Una Anatomía De Las Estrategias Comerciales Conrad Y Kaul

Por Harrison Hong, Terence Lim, Jeremy C. Stein - diario de las finanzas. 2000. Se han propuesto varias teorías para explicar el impulso de los retornos de las acciones. Probamos el modelo gradual de difusión de información de Hong y Stein (1999) y establecemos tres resultados clave. En primer lugar, una vez que se pasa de las poblaciones más pequeñas, la rentabilidad de las estrategias de impulso disminuye drásticamente con la empresa. Se han propuesto varias teorías para explicar el impulso de los retornos de las acciones. Probamos el modelo gradual de difusión de información de Hong y Stein (1999) y establecemos tres resultados clave. En primer lugar, una vez que se pasa de las existencias más pequeñas, la rentabilidad de las estrategias de impulso disminuye drásticamente con el tamaño de la empresa. En segundo lugar, manteniendo el tamaño fijo, las estrategias de impulso funcionan mejor entre las acciones con baja cobertura de analistas. Finalmente, el efecto de la cobertura del analista es mayor para las acciones que han perdido el pasado que para los ganadores anteriores. Estos resultados son consistentes con la hipótesis de que la información específica de la empresa, especialmente la información negativa, se difunde sólo gradualmente en el público inversor. VARIOS DOCUMENTOS RECIENTES HAN DOCUMENTADO que, en los horizontes de mediano plazo que oscilan entre tres y 12 meses, los retornos de las acciones muestran un impulso, es decir, los ganadores anteriores siguen funcionando bien y los perdedores pasados ​​siguen teniendo un desempeño pobre. Por ejemplo, Jegadeesh y Titman (1993), utilizando una muestra estadounidense de acciones de NYSE / AMEX durante el período de 1965 a 1989, encuentran que una estrategia que compra a los últimos seis meses ganadores (acciones en el decil de rendimiento superior) - los perdedores de un mes (acciones en el decil de rendimiento inferior) ganan aproximadamente un uno por ciento por mes durante los seis meses subsiguientes. Esto no sólo es una magnitud económicamente interesante, sino que el resultado también parece ser robusto: Rouwenhorst (1998) obtiene números muy similares en un por Jonathan B. Berk, Richard C. Green, Vasant Naik - Journal of Finance. 1999. Como consecuencia de las opciones óptimas de inversión, los activos de una empresa y las opciones de crecimiento cambian de manera predecible. Utilizando un modelo dinámico, mostramos que esto imparte previsibilidad a los cambios en el riesgo sistemático de una empresa, y su retorno esperado. Las simulaciones muestran que el modelo reproduce simultáneamente: Como consecuencia de las opciones de inversión óptimas, los activos de una empresa y las opciones de crecimiento cambian de manera predecible. Utilizando un modelo dinámico, mostramos que esto imparte previsibilidad a los cambios en el riesgo sistemático de una empresa, y su retorno esperado. Las simulaciones demuestran que el modelo reproduce simultáneamente: i la relación de series de tiempo entre la relación libro-mercado y los rendimientos de activos ii la relación transversal entre el valor en libros, el valor de mercado y el retorno iii efectos contrarios a corto plazo iv Los efectos de momento en horizontes más largos yv la relación inversa entre las tasas de interés y la prima de riesgo de mercado. INVESTIGACIÓN EMPÍRICA RECIENTE EN FINANZAS se ha centrado en las regularidades en la sección transversal de retornos esperados que parecen anómalos en relación con los modelos tradicionales. Las rentabilidades de las acciones están relacionadas con el valor en libros y el valor de mercado. 1 También se ha demostrado que las rentabilidades pasadas predicen el rendimiento relativo, a través del éxito documentado de las estrategias contraria y momentum. 2 Las explicaciones existentes de estos resultados son que se deben a sesgos de comportamiento o premios de riesgo para variables de estado omitidas. 3 Estas explicaciones competitivas son difíciles de evaluar sin modelos que vinculen explícitamente las características de interés con los riesgos y las primas de riesgo. Por ejemplo, con respecto al libro a mercado, Lakonishok et al. 1994 argumenta: El punto aquí es simple: aunque los retornos a la estrategia de B0M son impresionantes, B0M no es una variable limpia asociada únicamente con el eco - por Charles M. C. Lee, Bhaskaran Swaminathan - Diario de Finanzas. Este estudio muestra que el volumen de operaciones pasado proporciona un vínculo importante entre el impulso y las estrategias de valor. Específicamente, encontramos que las firmas con altas tasas de rotación pasadas muestran muchas características de valor de glamour, ganan retornos futuros más altos y tienen consistentemente más negatividad. Este estudio muestra que el volumen de operaciones pasado proporciona un vínculo importante entre el impulso y las estrategias de valor. Específicamente, encontramos que las firmas con altas tasas de rotación pasadas muestran muchas características de valor de glamour, ganan retornos futuros más altos y tienen consistentemente más sorpresas de ganancias positivas negativas en los próximos ocho trimestres. El volumen de operaciones anteriores también predice tanto la magnitud como la persistencia del impulso de los precios. Específicamente, los efectos del momentum de los precios revertirán en los próximos cinco años y los ganadores de los ganadores de alto volumen bajo experimentarán reversiones más rápidas. Colectivamente, nuestros hallazgos demuestran que el volumen pasado ayuda a conciliar la sub-reacción del horizonte intermedio y los efectos de la sobre-reacción del horizonte largo. ACADEMICOS FINANCIEROS Y PRACTICADORES han reconocido desde hace tiempo que el volumen de operaciones pasado puede proporcionar información valiosa sobre un valor. Sin embargo, hay poco acuerdo sobre cómo la información de volumen debe ser manejado e interpretado. Se conoce aún menos sobre cómo el volumen de operaciones anteriores interactúa con los rendimientos pasados ​​en la predicción de las rentabilidades futuras de las acciones. Y por Sung Wook Joh - Revista de Economía Financiera. Este estudio examina cómo la estructura de propiedad y los conflictos de intereses entre los accionistas bajo un sistema de gobierno corporativo deficiente afectaron el desempeño de la empresa antes de la crisis. Utilizando 5.829 empresas coreanas sujetas a auditorías externas durante 1993-1997, el documento encuentra que las empresas con baja propiedad se concentran. Este estudio examina cómo la estructura de propiedad y los conflictos de intereses entre los accionistas bajo un sistema de gobierno corporativo deficiente afectaron el desempeño de la empresa antes de la crisis. Utilizando 5.829 empresas coreanas sujetas a auditorías externas durante 1993-1997, el documento concluye que las empresas con baja concentración de propiedad muestran una baja rentabilidad de la empresa, controlando las características de la empresa y de la industria. Los accionistas controladores expropiaron los recursos de la empresa incluso cuando su concentración de propiedad era pequeña. Las empresas con una alta disparidad entre derechos de control y derechos de propiedad mostraron baja rentabilidad. Cuando un grupo empresarial transfirió recursos de una subsidiaria a otra, a menudo se desperdiciaron, lo que sugiere que se produjo un túnel. Además, los efectos negativos de la disparidad entre el control y la propiedad y la ineficiencia interna del mercado de capitales eran más fuertes en las empresas que cotizaban en bolsa que en las privadas. Agradezco a los participantes en el XII Seminario Anual NBER sobre Economía del Este Asiático y la reunión mundial de congresos de la sociedad econométrica para comentarios sobre La versión anterior de este documento. Estoy especialmente agradecido a Simon Johnson ya un árbitro anónimo por sus valiosas sugerencias. Sus útiles comentarios han mejorado mucho el trabajo. Sin embargo, todos los errores restantes son míos. Por tres razones por lo menos. En primer lugar, los investigadores han demostrado cierta ineficacia en los mercados incluso en los países más desarrollados (De Bondt y Thaler, 1985, 1987). Lo y MacKinlay, 1988 - Conrad y Kaul, 1998-. Los países en desarrollo también muestran ineficiencia del mercado de valores. 1 Por lo tanto, es probable que los precios de las acciones en Corea no reflejen toda la información disponible. En segundo lugar, Mossman, Bell, Swart y Turtle (1998) muestran que. Por Tarun Chordia, Lakshmanan Shivakumar. 