست.
الوسيط الرئيسي الذي أستخدمه هو بيبرستون و ستو (عبر توبترادر).
مرحبا شون لقد تم تداول هذه الاستراتيجية يدويا. هل لديك برنامج لأتمتة هذا؟ (حتى أنا لا & # 8217؛ ر لديك للحصول على ما يصل في منتصف الليل بعد الآن) شكرا على وقتك.
ليس من على الرف، ولكن ذلك & # 8217؛ ق شيء يمكننا أن نبني. تبادل لاطلاق النار لي رسالة بالبريد الالكتروني مع قواعد الدخول والخروج للحصول على تقدير. معلومات @ onestepremoved.
روبرت & # 8212؛ شكرا لردود فعل طيبة. شون لديه الأدوات المناسبة لتنفيذ هذا النوع من استراتيجية التداول، وأنا أتفق تماما مع توصيات وسيط له، شكرا مرة أخرى للتعليق! EF.

استراتيجية التداول المشترك بين العملات الأجنبية
آخر تحديث للصفحة.
16 فبراير 2003.
استراتيجيات التداول القائمة على التكامل المشترك:
نهج جديد لتعزيز تتبع المؤشرات والمراجحة الإحصائية.
البحث عن التقنيات الكمية المناسبة لبناء استراتيجيات قصيرة الأجل للأسهم ليس آخر تطورات اللحظة في الأسواق المالية. الوافدين الجدد في هذه اللعبة والانضمام باستمرار اللاعبين التقليديين، وفي الوقت الراهن، والباحثين الأكثر حماسا في الاستراتيجيات الكمية هي صناديق التحوط المشاركة في تداول الأسهم. إن المرونة التشغيلية وعدم وجود قيود مناسبة بشكل مثالي للسماح لها بالاستفادة من تطبيق هذه الأنواع من استراتيجيات التداول.
في هذا الخط من البحث، نقترح عدة استراتيجيات "التكامل المشترك"، مثل تتبع مؤشر والمراجحة الإحصائية. وتهدف الاستراتيجية الأولى إلى تكرار معيار مرجعي من حيث العائدات والتقلب، في حين تسعى الأخرى إلى تحقيق عوائد ثابتة في ظل جميع ظروف السوق. وعلی عکس الاستراتیجیات التجاریة التقلیدیة الأخرى، فإن تحسین المحفظة یستند إلی التکامل المشترك بدلا من الارتباط. عندما تطبق على الأسهم في دجيا، وقد أسفرت هذه الاستراتيجيات التجارية نتائج مطردة جدا. فعلى سبيل المثال، بين كانون الثاني / يناير 1995 وكانون الأول / ديسمبر 2001، أعادت استراتيجيات المراجحة الإحصائية ذات التمويل الذاتي الأكثر نجاحا (بعد خصم تكاليف المعاملات وتكاليف إعادة الشراء) قرابة 10 في المائة مع تقلب سنوي بنسبة 2 في المائة تقريبا، وارتباط ضئيل بالسوق (الكسندر وديميتريو، 2002). وبطبيعة الحال، فإن الاستراتيجيات الممولة التي نوقشت في تلك الورقة تعود إلى حد بعيد، ولكن لديها تقلبات أعلى قليلا. في معظم السنوات كانت استراتيجياتنا نسب شارب قريبة من واحد.
كان تطبيق تقنية التكامل المشترك لتخصيص الأصول رائدا من قبل لوكاس (1997) والكسندر (1999). وخصائصها الرئيسية، أي تعادل خطأ التتبع وتعزيز الأوزان للاستقرار والاستخدام الأفضل للمعلومات المتضمنة في أسعار الأسهم، وتتيح تصميما مرنا لمختلف استراتيجيات التداول الممولة والتمويل الذاتي، بدءا من الفهرس وتعزيز تتبع المؤشرات، وتقنيات نقل السوق المحايدة وألفا.