2001. Un número creciente de investigadores sostienen que los patrones de series de tiempo en los retornos se deben a la irracionalidad del inversionista y, por lo tanto, pueden traducirse en ganancias anormales. La continuación de los retornos a corto plazo o el impulso es uno de esos patrones que ha desafiado cualquier explicación racional y está en desacuerdo con la eficacia del mercado. Un número creciente de investigadores sostienen que los patrones de series de tiempo en los retornos se deben a la irracionalidad del inversionista y, por lo tanto, pueden traducirse en ganancias anormales. La continuación de los retornos a corto plazo o el impulso es uno de esos patrones que ha desafiado cualquier explicación racional y está en desacuerdo con la eficiencia del mercado. Este artículo muestra que las estrategias de beneficios a momentum pueden ser explicadas por un conjunto de variables macroeconómicas rezagadas y los beneficios de las estrategias de impulso desaparecen una vez que las rentabilidades de las acciones se ajustan para su previsibilidad en base a estas variables macroeconómicas. Nuestros resultados proporcionan un posible papel para los retornos esperados que varían en el tiempo como una explicación de los retornos de impulso. ESTE DOCUMENTO EXAMINA LA RELATIVA importancia de factores comunes e información específica de la empresa para explicar la rentabilidad de las estrategias de negociación basadas en el impulso, documentadas por Jegadeesh y Titman 1993. La rentabilidad de las estrategias de impulso ha sido particularmente intrigante, ya que sigue siendo la única anomalía relacionada con el CAPM Inexplicado por el FamaFrench por Ravi Bansal, Robert F. Dittmar, Christian T. Lundblad. 2004. En este artículo mostramos que los riesgos económicos incorporados en los flujos de efectivo representan una gran parte de las diferencias transversales en las primas de riesgo entre los activos. Específicamente, modelamos la dinámica conjunta del consumo agregado observado y las tasas de crecimiento del flujo de efectivo de los activos como un vector-autorregresión (VAR). En este artículo mostramos que los riesgos económicos incorporados en los flujos de efectivo representan una gran parte de las diferencias transversales en las primas de riesgo entre los activos. Específicamente, modelamos la dinámica conjunta del consumo agregado observado y las tasas de crecimiento del flujo de efectivo de los activos como un vector-autorregresión (VAR). Desde el VAR, se mide el flujo de efectivo beta, que es el consumo beta de noticias relativas a la suma descontada constante de las tasas de crecimiento del flujo de efectivo esperado. Las diferencias transversales en las betas de flujos de efectivo representan más de 60 de la variación transversal de las primas de riesgo en 30 carteras, que incluyen 10 carteras clasificadas, 10 carteras clasificadas a la venta y 10 cargas de mercado. Nuestro trabajo empírico muestra que la compensación por este riesgo de consumo en los flujos de efectivo es positiva y altamente significativa. Nuestros betas de flujo de efectivo tienen mejores resultados que los modelos de referencia alternativos para explicar las diferencias transversales en los retornos medios de los activos. Proporcionamos una interpretación económica para nuestros resultados empíricos por Cars Hommes, Joep Sonnemans, Jan Tuinstra, Henk Van De Velden - Revisión de Estudios Financieros. 2005. Resumen: Se investiga la formación de expectativas en un entorno experimental controlado. Se pide a los sujetos que prevean el precio en un modelo estándar de tasación de activos. No tienen conocimiento de las ecuaciones de equilibrio de mercado subyacentes, pero conocen todos los precios realizados en el pasado y sus propias predicciones. Resumen: Se investiga la formación de expectativas en un entorno experimental controlado. Se pide a los sujetos que prevean el precio en un modelo estándar de tasación de activos. No tienen conocimiento de las ecuaciones de equilibrio del mercado subyacente, pero conocen todos los precios realizados en el pasado y sus propias predicciones. La demanda agregada del activo de riesgo depende de las previsiones de los participantes. El precio realizado se obtiene entonces del equilibrio del mercado con retroalimentación de las expectativas individuales. Cada mercado está poblado por seis sujetos y una pequeña fracción de los comerciantes fundamentalistas. Los precios realizados difieren significativamente de los valores fundamentales. En algunos grupos el precio de los activos converge lentamente al precio fundamental, en otros grupos hay oscilaciones regulares alrededor del precio fundamental. En todos los grupos los participantes se coordinan en una estrategia de predicción común. Las estrategias de predicción individual pueden ser estimadas y corresponden, para una gran mayoría de participantes, a simples reglas lineales de previsión autorregresiva. Por Soeren Hvidkjaer - REVISIÓN DE ESTUDIOS FINANCIEROS. 2006. Este artículo utiliza datos de transacciones para todas las acciones de NYSE / AMEX en el período 19832002 para estudiar cómo los inversionistas comercian en las carteras de impulso de Jegadeesh y Titmans (1993). Entre los pequeños oficios, hay una reacción extremadamente lenta a los retornos pasados. Por ejemplo, una inicial de compra de pequeña compra pressur. Este artículo utiliza datos de transacciones para todas las acciones de NYSE / AMEX en el período 19832002 para estudiar cómo los inversionistas comercian en las carteras de impulso de Jegadeesh y Titmans (1993). Entre los pequeños oficios, hay una reacción extremadamente lenta a los retornos pasados. Por ejemplo, existe una presión inicial de compra de pequeños comercios para las acciones perdedoras, y se convierte gradualmente en una intensa presión de venta durante el año siguiente. Los resultados son consistentes con la sub-reacción inicial seguida por la reacción tardía entre los pequeños comerciantes. Por otra parte, los desequilibrios de los pequeños intercambios durante el período de formación afectan significativamente los retornos de impulso, lo que sugiere que la falta de reacción entre los pequeños comerciantes contribuye al efecto momentum. Los grandes comerciantes, por el contrario, no muestran evidencia de sub-reacción, y los desequilibrios de los largetrade tienen poco impacto en los retornos posteriores. En general, los resultados sugieren que el impulso podría ser en parte impulsado por el comportamiento de los pequeños comerciantes. De Dimitri Vayanos, Paul Woolley. 2008. Proponemos una teoría racional del impulso y la reversión basada en la gestión delegada de cartera. Un inversor competitivo puede invertir a través de un fondo de índice o un fondo activo dirigido por un gerente con capacidad desconocida. Después de un shock de flujo de efectivo negativo a los activos en poder del fondo activo, el inversor se actualiza. Proponemos una teoría racional del impulso y la reversión basada en la gestión delegada de cartera. Un inversor competitivo puede invertir a través de un fondo de índice o un fondo activo dirigido por un gerente con capacidad desconocida. Después de un shock de flujo de efectivo negativo a los activos mantenidos por el fondo activo, el inversor se actualiza negativamente sobre la capacidad de los gerentes y migra al fondo índice. Si bien los precios de los activos en poder del fondo activo caen en previsión de las salidas de los inversores, se espera que la caída continúe, lo que dará impulso. Debido a que los flujos de salida empujan los precios por debajo de los valores fundamentales, los rendimientos esperados eventualmente aumentan, dando lugar a la inversión. Los flujos de fondos generan movimientos similares y efectos de lead-lag, siendo la previsibilidad más fuerte para activos con alto riesgo idiosincrásico. Derivamos soluciones explícitas para los precios de los activos, dentro de un equilibrio normal-lineal en tiempo continuo. Por Joseph Kang, Ming-hua Liu, Xiaoyan Ni - Diario. 2002. Utilizando acciones A accesibles sólo a los inversionistas locales (que representan 99 de los inversionistas en acciones en China), este documento analiza si las estrategias de inversión con horizonte temporal y horizonte intermedio generan beneficios anormales. Encontramos beneficios estadísticamente significativos anormales tanto para el arbitraje po. Utilizando acciones A accesibles sólo a los inversionistas locales (que representan 99 de los inversionistas en acciones en China), este documento analiza si las estrategias de inversión con horizonte temporal y horizonte intermedio generan beneficios anormales. Encontramos ganancias anormales estadísticamente significativas para ambas estrategias de inversión de cartera de arbitraje. El análisis detallado indica que: 1) el dominio absoluto de los inversores no institucionales conduce a un entorno de especulación excesiva y, por lo tanto, a una excesiva reacción excesiva a la información específica de la empresa; 2) la reacción excesiva a la información específica de la empresa es la fuente más importante de la (3) los rendimientos de las acciones en el horizonte intermedio exhiben una reacción excesiva a los factores comunes y (4) la reacción excesiva al factor común es la principal razón detrás de la ganancia de impulso a plazo intermedio. Estos hallazgos son robustos, entre otras cosas, para la propagación de oferta y demanda y el comercio no sincrónico. Una mayor parte de las rentabilidades pasadas (el único efecto) se asocian con un mayor impulso. Conrad y Kaul (1998) sugieren que los beneficios del momento son atribuibles a la variación racional del tiempo en los retornos esperados. Sin embargo, Jegadeesh y Titman (2002) muestran que los resultados de Conrad y Kaul son impulsados ​​por un pequeño sesgo de muestra. Quot Mostrar el resumen Ocultar el resumen RESUMEN: Los beneficios de impulso reportados anteriormente pueden no estar disponibles para los inversores individuales que tienen más restricciones comerciales. Por lo tanto, examino la rentabilidad de las estrategias de impulso con los iShares internacionales y los fondos negociados en bolsa del sector estadounidense (ETF) cotizados en la NYSE. Los ETF de índice proporcionan a los inversores individuales un fácil acceso a los mercados de valores internacionales ya los sectores estadounidenses para la asignación de activos. El uso de estrategias de momento transversal, en contraste con la investigación previa, me parece que los beneficios momentum son insignificantes para finales del período de 1990 a 2014. Pocos ETFs del país y de la industria producen resultados positivos usando el ímpetu de la serie de tiempo, y el funcionamiento total es peor que la estrategia del buy-and-hold. El impulso de las series de tiempo ofrece ganancias significativas durante la crisis financiera global de 2008, pero las ganancias disminuyen abruptamente para el período posterior a la crisis. Texto completo Artículo Jul 2017 Yiuman Tse quotIn CAPM. Se examinará si los beneficios de impulso han sido explicados o no por CAPM. Muchos autores bien conocidos. por ejemplo. Fama y French (1996). Grundy y Martin (2001). Jegadeesh y Titman (2001). Conrad y Kaul (1998). Moskowitz y Grinblatt (1999) han utilizado CAPM como modelo estándar basado en riesgo para explicar los beneficios de la estrategia de inversión momentánea. Pero CAPM nunca explicó completamente el efecto momentáneo a corto plazo. RESUMEN: El objetivo de este trabajo es encontrar el efecto momentáneo a corto plazo en los mercados bursátiles de Oriente Medio y examinar si las ganancias de impulso a corto plazo pueden explicarse por el modelo CAPM basado en el riesgo. Se seleccionaron siete mercados de valores importantes de Medio Oriente. El efecto momentáneo a corto plazo se encontró en los siete mercados de valores y el CAPM no explica adecuadamente las ganancias de momentum a corto plazo, pero los retornos de la cartera de impulso son estadísticamente significativos. Este documento es el primer intento de reunir los principales mercados de valores de Oriente Medio y examinarlos para el fenómeno de efecto momentum a corto plazo. La investigación futura debería incluir más mercados de valores con el fin de tener una mejor comprensión de los mercados bursátiles del Medio Oriente. Juegadeesh y Titman (1993) muestran en primer lugar la presencia de ganancias de impulso en el mercado de los Estados Unidos para el horizonte de inversión de tres a 12 meses, incluso después de que el riesgo de mercado se contabilice. Conrad y Kaul (1998) sostienen que las ganancias de impulso se producen debido a las diferencias transversales en el riesgo, es decir, los retornos esperados. Moskowitz y Grinblatt (1999) sugieren que el impulso en los factores de riesgo de la industria explica las ganancias de impulso observadas. RESUMEN: M Arifur Rahman Profesor titular, Universiti Brunei Darussalam, Brunéi Darussalam arifur. rahmanubd. edu. bn Resumen Finalidad Dos regularidades de retorno más conocidas son las ganancias contraria y momentum. Este trabajo, utilizando datos semanales para el período 2002 a 2013, investiga la presencia de ambos contraria y las ganancias de impulso y sus fuentes en el mercado bursátil de Bangladesh. Diseño / metodología / enfoque El documento sigue la metodología de Lo y MacKinlay (1990) para formar carteras con un esquema de fuerza relativa ponderada. Metodología de Jegadeesh y Titman (1995) se utiliza para descomponer las ganancias de contrario / momento en tres elementos: la compensación por el riesgo transversal, el efecto de retraso de plomo en series temporales con respecto al factor común y el patrón de series temporales de retornos de existencias. La robustez de los resultados se verifica considerando los factores de riesgo del mercado. Resultados Los resultados proporcionan la evidencia de beneficios contrarios significativos para el período de tenencia de una a ocho semanas. Hay una mayor presencia de beneficios contrarios durante 2002-08. El patrón de series de tiempo es la principal fuente de beneficios contrarios, lo que sugiere que la información idiosincrásica (específica de la empresa) es el principal contribuyente a los beneficios contrarios. Curiosamente, la influencia de la información idiosincrásica sobre estas ganancias ha disminuido gradualmente desde 2008. Los beneficios contrarios son robustos al sentimiento del mercado y otros factores de riesgo sistemáticos. Originalidad / valor Este es el primer estudio detallado sobre la presencia de beneficios contrarios y de impulso y sus fuentes en el mercado bursátil de Bangladesh. Más específicamente, ningún estudio previo se ha centrado en las fuentes de dichos beneficios, aunque es una cuestión importante en lo que respecta a la eficiencia del mercado. Artículo completo Artículo Enero 2017 Versailles teorija ir praktika Shah Saeed Hassan Chowdhury Rashida Sharmin M. Arifur Rahman489 - Anatomía de las estrategias de negociación Jennifer Conrad. Este es el final de la vista previa. Regístrese para acceder al resto del documento. En este artículo usamos un único marco unificador para analizar las fuentes de protones a un amplio espectro de estrategias de negociación basadas en el retorno implementadas en la literatura. Mostramos que menos de 50 de las 120 estrategias implementadas en el artículo producen apoyos estadísticamente significativos y, incondicionalmente, las estrategias de impulso y contraria tienen igual probabilidad de tener éxito. Sin embargo, cuando condicionamos el horizonte de retorno (corto, medio o largo) de la estrategia, o el período de tiempo durante el cual se implementa, surgen dos patrones. Una estrategia de impulso suele ser protable en el horizonte medio (de 3 a 12 meses), mientras que una estrategia contraria establece redes de apoyo estadísticamente significativas en horizontes largos, pero sólo durante el subperíodo 1926 de 1947. Más importante aún, nuestros resultados muestran que la variación transversal de los rendimientos medios de los valores individuales incluidos en estas estrategias juega un papel importante en su proba - bilidad. La variación transversal puede potencialmente dar cuenta de la proba - bilidad de las estrategias de momentum y también es responsable de la aten - ción. Litekin, Narasimhan Jegadeesh, Charles Jones, Roni Michaely, Steve Manaster, u Vasant Naik, Sheridan Titman, Jamie Zender y participantes del seminario en la Universidad Estatal de Arizona, la Universidad Cornell, la Universidad Estatal de Michigan, la Universidad de Arizona, la Universidad de Columbia Británica. Carolina del Norte, Universidad de Notre Dame, Universidad de Utah, Conferencia de Finanzas de Invierno en la Universidad de Utah, Reuniones de la American Finance Association, San Francisco y Seminario de Finanzas de Verano en la Universidad de Tel Aviv para comentarios y sugerencias útiles. Estamos especialmente agradecidos a un árbitro anónimo ya Bob Korajczyk y Ravi Jagannathan por ayudarnos a enfocarnos en los principales temas tratados en este artículo, a Michael Cooper por su invaluable ayuda de investigación ya Sonja Dodenbier por