لماذا تستخدم التكامل المشترك في إدارة المحافظ؟
وقد طبق مفهوم التكامل المشترك على نطاق واسع في الاقتصاد القياسي المالي فيما يتصل بتحليل السلاسل الزمنية والاقتصاد الكلي. وقد تطورت على أنها تقنية إحصائية قوية للغاية لأنها تسمح بتطبيق أساليب تقدير بسيطة (مثل العادي العادي الحد الأدنى وأقصى احتمال) للمتغيرات غير ثابتة. ومع ذلك، فإن أهميتها بالنسبة لتحليل االستثمار كانت محدودة إلى حد ما حتى اآلن، ويرجع ذلك أساسا إلى حقيقة أن المعيار في إدارة المحفظة وقياس المخاطر هو تحليل ارتباط عائدات األصول.
ومع ذلك، فإن تحليل الارتباط صالح فقط للمتغيرات الثابتة. ويتطلب ذلك عدم التجاهل في الأسعار والمتغيرات المالية الأخرى التي عادة ما يتم دمجها في النظام الواحد أو أعلى. أخذ الفارق الأول في أسعار السجل هو الإجراء القياسي لضمان الاستقرارية ويقود كل الاستدلال الإضافي إلى أن يقوم على العوائد. بيد أن هذا الإجراء ينطوي على عيب فقدان المعلومات القيمة. وعلى وجه الخصوص، فإن إزالة المتغيرات قبل التحليل يزيل أي إمكانية للكشف عن الاتجاهات المشتركة في الأسعار. على النقيض من ذلك، فإن الهدف من تحليل التكامل المشترك هو الكشف عن أي اتجاه مؤشر ستوكاستيك في بيانات الأسعار واستخدام هذه الاتجاهات المشتركة لتحليل ديناميكي للارتباط في العائدات (الكسندر، 2001).
والملاحظة الأساسية التي تبرر تطبيق مفهوم التكامل المشترك، على سبيل المثال، تحليل أسعار الأسهم، هي أن نظام أسعار الأسهم غير الثابتة في المستوى يمكن أن يشترك في الاتجاهات العشوائية المشتركة (ستوك أند واتسون، 1991). وفقا ل بيفريدج ونيلسون (1981)، متغير لديه اتجاه مؤشر ستوكاستيك إذا كان الفرق له أرما الثابتة (p، q) التمثيلية بالإضافة إلى عنصر حاسم. وبما أن نماذج أريما (p، 1، q) يبدو أنها تميز العديد من المتغيرات المالية، فإنه يتبع أن النمو في هذه المتغيرات يمكن وصفه من خلال اتجاهات مؤشر ستوكاستيك.
وعند تطبيقه على أسعار األسهم في مؤشر سوق األسهم، فإن التكامل المشترك موجود عندما توجد محفظة واحدة على األقل من األسهم ذات خطأ تتبع ثابت) نستخدم خطأ تتبع المصطلح كما يفعل اإلحصائيون، لإلشارة إلى الفرق بين المؤشر والمحفظة (، . وبعبارة أخرى، يحدث التكامل المشترك عندما يكون هناك انعكاس في انتشار السعر بين المحفظة والمؤشر. ولا توفر هذه النتيجة أي معلومات للتنبؤ بالأسعار الفردية في النظام، أو موقف النظام في مرحلة ما في المستقبل، ولكنها توفر معلومات قيمة، بصرف النظر عن موقعها، وأسعار الحافظة والمؤشر ستبقى معا على المدى الطويل.
مخطط استراتيجيات التداول.
وبالنظر إلى ما ذكر أعلاه، فإن إيجاد علاقة التكامل المشترك، أي مزيج خطي ثابت من مؤشر السوق وعدد من المخزونات من مكوناته (عادة ما تكون محددة على أنها أسعار السجل)، يعادل وجود متوسط عائد متكرر بين مؤشر السوق وحافظة تتبع . وفي ظل هذه الظروف، عن طريق التشييد، فإن عوائد محفظة التعقب سوف تساوي عوائد المؤشر، على المدى الطويل.