ayudar a preparar este manuscrito. La financiación parcial para este proyecto es proporcionada por la Kenan-Flagler Business School, la Universidad de Carolina del Norte y la Universidad de Michigan Business School. Dirección de la correspondencia a Gautam Kaul, Departamento de Finanzas, Universidad de Michigan Business School, Ann Arbor, MI 48109-1234. La revisión de los estudios financieros Fall 1998 Vol. En el caso de la Sociedad de Estudios Financieros, la Sociedad de Estudios Financieros / Rev. Las estrategias de negociación que al parecer superaron el mercado se remontan al inicio de la negociación de activos financieros. Varios practicantes y académicos en la era de pre-mercado-ecuación (es decir, antes de 1960) creían que los patrones predecibles en los retornos de las acciones podrían conducir a promesas anormales a las estrategias comerciales. De hecho, Keynes (1936) resumió sucintamente las opiniones de muchos al afirmar que la mayoría de las decisiones de los inversores sólo pueden tomarse como resultado de los espíritus animales. En los últimos años ha habido un resurgimiento dramático del interés académico en la predictibilidad de los rendimientos de los activos basados ​​en su historia pasada. Un número cada vez mayor de investigadores sostienen que los patrones de series temporales en los retornos se deben a las ineficiencias del mercado y, en consecuencia, pueden ser consistentemente traducidos en prótesis anormales.1 En términos generales, estos artículos analizan dos estrategias diametralmente opuestas en filosofía y ejecución: La estrategia contraria que se basa en las reversiones de precios y la estrategia de impulso basada en la continuación de los precios (o el impulso en los precios de los activos). Hasta hace poco tiempo se ha hecho relativamente más hincapié en las estrategias contraria, pero hay cada vez más evidencia de que las continuaciones de precios resultan en constantes anormales consistentes en estrategias de impulso. Uno de los aspectos más desconcertantes de esta literatura es que estas dos estrategias diametralmente opuestas parecen funcionar simultáneamente, aunque para diferentes horizontes de inversión. Específicamente, las estrategias contrarias son aparentemente protables para los intervalos a corto plazo (semanal, mensual) ya largo plazo (3 a 5 años, o más), mientras que la estrategia momentánea es protable a mediano plazo (3 a 12- Mes) períodos de tenencia. En este artículo intentamos determinar las fuentes de los beneficios esperados de toda la clase de estrategias de negociación que se basan en la información contenida en los rendimientos anteriores de los valores individuales. La fuerza de nuestro análisis es que utilizamos un marco único, que se basa en los análisis de Lehmann (1990) y Lo y MacKinlay (1990), para descomponer los protones de todas las estrategias, contraria o momentum ya corto plazo a largo plazo. Esta descomposición es importante debido a que las estrategias de negociación basadas en estos patrones, incluyen entre otros, Alexander (1961, 1964), Cootner (1964), Fama 1963, 1970), Fama y Blume (1966), Levy (1967), Van Horne y Parker (1967), James (1968) y Jensen y Bennington (1970). Conrad y Kaul (1988, 1989), Fama y French (1988), Lo y MacKinlay (1988), Porterba y Summers (1988), Campbell, Grossman y Wang (1988) son algunos de los numerosos artículos recientes que tratan sobre la previsibilidad del retorno. 1993), Richardson (1993), Boudoukh, Richardson y Whitelaw (1994), Conrad, Hameed y Niden (1994) y Jones (1994). DeBondt y Thaler (1985), Chan (1988), Sweeney (1988), Jegadeesh (1990), Lehmann (1990), Lo y MacKinlay (1990), entre los artículos recientes que documentan la aparente proba - bilidad de las estrategias de negociación basadas en dicha previsibilidad ), Levch y Thomas (1991), Brock, Lakonishok y LeBaron (1992), Chopra, Lakonishok y Ritter (1992), Allen y Karjalainen (1993), Jegadeesh y Titman (1993, 1995a) y Asness (1994). Kaul (1997) proporciona una revisión de las metodologías empíricas utilizadas para descubrir la previsibilidad de retorno. El rendimiento de los valores en el pasado tiene dos componentes: uno que resulta de la previsibilidad de las series temporales en los retornos de seguridad y otro que surge como consecuencia de la variación transversal de los rendimientos medios de los valores que componen la cartera. La mayoría de las estrategias de comercio basadas en el retorno implementadas en la literatura se basan exclusivamente en la existencia de patrones de series de tiempo en los retornos. Específicamente, todas estas estrategias se basan en la premisa de que los precios de las acciones no siguen los paseos aleatorios. Sin embargo, los propósitos reales a las estrategias de negociación implementadas sobre la base del rendimiento pasado contienen un componente transversal que surgiría incluso si los precios de las acciones son completamente impredecibles y siguen los paseos aleatorios. Consideremos, por ejemplo, una estrategia de impulso. La compra repetida de ganadores a partir del producto de la venta de perdedores será, en promedio, equivalente a la compra de valores de alta media de la venta de valores bajas. En consecuencia, mientras exista una dispersión transversal en los retornos medios del universo de valores, una estrategia de impulso será protable. Por el contrario, una estrategia contraria será inprograble en promedio, incluso en un mundo donde los precios de las acciones siguen los paseos aleatorios. Es importante determinar las fuentes de la aparente protabilidad de las estrategias de negociación debido a (i) la hipótesis explícita en la literatura de que los patrones de series temporales en los precios de las acciones constituyen la única base de las estrategias comerciales basadas en el retorno, y (ii) La falta de previsibilidad en los rendimientos de las acciones es vista por algunos como sinónimo de efciencia del mercado, véase Fama (1970, 1991). Implementamos y analizamos un amplio espectro de estrategias de negociación durante el período 19261989 y durante los subperíodos dentro, utilizando toda la muestra de valores NYSE / AMEX disponibles. Específicamente analizamos ocho estrategias básicas con períodos de espera que oscilan entre 1 semana y 36 meses. De hecho, 55 de las 120 estrategias de negociación implementadas utilizando todos los valores de NYSE / AMEX generan signos estadísticamente significativos. Las probabilidades incondicionales de éxito de las estrategias de impulso y contraria son aproximadamente iguales: de las 55 estrategias estadísticamente protables, 30 son impulso, mientras que 25 son estrategias contraria. Más importante aún, cuando ex post condición en el horizonte de retorno de la estrategia y / o el subperíodo durante el cual se implementa, aparecen dos patrones que son consistentes con la literatura sobre las estrategias de negociación basadas en retornos ver, p. DeBondt y Thaler (1985) y Jegadeesh y Titman (1993). La estrategia de impulso por lo general suele ser positiva, y frecuentemente estadísticamente signi fi cativa, en los horizontes medianos, excepto durante el subperíodo 19261947, mientras que una estrategia contraria es exitosa en horizontes largos, aunque los protones a estas estrategias son estadísticamente significativos sólo durante el subperíodo 19261947. Una descomposición empírica de los protones de las estrategias sugiere que la variación transversal de los rendimientos medios de los valores individuales incluidos en la estrategia es un determinante importante de su proba - bilidad. Específicamente, no podemos rechazar la hipótesis de que la variación seccional de la muestra en los rendimientos medios puede explicar la proba - bilidad de las estrategias de impulso. La dispersión transversal en los retornos medios parece ser también responsable de la escasez de estrategias contraria estadísticamente protables. Aunque constantemente observamos reversiones significativas de precios en prácticamente todos los horizontes, las protestas que emanan de estas inversiones son neutralizadas por las pérdidas debido a la gran variación transversal de los retornos medios. Consecuentemente, los apoyos netos estadísticamente significativos a estrategias contrarias se observan solamente en el inusual subperíodo 19261947. Es importante señalar que nuestra descomposición de los préstamos comerciales se basa en el supuesto de estacionaridad media de los rendimientos de los valores individuales durante el período en que se implementan las estrategias. Además, los retornos medios se estiman para una amplia