وباإلضافة إلى ذلك، فإن األوزان الحافظة، التي يجري بناؤها على تاريخ طويل نسبيا من األسعار، تميل إلى تجاهل الحركات قصيرة األجل في أسعار األسهم، مثل الفقاعات أو الضجيج فقط، والتركيز على سلوك األسعار على المدى الطويل. وكما هو مبين من قبل، فإن حقيقة أن خطأ التتبع هو، حسب الإنشاء، يعني أن التراجع يضمن أن تبقى محفظة التعقب "مرتبطة ببعضها" بالمؤشر على المدى الطويل، بصرف النظر عن التحركات قصيرة الأجل في أسعار الأسهم الفردية. ومع ذلك، يمكن أن يكون هناك ارتباطات قصيرة الأجل بين محفظة التتبع والمؤشر. في الواقع، وهذا هو مصدر محتمل لل "ألفا"، أي العائد الزائد، في محافظ التعقب.
ويمكن بناء عدد من استراتيجيات التداول على أساس علاقات التكامل المشترك:
أ. تتبع الفهرس.
إن أول استراتيجية تجارية قائمة على التكامل المشترك، هي عبارة عن تتبع مؤشر كلاسيكي يهدف إلى تكرار معيار مرجعي من حيث العائد والتقلب. وتستتبع عملية تتبع الفهرس مرحلتين، بنفس الدرجة من الأهمية: أولا، اختيار المخزونات التي ستدرج في محفظة التتبع، ثم تحديد حيازات الحافظة في كل مخزون على أساس تقنية التحسين المشترك.
المرحلة الأولى، اختيار الأسهم، يمكن أن يكون نتيجة لنماذج اختيار الملكية، التحليل الفني، أو مجرد مخزون قطف مهارات مدير محفظة. وستعتمد درجة التكامل المشترك وبالتالي أداء التتبع كثيرا على عملية الاختيار. ومع ذلك، فإن عملية الانتقاء لا تتسم بخصائص خاصة في أسلوب التتبع القائم على التكامل المشترك. ويشكل ذلك متغيرا سيطريا في تحديد استراتيجية التتبع الأنسب.
وتتعلق المرحلة الثانية من تتبع المؤشرات بتحديد حيازات الحافظة في كل من الأسهم المختارة في المرحلة السابقة. وتقدر أوزان األسهم في كل محفظة على أساس المعامالت العادية األقل مربعة من معادلة التكامل المشترك التي تفسر سعر سجل المؤشر على سجل مخزونات المحفظة على مدى فترة معايرة معينة قبل لحظة إنشاء المحفظة. ونلاحظ أن تطبيق عملية شريان الحياة للسودان على المتغيرات التابعة غير الثابتة مثل السجل (الفهرس) لا يسري إلا في الحالة الخاصة لعلاقة التكامل المشترك. وما لم تكن المخلفات المتبقية من انحدار التكامل المشترك ثابتة، فإن معاملات عملية شريان الحياة للسودان ستكون غير متناسقة، وسيكون الاستدلال الإضافي القائم عليها غير صالح. ولذلك، فإن اختبار التكامل المشترك هو خطوة أساسية في بناء محافظ التعقب القائم على التكامل المشترك.
بالإضافة إلى التقدير، يتم تطبيع معاملات عملية شريان الحياة للسودان لتلخيص واحد، وبالتالي توفير أوزان كل سهم في محفظة التتبع.
كما هو مبين في ألكسندر وديميتريو (2002)، وحتى باستخدام قواعد بسيطة لاختيار الأسهم مثل ترتيب الأسهم حسب وزنها في المؤشر، والمحافظ تتبع بناء على أساس هذه المنهجية يمكن تكرار بدقة مؤشر السوق.
باء - تعزيز تتبع المؤشرات والمراجحة الإحصائية.