sección transversal de rms con un conjunto nito de observaciones de series de tiempo, lo que resultará en una exageración de la importancia de la variación transversal en los retornos medios. Para calibrar la robustez de nuestra descomposición empírica de los protones de las estrategias de negociación, realizamos simulaciones de bootstrap y Monte Carlo de las estrategias de mediano plazo (3 a 12 meses) en las que intentamos eliminar las propiedades de las series de tiempo de los rendimientos de seguridad, Sus incondicionales características transversales. Los resultados de las simulaciones son consistentes con la hipótesis de que las promesas de las estrategias de impulso se deben en gran medida a la variación transversal en los retornos medios. Our Monte Carlo experiments also suggest that our results are robust to the exclusion of extreme in-sample mean returns. Finally, we present some alternative estimates of the relative importance of the cross-sectional variation in mean returns in generating the prots of trading strategies. Even the most conservative estimates suggest that the cross-sectional variation in mean returns is a nontrivial determinant of the protability of trading strategies. Clearly, different specications for the expected returns of individual securities could alter our conclusions. In addition, traders may view the cross-sectional variation in mean returns as a source of abnormal prots. We do not attempt to analyze the sources, rational or irrational, of the crosssectional variation in mean returns, that is, we do not attempt to explain cross-sectional differences in mean returns using an asset-pricing model. Our goal is to determine the relative importance of cross-sectional versus time-series properties of asset returns in determining the protability of trading strategies. We believe our analysis and results should be of interest to both technical traders and producers of asset-pricing models. Section 1 contains a description of the trading strategies implemented in this article and their protability when applied to NYSE/AMEX securities during various time periods. In Sections 2 and 3 we present a detailed analysis of the decomposition of the prots of the strategies. Section 4 contains a brief summary and our conclusions. 492 An Anatomy of Trading Strategies 1. The Protability of Trading Strategies We consider a set of trading strategies that either explicitly mimic or capture the essence of previously implemented strategies. Specically, consider buying or selling stocks at time t 1 based on their performance from time t 2 to t 1, where the period spans any nite time interval. Also, assume that the performance of a stock is determined relative to the average performance of all stocks that are used in the trading strategy. Consequently, if the entire universe of assets is included in the strategy, then each stocks performance is measured relative to the return on the equalweighted market portfolio, Rmt. Finally, let wit 1 denote the fraction of the trading strategy portfolio devoted to security i see Lehmann (1990) and Lo and MacKinlay (1990), that is, wit 1 (k ) 1 Rit 1 (k ) Rmt 1 (k ) N (1) where Rit 1 (k ) is the return on security i at time t 1, i 1. N. Rmt 1 (k ) is the return on equal-weighted portfolio of all securities, and k is the length of the time-interval . Since the weights are based entirely on information at time t 1, wit 1 has a subscript of t 1. The expression for the weights in Equation (1) succinctly captures the philosophy of all return-based trading strategies. First, the positive or negative sign preceding the expression on the right-hand side reects an investors (institutions) beliefs that is, whether the investor believes in price continuations or reversals (and therefore recommends and/or follows a momentum or a contrarian strategy). Second, it is important to note that, regardless of whether a strategy is contrarian or momentum, the premise is that its success is based on the time-series behavior of asset prices. Specically, a securitys past performance relative to some benchmark (e. g. the average return of the portfolio of all securities) is supposed to be informative about future innovations in the securitys prices. This is quite contrary, for example, to the random walk model of stock prices which implies that changes in stock prices are completely unpredictable (see Section 2 for further details). Third, the dollar weights in Equation (1) i. e. w1t 1 (k ). w N t 1 (k ) lead to an arbitrage (zero cost) portfolio by construction N wit 1 (k ) 0 k. (2a) i 1 and the dollar investment long (or short) is given by It 1 (k ) 1 2 N wit 1 (k ). (2b) i 1 493 The Review of Financial Studies / v 11 n 3 1998 Fourth, since the weights in Equation (1) are proportional to the absolute value of the deviations of a securitys return from the return of an equal-weighted portfolio of all securities, they capture the general belief that extreme price movements are followed by extreme movements see, e. g. DeBondt and Thaler (1985), Lehmann (1990), Lo and MacKinlay (1990), and Jegadeesh and Titman (1993). Finally, and most importantly, the weights in Equation (1) allow us to conveniently decompose the profits of the trading strategies see Lehmann (1990) and Lo and MacKinlay (1990), again regardless of the inherent nature of the strategy (i. e. whether it is a contrarian or a momentum strategy). This, in turn, permits us to determine the relative importance of the different components.2 The realized prots at time t. t (k ), to the trading strategies implied by the weights in Equation (1) are given by N t (k ) wit 1 (k ) Rit (k ). (3) i 1 Since all the strategies considered in this article (and typically in the literature) are zero-cost strategies, only the dollar prots (and not the returns) are dened as in Equation (3). And if the markets are frictionless, the weights can be arbitrarily scaled to obtain any level of prots. We therefore will largely rely on the sign and statistical signicance of the averages of the time series of the t (k )s that is, we examine whether expected prots are statistically signicantly positive (or negative). Table 1 contains average/expected prots for trading strategies implemented during different time periods and for different holding periods (i. e. different k ). We consider ve time periods: 19621989 19261989, and three equal-size subperiods within the 19261989 period (January 1926 April 1947, May 1947August 1968, September 1968December 1989). We rst implement the strategies for the 19621989 period because it corresponds with the time period used in several past studies see, e. g. Lehmann (1990), Lo and MacKinlay (1990), and Jegadeesh and Titman (1993). The 1926-1989 period is used (for all but the weekly holding period) because it covers a much longer time interval, and this interval (and the subperiods within it) provide a robustness check for the potential protability of trading strategies. We use eight different holding periods k. where k ranges from 1 week 2 Jegadeesh and Titman (1993) use a variant of this strategy in which securities are ranked based on their past performance and are then combined into 10 portfolios that are held for a specic period of time. An arbitrage portfolio is also formed by buying the top performers and selling the worst performers. They note that the correlation between the returns to the strategy used in this article and their work is 0.95 however, the prots of their strategy cannot be readily decomposed. We follow the weighting scheme implied in Equation (1) instead, especially since a decomposition of the prots is central to this article. The weights in Equation (1), however, do retain the same philosophy as the other return-based strategy. 