وبعد إنشاء إستراتيجية تتبع بسيطة، فإن امتدادا طبيعيا لاستغلال إمكانيات التتبع للمحافظ المشتركة، يتمثل في تكرار الفهارس الصناعية "زائد" أو "ناقص"، والتي يتم إنشاؤها على أساس الأداء المفرط خطيا أو ضعف أداء مؤشر السوق من خلال مبلغ معين سنويا. وبعد ذلك، يمكن وضع استراتيجيات التمويل الذاتي طويلة الأجل عن طريق اختصارها على محفظة تتبع معيار "ناقص"، وطويلة على محفظة تتبع مؤشر "زائد".
هذا النوع من إستراتيجية المراجحة الإحصائية يجب أن يولد عوائد وفقا ل "زائد" / "ناقص" انتشار (أي ألفا مزدوج) مع تقلب منخفض إلى حد ما ولا علاقة كبيرة مع عائدات السوق. ونتوقع أن نجد صعوبة متزايدة في العثور على حافظات متداخلة كقيمة للفارق بين الزيادات المتراكمة المعيارية. إن علاقة التكامل المشترك بين مؤشر السوق وأرصدة مكوناته لها أساس منطقي قوي، ولكن ليس هذا هو الحال بالضرورة بالنسبة للمحافظ التي تتبع معايير صناعية، والتي يمكن اختيارها لإفراط في أداء مؤشر السوق بنسبة 50٪، على سبيل المثال. وتؤدي الصعوبة في إيجاد علاقة مناسبة للتكامل المشترك إلى زيادة عدم استقرار الأوزان، وارتفاع تكاليف المعاملات، وارتفاع تقلب العائدات. ولتجنب ذلك، من الضروري التأكد من أن جميع المحاور تتبع "زائد" أو "ناقص" تمر اختبار التكامل المشترك.
ج - الجمع بين تتبع الفهرس والمراجحة الإحصائية.
وفي حالة عدم وجود شرط حياد السوق والتعرض لمؤشر السوق، فإن هناك احتمالا آخر يتمثل في نقل ألفا المكتسب في الإطار المحايد للسوق إلى فهرس، من خلال استخدام المشتقات (مثل العقود الآجلة للمؤشرات). أو، عوضا عن المشتقات، يمكن تنفيذ إجراء معزز لتتبع المؤشرات القائمة على التكامل المشترك.
وينبغي أن يكون لهذا النوع من الاستراتيجية، الذي يجمع بين تتبع المؤشر المعزز والمراجحة الإحصائية، علاقة وثيقة مع مؤشر السوق، بينما يكتسب ألفا من مصدرين: الأول، العائد الزائد من تعقب المؤشر المعزز، ثم ألفا مزدوجا من المراجحة الإحصائية. عند تطبيق استراتيجيات نقل ألفا إلى الأسهم في دجيا، ألكسندر وديميتريو (2002) قد حصلت على نسب أفضل بكثير شارب ثم في السوق، حتى بعد احتساب تكاليف المعاملات والريبو.
وکما أشیر سابقا، فإن لمفھوم التکامل المشترك عدد من السمات الجذابة في نمذجة أسعار الأصول، مما یوصی بھ کبدیل أفضل بکثیر عن تحلیل الارتباطات التقلیدیة في إدارة المحفظة. وخصائصه الرئيسية، أي تعني عائد خطأ التتبع، وتعزيز الأوزان الاستقرارية، والاستخدام الأفضل للمعلومات المتضمنة في أسعار الأسهم، والسماح بتصميم مرن لاستراتيجيات التداول، من تتبع المؤشرات المعزز إلى المراجحة الإحصائية. وعلاوة على ذلك، فإن تطبيقه في بناء استراتيجيات التداول داخل أسهم دي جي إيه قد أسفر عن نتائج مشجعة، والتي يمكن زيادة صقلها.
الكسندر، C. O. (1999) & كوت؛ التحوط الأمثل باستخدام التكامل المشترك & كوت؛ المعاملات الفلسفية للجمعية الملكية A 357، pp.2039-2058.
الكسندر، C. O. (2001) نماذج السوق: دليل لتحليل البيانات المالية، جون وايلي، ص 347-388.