494 An Anatomy of Trading Strategies Table 1 Average prots to trading strategies for different horizons and periods Strategy interval Subperiods (19261989) (I) 19261946 (II) 19471967 (III) 19681989 19621989 19261989 0.035 (23.30) 3 months 0.027 (0.67) 0.165 (2.42) 0.557 (2.99) 0.070 (2.91) 0.020 (0.43) 6 months 0.360 (4.55) 0.147 (1.91) 0.204 (1.03) 0.333 (4.97) 0.273 (3.63) 9 months 0.708 (5.81) 0.488 (5.48) 0.276 (1.37) 0.487 (5.09) 0.634 (5.44) 12 months 0.701 (4.64) 0.198 (1.29) 0.557 (-1.44) 0.372 (3.80) 0.611 (3.70) 18 months 0.094 (0.35) 0.761 (2.88) 2.466 (3.49) 0.117 (0.77) 0.444 (1.51) 24 months 0.501 (0.97) 1.181 (2.98) 2.831 (2.92) 0.434 (1.62) 0.792 (1.54) 36 months 3.304 (3.39) 4.176 (6.48) 7.727 (6.08) 0.922 (1.24) 0.873 (0.84) 1 week This table contains average prots to zero-cost trading strategies that buy NYSE/AMEX winners and sell losers based on their past performance relative to the performance of an equal-weighted index of all stocks. The dollar prots are given by t (k ) iN 1 wit 1 (k ) Rit (k ) i 1. N. where t (k ) is the dollar prot at time t from a k-period trading strategy, 1 1N wit 1 (k ) N Rit 1 (k ) Rmt 1 (k ) and Rmt 1 (k ) N i 1 Rit 1 (k ), where k 1 week, and 3, 6, 9, 12, 18, 24, and 36 months. The numbers in parentheses are z-statistics that are asymptotically N (0, 1) under the null hypothesis that true prots are zero and are robust to heteroscedasticity and autocorrelation, and account for any cross-correlation in the realized prots of strategies within a horizon class (short, medium, or long horizon) of strategies. All prot estimates are multiplied by 100. to 36 months. For brevity we implement strategies for which the length of the past performance evaluation periods and the future holding periods are identical. For example, if we evaluate a securitys performance over the past 3-month period, the holding period of the trading strategy is also 3 months. Due to data availability considerations, we implement the weekly trading strategy only during the 19621989 period. To minimize small-sample biases in estimators of the components of the prots of trading strategies (see Appendix), and to increase the power of our tests, we implement trading strategies for overlapping holding periods on a monthly frequency (for all k except k 1 week). Specically, we determine the weights, wit 1 (k ). at time t 1 for all the different k s based on the returns from time t 2 to t 1. The different holding period strategies can therefore contain different sets of securities. We then calculate the realized prots at time t using Equation (3) for each k. To avoid potential survival biases see, e. g. Brown, Goetzmann, and Ross (1995), we do not require that all securities included in a particular strategy at time t 1 also have prices available at time t. If a security is included in a k - period strategy based on its past k - period performance, but it survives for less than k periods in the 495 The Review of Financial Studies / v 11 n 3 1998 future (because it is delisted), we use a (k j ) period return in calculating t (k ), where j is the period of delisting. The estimates in Table 1 are the time-series averages, for each k. of the prots at each time t. t (k ). Finally, since the prots of momentum (contrarian) strategies are exactly equal to the losses of contrarian (momentum) strategies see Equations (1) and (3), we implement only momentum strategies (i. e. we use the weights 1 wit 1 N Rit 1 (k ) Rmt 1 (k ) k ). Consequently, a positive (negative) estimate in Table 1 implies that on average a momentum (contrarian) strategy is protable. Table 1 also contains the z - statistics in parentheses to test the statistical signicance of the average prots (losses) these statistics are asymptotically N (0, 1) under the null hypothesis that the true prots are zero. We use a generalized method of moments see Hansen (1982) procedure to calculate standard errors. This procedure takes into account cross-sectional correlations (within a particular time period) in the realized prots of multiple strategies within the medium - and long-term classes, as well providing standard errors that are robust to heteroscedasticity and autocorrelation. Several interesting features of the protability of trading strategies emerge from an inspection of Table 1. First, the number of positive and negative estimates of average prots are exactly the same 18 versus 18. Therefore, unconditionally, momentum and contrarian strategies are equally likely to be successful (at least based on the 36 strategies evaluated in Table 1). This nding is noteworthy given that momentum and contrarian strategies are (as noted in the introduction) diametrically opposed in philosophy. Second, 21 of the 36 trading strategies are statistically signicantly profitable again the number of statistically signicant contrarian versus momentum strategies is approximately the same, 11 versus 10, respectively. Third, once we condition on the return horizon and/or the time period, however, the similarities between contrarian and momentum trading strategies disappear. Specically, there is a systematic relation between the horizon of the strategy and the trading philosophy that appears to work. A momentum strategy is usually protable at the medium (3- to 12-month) horizons: of the 20 medium-term strategies reported in Table 1, a momentum strategy is protable in 15 of the cases. More importantly, all 11 of the momentum strategies that yield statistically signicant prots are medium-horizon strategies. To gauge the success of the momentum strategy at the medium horizon, we test for the joint signicance of the 3- to 12-month strategies within each time period. Not surprisingly, there is strong evidence that the medium-horizon momentum strategy is protable in all time periods except the 19261947 subperiod: the chi-square statistics for each of the other four time periods have p - values of zero. During the 19261947 subperiod, however, a contrarian strategy is successful at the medium horizon the chisquare statistic for the joint signicance of the 3- to 12-month strategies has a p - value of 0.016. 496 An Anatomy of Trading Strategies On the other hand, the success of contrarian strategies is dependent on one subperiod, 19261947. Of the 10 contrarian strategies that earn statistically signicant prots, four occur in the 19261947 period and they are also responsible for the statistical signicance of the contrarian prots of four more strategies in the overall 19261989 period. More signicantly, a contrarian strategy is statistically protable only twice in the three postwar subperiods. We again conduct statistical tests for the joint signicance of the long-term (18- to 36-month) contrarian strategies. The chi-square statistic for the 1926-1989 period strongly supports the protability of the long-run contrarian strategy with a p - value of zero, but this evidence is dependent on one time interval, the 19261947 subperiod. While the p - value for the chi-square statistic is 0.009 for the 19261947 subperiod, it is 0.193 for the 19481968 subperiod and 0.203 for the 19691989 period.3 Hence, the net protability of the contrarian strategy is limited to the long-run and to the pre-1947 data. This evidence is also consistent with the results of Fama and French (1988) and Kim, Nelson, and Startz (1991), who nd that long-term mean reversion in the prices of portfolios of securities is peculiar to the prewar period. Finally, although a contrarian strategy is obviously protable at the weekly horizon in the 19621989 period, recent research shows that the protability of short-term strategies may be spurious because it is generated by market microstructure biases.4 The most convincing evidence in Table 1 consequently is in favor of the momentum strategy, which provides support to proponents of the momentum strategy, both on Wall Street and among academicians see, e. g. Asness (1994), Grinblatt, Titman, and Wermers (1994), Jegadeesh and Titman (1993,1995a), and Levy (1967) Hendricks, Patel, and Zeckhauser (1993) provide related evidence. For example, in the most recent study on trading strategies, Jegadeesh and Titman (1993) implement 32 different 3- to 12-month momentum strategies over the 19621989 period and nd each one to be protable. Also, Grinblatt, Titman, and Wermers (1994) show that about 77 of the 155 mutual funds in their sample follow momentum 3 We reestimate all the average prots in Table 1 conditional on the behavior of the market, that is, we regress the realized prots on the market return in excess of the risk-free rate. The alphas of these regressions are typically similar to the unconditional average prots reported in Table 1. For example, apart from rendering the average prots of the 12-month momentum strategy statistically signicant, the average estimates of the prots of all other strategies and their statistical signicance remain largely unchanged for the overall 19261989 period. During the subperiods, the only notable difference is that the 24- and 36-month contrarian strategies in the 19471967 subperiod and the 36-month strategy in the 19681989 subperiod yield statistically signicant conditional prots. This last result provides some support for the Ball, Kothari, and Shanken (1995) nding that risk-adjusted contrarian prots are higher relative to the raw prots in the postwar period. 