الكسندر، C. O. أند ديميتريو (2002) & كوت؛ التكامل المشترك ألفا: تعزيز تتبع المؤشر والأسواق قصيرة الأجل استراتيجيات محايدة & كوت ؛، ورقة مناقشة 2002-08، ورقات مناقشة مركز إسما في سلسلة المالية.
بيفريدج، S. أند C. R. نيلسون (1981) & كوت؛ A نيو أبروتش تو ديكولبوسيتيون أوف إكونوميك تايم سيريز إن بيرماننت أند ترانزيتوري كومبونينتس ويث إكسيرتيفنتيون تو ماسوريمنت أوف ذي بوسينيس سيكل & كوت؛، جورنال أوف مونيتاري إكونوميكس 7، pp.151-74.
لوكاس، A. (1997) & كوت؛ الاستراتيجية والتكتيكية الأصول تخصيص وتأثير طويل التوازن التوازن العلاقات & كوت؛، مذكرة البحوث 1997-42، جامعة فرايج أمستردام.

جيكو كوانت - التداول الكمي.
التداول الكمي، التحكيم الإحصائي، تعلم الآلة والخيارات الثنائية.
آخر الملاحة.
إربيتال أربتريج & # 8211؛ تداول زوج مشترك.
في آخر مشاركة جيكوكانت / 2018/12/17 / إحصائي-التحكيم-اختبار-ل - التكامل المشترك-زيادة-ديكي-أكمل / أثبتت التكامل المشترك، وهو اختبار رياضي لتحديد أزواج ثابتة حيث يجب أن يكون الانتشار حسب التعريف يعني العودة.
في هذا المنصب أعتزم أن أشرح كيفية تداول زوج مشترك، وسوف تستمر في تحليل أسهم رويال داتش شل A مقابل B (ونحن نعلم أنها & # 8217؛ كوينتيغراتد من آخر مشاركة بلدي). تداول زوج كوينغراتد هو مستقيم إلى الأمام، ونحن نعرف متوسط والتباين في انتشار، ونحن نعلم أن تلك القيم هي ثابتة. نقطة الدخول ل أرب ستات هي مجرد البحث عن انحراف كبير بعيدا عن المتوسط.
وتتمثل الاستراتيجية الأساسية فيما يلي:
إذا انتشرت (t) & غ؛ = يعني سبرياد + 2 * الانحراف المعياري ثم انتقل شورت إف سبرياد (t) & لوت؛ = مين سبرياد & # 8211؛ 2 * الانحراف المعياري ثم يذهب طويل.
إذا كان معدل الانتشار (t) & غ؛ = ناداي موفينغ أفيراج + 2 * ناداي رولينغ ستاندارد ديفياتيون ثين غو شورت إف سبرياد (t) & لوت؛ = ناداي موفينغ أفيراج & # 8211؛ 2 * ناداي المتداول الانحراف المعياري ثم يذهب طويلا.
إذا انتشرت (t) & لوت؛ = متوسط انتشار + 2 * الأمراض المنقولة جنسيا وانتشار (t-1) & غ؛ متوسط انتشار + 2 * ستد إذا انتشار (t) & غ؛ = يعني سبرياد & # 8211؛ 2 * الأمراض المنقولة جنسيا وانتشار (t-1) & لوت؛ مين سبرياد & # 8211؛ 2 * ستد ميزة هي أننا التجارة فقط عندما نرى متوسط انعكاس، حيث كما نماذج أخرى تأمل في متوسط انعكاس على انحراف كبير عن المتوسط (هو انتشار تهب؟)
ستنظر هذه المشاركة في المتوسط المتحرك ونموذج الانحراف المعياري المتداول لأسهم شركة رويال داتش شل A مقابل B، وسوف تستخدم نسبة التحوط الموجودة في آخر مشاركة.
شارب راتيو شل A & أمب؛ B ستات أرب شل A.