4 Market microstructure effects (e. g. the bid-ask bounce and inventory effects) present in transaction returns can explain signicant proportions of the price reversals that lead to the apparent success of short-term contrarian strategies see Jegadeesh and Titman (1995b) and Conrad, Gultekin, and Kaul (1997). Any remaining prots to these short-term strategies disappear at low levels of transaction costs even for large institutional investors see Bessembinder and Chan (1994) and Conrad, Gultekin, and Kaul (1997). 497 The Review of Financial Studies / v 11 n 3 1998 strategies, and apparently quite successfully. Momentum is also an explicit stock selection criterion for several mutual funds see Bernard (1984) and Grinblatt and Titman (1989).5 2. Sources of Prots to Trading Strategies In this section we provide a decomposition of the expected prots to returnbased trading strategies. Following Lehmann (1990) and Lo and MacKinlay (1990), the prots (losses) of the trading strategies considered in the literature (and in this article) can be directly and conveniently decomposed by taking the expectation of t (k ) in Equation (3), and again assuming that we implement momentum strategies, E t (k ) Cov Rmt (k ), Rmt 1 (k ) 1 N 1 N N Cov Rit (k ), Rit 1 (k ) i 1 N it 1 (k ) mt 1 (k )2 i 1 C1 (k ) O1 (k ) 2 (k ) P (k ) 2 (k ) (4) where P (k ) C1 (k ) O1 (k ) is the predictability-protability index, it (k ) is the unconditional mean of security i for the interval of 1 length k. and mt (k ) N iN 1 i (k ) is the unconditional single-period mean return of the equal-weighted market portfolio at time t. Under the assumption of mean stationarity of individual security returns, the above decomposition shows that total expected prots of trading strategies result from two distinct sources: time-series predictability in asset returns, measured by P (k ), and prots due to cross-sectional dispersion in mean returns of securities, denoted by 2 (k ). The rst term in P (k ) is the negative of the rst-order autocovariance of the return on the equalweighted market portfolio, denoted by C1 (k ), and is almost completely determined by cross-serial covariances of individual security returns (see Appendix) the second term, denoted by O1 (k ), is the average of rst-order autocovariances of the N individual securities included in the zero cost portfolio. Since P (k ) is entirely determined by return predictability which, in turn, forms the basis of all return-based trading strategies, we term it the predictability-protability index. Lo and MacKinlay (1990) also dene an identical protability index. However, their motivation is to deemphasize 5 For example, past research has demonstrated the abnormal protability of trading strategies that use the Value Line timeliness rankings which are based on price momentum, determined by price performance over the past 12 months see Copeland and Mayers (1982) and Stickel (1985). 498 An Anatomy of Trading Strategies the role of 2 (k ) since it has a small effect on prots to trading strategies that use weekly returns (see also Tables 2 and 4). We, on the other hand, dene P (k ) to emphasize that total expected prots to return-based trading strategies do not result entirely from time-series predictability in returns. 2.1 The random walk model Although Equation (4) provides a convenient decomposition of expected prots, we need a benchmark model for the return-generating process of nancial assets to interpret the two different potential sources of prots to trading strategies. Let us assume that all security prices follow random walks, so that returns can be depicted as Rit (k ) i (k ) it (k ) i 1. N (5) where E it (k ) 0 i. k and E it (k ) jt 1 (k ) 0 i. J. k .6 The usefulness of the random walk model in Equation (5) as a benchmark, particularly for this study, becomes obvious since trading strategies that rely on time-series predictability in returns cannot be protable by construction because Cov Rit (k ), R jt 1 (k ) 0 i. J. k .7 Equivalently, Equation (5) implies that there is no return predictability in either individual securities or across different securities, and hence the very basis of return-based trading strategies is ruled out. The model in Equation (5) also has economic appeal as a benchmark because changes in stock prices will (generally) be unpredictable in a risk-neutral world with an informationally efcient stock market see, e. g. Samuelson (1965). The most important property of the model in Equation (5), when combined with the decomposition of total expected prots in Equation (4), however, lies in the fact that it helps demonstrate that momentum (contrarian) strategies will be protable (unprotable) even if asset returns are completely unpredictable. More specically, from Equations (4) and (5) it follows that E t (k ) 2 (k ). (6) Equation (6) implies that as long as there are any cross-sectional differences in mean returns of individual securities, momentum strategies will generate prots equal to 2 (k ). Conversely, contrarian strategies will generate losses of an equal amount. Under the assumption that the mean returns of individual securities are stationary, these prots (losses) have no relation to any time-series predictability in returns. The prots in Equa6 Technically, all we need in our benchmark model is that the it s are uncorrelated but for ease of exposition, we assume a random walk model for stock prices. 7 Of course, although predictability in asset returns is a necessary condition for the success of trading strategies considered in this article, it is not a sufcient condition for abnormal gains to be reaped from these strategies. As others have pointed out, time variation in expected returns could also lead to predictability in stock returns see, e. g. Fama (1970, 1991). 499 The Review of Financial Studies / v 11 n 3 1998 Table 2 The decomposition of average prots to trading strategies Strategy interval E t (k ) P (k ) c1 (k ) o1 (k ) 2 (k ) Panel A: 19621989 0.035 1 week (23.30) 0.035 (19.95) 0.001 (18.95) 101.45 1.45 3 months 0.027 (0.67) 0.071 (1.78) 0.098 (27.22) 265.92 365.92 6 months 0.359 (4.55) 0.027 (0.34) 0.387 (31.16) 7.60 107.60 9 months 0.708 (5.81) 0.159 (1.27) 0.868 (32.75) 22.49 112.49 12 months 0.701 (4.64) 0.849 (5.44) 1.550 (35.23) 121.09 221.09 18 months 0.094 (0.35) 3.508 (12.40) 3.602 (55.41) 3,747.76 3,847.76 24 months 0.501 (0.97) 7.252 (12.61) 6.751 (51.93) 1,446.91 1,346.91 36 months 3.304 (3.39) 21.140 (17.47) 17.836 (46.08) 639.77 539.77 Panel B: 19261989 3 months 0.165 (2.42) 0.234 (3.40) 0.070 (17.95) 142.31 42.31 6 months 0.147 (1.91) 0.117 (1.53) 0.265 (18.93) 79.57 179.57 9 months 0.488 (5.48) 0.098 (1.09) 0.585 (20.10) 20.02 120.02 12 months 0.198 (1.29) 0.870 (5.32) 1.069 (20.96) 439.10 539.10 18 months 0.761 (2.88) 3.134 (11.00) 2.372 (26.06) 411.60 311.60 24 months 1.181 (2.98) 5.438 (12.36) 4.257 (27.41) 460.34 360.34 36 months 4.176 (6.48) 14.461 (29.61) 10.285 (19.18) 346.30 246.30 0.114 (13.57) 120.40 20.40 Panel C1: Subperiod I (January 1926April 1947 3 months 0.557 0.671 (2.99) (3.61) P (k ) 2 (k ) 6 months 0.204 (1.03) 0.624 (3.20) 0.420 (14.38) 305.63 205.63 9 months 0.276 (1.37) 0.668 (3.36) 0.944 (16.28) 242.19 342.19 12 months 0.557 (1.44) 2.489 (6.13) 1.932 (18.40) 446.54 346.54 18 months 2.466 (3.49) 7.033 (9.48) 4.567 (22.50) 285.16 185.16 24 months 2.831 (2.92) 11.250 (10.83) 8.419 (26.39) 397.42 297.42 36 months 7.727 (6.08) 27.882 (21.17) 20.155 (40.64) 360.84 260.84 500 An Anatomy of Trading Strategies Table 2 (continued) Strategy interval E t (k )b P (k ) c1 (k ) o1 (k ) Panel C2: Subperiod II (May 1947August 1968) 3 months 0.070 0.007 (2.91) (0.30) 2 (k ) P (k ) 2 (k ) 0.063 (10.50) 10.17 89.83 6 months 0.333 (4.97) 0.059 (0.88) 0.274 (10.15) 17.67 82.33 9 months 0.487 (5.09) 0.195 (1.73) 0.682 (9.61) 40.16 140.16 12 months 0.372 (3.80) 0.927 (5.81) 1.299 (9.41) 249.11 349.11 18 months 0.117 (0.77) 3.135 (10.02) 3.017 (10.93) 2,672.29 2,572.69 24 months 0.434 (1.62) 5.583 (10.15) 5.149 (11.39) 1,287.77 1,187.77 36 months 0.922 (1.24) 14.150 (7.99) 13.228 (11.12) 1,535.33 1,435.33 682.83 582.83 Panel C3: Subperiod III (September 1968December 1989) 3 months 0.020 0.135 0.115 (0.43) (3.00) (26.74) 6 months 0.273 (3.63) 0.171 (2.28) 0.444 (29.60) 62.84 162.84 9 months 0.634 (5.44) 0.321 (2.68) 0.955 (31.83) 50.62 150.62 12 months 0.611 (3.70) 1.041 (6.12) 1.651 (36.69) 170.44 270.44 18 months 0.444 (1.51) 3.205 (4.32) 3.649 (17.98) 721.82 821.82 24 months 0.792 (1.54) 5.854 (5.37) 6.646 (20.83) 739.50 839.50 36 months 0.873 (0.84) 19.363 (14.70) 18.490 (37.51) 2,217.74 2,117.74 This table contains the