نسبة شارب السنوية (رف = 0٪):
شل A & أمب؛ B ستات أرب 0.8224211.
شل A 0.166307.
The stat arb has a Superior Sharpe ratio over simply investing in Shell A. At a first glance the sharpe ratio of 0.8 looks disappointing, however since the strategy spends most of it’s time out of the market it will have a low annualized sharpe ratio. To increase the sharpe ratio one can look at trading higher frequencies or have a portfolio pairs so that more time is spent in the market.
22 أفكار حول & لدكو؛ Statistical Arbitrage – Trading a cointegrated pair ”
it also means that when identified the maximum divergence i can take position in derivatives like options?
-selling ATM Call option on first stock.
-buy Call option on the second one.
or with a BacKSpreadCall on the first and a BackSpreadPut on the second so I can set the protections and I can roll them if they go out control…
The short positions should be moneyness ATM or lightly OTM in my opinion.
What do yo think about?
Did you tried using Johansen’s testing approach in order to perform a more rigorous testing of cointegration? What do you think about combining Engle-Granger with Johansen?
The spread in the above does not oscillate around it mean, ideally, a cointegrated pair should trade sideways not in a trending manner as shown above….your write-up was perfect on proper cointegration you demonstrated. but this spread is not a perfect spread.
I 100% agree with you.
However for practical purposes as long as the mean reversion happens faster than the mean changes then you’ll do well.
I guess that’s something I’ve missed, how to quantify the half life/reversion speed.
Please note that in the above demo the look back period is 90days. This is fairly short. Choosing 200 days will result in a mean that is less responsive / changes direction. It will most likely increase the size of the standard deviation bands and result in less trades per year. This usually results in a lower Sharpe ratio.
Very interesting post. Would love to see the implementation on a basket of pairs.
I do some changes in your programme to calculate the bollinger bands and I wanna know why you’re put the Standard deviation to the right? (movingStd = rollapply(spread, lookback, sd, align=”right”, na. pad=TRUE))
OK thank you for answering!
Your blog give me the chance to implement and build more quickly my stat arb strategy.
I am going to test different models for statistical arbitrage. I keep all the visitors in the loop!
In your program, the martingale effect is not here. How can I add this effect?
I am running my iwn backtests with differents programs (Excel, R et ProRealTime (a french platform)) and in order to do some comparison, I need to add the martingale effect.
Thanks for the clarification. By the same argument, rollmean has to have the same: rollmean(spread, lookback, na. pad=TRUE, align=’right’)
With this new modification the Sharpe ratio drops dramatically ..
Great stuff!! I think there are two bugs in your code, though. First one is in calculation of moving average. You forgot to set align parameter to “right” (like you do for standard deviation). Function uses default “center” and your data – spread and moving average are not aligned. You can see this from the plot as well. Moving average ends 45 days before the spread. Second bug is in calculation of trading returns. I think you should take return from the next day as we enter the position at the closing price.
Thanks for your elegant code. I noticed that your line of code:
is meant to apply the function shortPositionFunc to (-1aboveUpperBand+belowMAvg).
However, the function shortPositionFunc takes two arguments x and y.
Is there any typo in the code?
Thank you for your clarification!
Thanks Gekko for the backtesting code. It is very useful. Couple of comments below:
1) Another reader has already commented about this above. movingAvg needs to be amended by adding align=”right” in order to have the first moving avg number on day 90:
movingAvg = rollmean(spread, lookback, align=”right”, na. pad=TRUE)
2) since we enter trades at end of day, the return on trade date shouldn’t count. we can simply shift every element in the “positions” vector down by using the “shift” function in the taRifx library.
Also, I don’t believe daily return is (aRet – stockPair$hedgeRatiobRet). Imagine if you had a large hedge ratio, i. e. if stock A is priced at $100 and stock B is priced at $10, then the hedgeRatio would be in the neighborhood of 10. Since aRet and bRet are in % terms, the formula won’t work. Daily return should be aRet – bRet * (ratio between dollar neutral ratio vs hedge ratio).
#Calculate spread daily ret.
dailyRet <- aRet – bRethedgeRatioOVERdollarNeutralRatio.
tradingRet <- dailyRet shift(positions,-1)
I am looking for new strategies in equity pair trading that improve the standard cointegration approach (for instance I started looking into the pair trading with copulas, which still seems an “unstable” alternative to cointegration). Do you have any new paper to suggest me? Thank you very much and congrats for the great blog.
The second half of the book goes through lots of more advanced techniques for hedging a portfolio / finding stationary pairs.
i am a bit confused in this step.
when i plotted the longPositions and ShortPositions along with the spread, bands and moving average lines found then there are consecutive long signals and short signals. According to my understanding.
longPostions <- if spread is below lowerband.
longExit <- if spread is above movAvg while long.
shortPostions <- if spread is above upperband.
shortExit <- if spread is below movAvg while short.
is this same thing your code is doing. Please help me understand this part.
Hi Gekko, I read the books of EP Chan that talks about this topic and I a little bit confused about mean reservion. When two assets ara cointegrated we are supposing that they will come back to their mean, but their moving average or their total mean in a fixed period? I’m giving better results using static parameters than using bollinger bands. I will show you an image with my doubt. prntscr/51jofw Could you write another article of mean reversion! Thanks for all.
Hi Gekko. Great Code. Could you closer explain an idea behind this cappedCumSum function ? I do not understand the moment when you are specifing two input variables, but in Reduce() function is only one parameter, – is it because of 0?
There is a mistake. Your algorithm looks in the future, the problem in rollmean function. Algorithm using moving average from future days to close position.

Mechanical Forex.
Trading in the FX market using mechanical trading strategies.
Cointegration in the Forex market.
From the many different types of statistical arbitrage available, pairs trading is perhaps one of the most popular. In pairs trading a trader will attempt to exploit the linear relationship between the values of two instruments, attempting to buy/sell them when the relationship between their values increases/decreases to values that offer enough profit potential. However pairs trading does not only require a linear correlation to exist but it also requires the instruments to be cointegrated, a fundamental property that ensures a fundamental connection between the instruments that diminishes the probability of the spread between both instruments “blowing up” (widening far beyond what is statistically expected). Although pairs trading is usually described in stocks/commodities, we rarely see any study of cointegration in the FX market. Today we’re going to look at some potential cointegrations in the FX market, why they exist and how they might be exploited.
Let us begin by defining what we mean by cointegration. Two series are cointegrated when they share a common stochastic drift. The typical example to explain cointegration talks about a man who goes to a bar with his dog. After getting drunk and leaving the bar both the man and the dog walk the same path home, although their stochastic drift – which is the random way in which the man walks and the dog wonders along the way – are different. When this happens their paths are in fact correlated but they are not cointegrated. 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 . I hope you enjoyed this article ! :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 EngleвЂ“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 strategy 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]
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Here’s a very simple algorithm based on the approach presented in the notebook.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thanks for this. Very useful indeed. 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?
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
شكر. 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.
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@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.
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@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.
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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).
عمل جيد. 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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
Not precisely. 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. but why? 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.
بلى. 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. ومثل. 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.
O. K. 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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thank you for your quick reply.
This is actually a very valuable response, as I was afraid I might have missed something obvious.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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 2017 to Feb 2018 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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
Cool. 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.
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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.
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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' folder. 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.
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May 28 algo falls below benchmark if extended to date and -43% PvR with default slippage and commissions, tanking thru 2018.
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.
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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.
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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.
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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.
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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 2018.
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.
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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.
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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.
شكرا جزيلا. 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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
Thanks, Delaney. I submitted the PR to the specified branch.
شكر! 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!
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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" to deal with. Then, if you like, you can delay buying until the X_ask_zscore < threshold, and delay selling until the X_bid_zscore > exit_threshold.
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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.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
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?
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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.
In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.
In addition, the material offers no opinion with respect to the suitability of any security or specific investment. 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. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.

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