decomposition of average prots of trading strategies using NYSE/AMEX stocks. The decomposition of the average dollar prots is given by E t (k ) P (k ) 2 (k ), where the predictability-protability index is given by P (k ) C1 (k ) O1 (k ), C1 (k ) is (approximately) equal to the rst-order autocovariance of the return of the equal-weighted portfolio of all securities used in the zero-cost strategy, O1 (k ) is the average rst-order autocovariance of the returns of the N individual securities in the zero-cost portfolio, and 2 (k ) measures the cross-sectional variance of the mean returns of the N individual securities. The numbers in parentheses are z-statistics that are asymptotically N (0, 1) under the null hypothesis that the relevant parameter is zero and are robust to heteroscedasticity and autocorrelation, and account for any cross-correlation in the realized prots and the realized components of prots within a horizon class (short, medium, or long horizon) strategies. All prot estimates are multiplied by 100. All protable relative-strength strategies are shown in bold, while all protable contrarian strategies are in normal print. tion (6) are realized simply because in a world where security prices follow random walks (with drifts), following a momentum strategy amounts, on average, to buying high-mean securities using the proceeds from the sale of low-mean securities. That is, although a winner (loser) can have a high 501 The Review of Financial Studies / v 11 n 3 1998 (low) realization of a return due to either being a high - (low-) mean security or due to a high (low) current shock, on average winners (losers) will be high - (low-) mean securities. Consequently, this strategy will gain from any cross-sectional dispersion in the unconditional mean returns of the securities included in the portfolio of winners and losers. Conversely, if a contrarian strategy is followed, expected prots in Equation (6) will equal 2 (k ): contrarians will lose any cross-sectional variation in mean returns by on average selling high-mean securities and buying low-mean securities with the proceeds. These prots (losses) to trading strategies will disappear only under the assumption that all securities have identical mean returns. The random walk model provides economic content to the time-series versus cross-sectional decomposition of the expected prots of return-based trading strategies. Given that all return-based trading strategies are based on time-series patterns in stock prices, an empirical implementation of the decomposition will help us determine the legitimacy of this fundamental premise of trading strategies. Note that if one were to assume that crosssectional differences in mean returns are due entirely to differences in risk characteristicsa viewpoint not uncommon even among proponents of the return-based trading strategies see, e. g. Jegadeesh and Titman (1993, 1995a) and Lehmann (1990)the empirical decomposition will help provide deeper insights into the potential efciency or inefciency of asset prices. Table 2 contains estimates of the total average prots, E t (k ), and its (k ) and 2 (k ), for all holding periods, k. and for all two components, P ve time periods, 19621989 (panel A), 19261989 (panel B), and the three subperiods (panels C1C3). The numbers in parentheses below E t (k ), P (k ), and 2 (k ) are their respective z - statistics, which are autocorrela tion and heteroscedasticity consistent and take into account cross-sectional correlations in the realized prot of all strategies among each holding-period class. The Appendix contains the exact formulae and procedures used to estimate each of the three components of total average prots. Since the empirical decomposition of the prots is critically dependent on estimates of the unconditional means of the returns of individual securities, it is important to note again that the components are estimated under the assumption that the unconditional mean return of each security is constant over the entire sample period under consideration. We estimate the unconditional means using all data in a particular time period, and calculate the components of the prots of a particular strategy in a particular period based only on the securities included in that strategy in that specic period. In addition, we conduct subperiod analyses to evaluate the effect of our strong mean stationarity assumption on our inferences the inferences remain largely unchanged. We use overlapping data to minimize small-sample biases in estimates of the components of prots to trading strategies, but we 502 An Anatomy of Trading Strategies recognize that measurement errors in in-sample mean returns could nevertheless affect our inferences (see Appendix). Consequently, we devote Section 3 entirely to empirically evaluate the extent to which measurement errors may affect our results and inferences. Clearly, since there are relatively few long-horizon (say 3-year) returns even in the 19261989 period, the decomposition results for the long-horizon strategies should be interpreted with special caution. The rst important aspect of the results in Table 2 is the signicant effect of the cross-sectional variance of mean returns, 2 (k ), on the prots of all trading strategies. Specically, the cross-sectional component of the prots is both the predominant source of prots to the momentum strategy at medium horizons, and a major source of losses to contrarian strategies at long horizons. Note that the 2 (k )s are always statistically signicantly greater than zero. To gauge the economic role of the cross-sectional dispersion in mean returns in determining the prots of the different trading strategies, con sider rst the dramatic increase in the absolute magnitude of 2 (k ) with the investment horizon in each of the ve sample periods. This nding is important to emphasize because a similar pattern would be observed in the data if security prices follow the random walk process in Equation (5) or, equivalently, even if there is no predictability in returns. Specically, given Equation (5), the expected prots from a momentum strategy applied to a trading horizon of k periods and continuously compounded returns is given by see Equation (6) E t (k ) k 2 2 (1) k 2 E t (1). (8) Equation (8) shows that the expected prots (losses) from a momentum (contrarian) strategy will increase geometrically with the holding period k because the cross-sectional dispersion of mean returns increases with the (square of the) length of the holding period (relative to the length of the base holding period). For example, given Equation (5), the cross-sectional dispersion of the means of 36-month holding period returns will be 144 times i. e. (36/3)2 times the cross-sectional dispersion of the means of 3-month holding period returns. An inspection of the estimates of 2 (k ) in Table 2 shows that they do increase dramatically with the investment horizon in each sample period. This nding suggests that the protability of momentum strategies at medium horizons may not be due to price continuations potentially induced by market inefciencies. Moreover, the lack of statistically profitable contrarian strategies may be because these strategies lose the crosssectional dispersion in means, with this loss being particularly severe at long horizons. 503 The Review of Financial Studies / v 11 n 3 1998 2.2 Momentum strategies Recall that the momentum strategy is usually protable at medium horizons. To evaluate the relative importance of the cross-sectional versus time-series sources of these prots, however, it is instructive to evaluate the percentage contributions of P (k ) and 2 (k ) to total prots, as well as the sign and statistical signicance of the P (k )s. Note that if stock prices follow random walks, the percentage contributions of 2 (k ) should be constant and equal to 100 see Equation (6). The evidence in Table 2 demonstrates the important role of the cross-sectional variation in mean returns, as opposed to time-series patterns in security prices, in determining the protability of momentum strategies. Of the 18 cases in which positive prots are observed for momentum strategies (see estimates in bold in Table 2), the percentage contributions of 2 (k ) are typically greater than 100. There are only two occasions on which the contribution of the cross-sectional dispersion in mean returns to momentum strategies is less than 100: the 3-month and the 6-month strategies in subperiod II, panel C.2. Even in these two cases, however, the contribution of 2 (k ) is over 80. An alternative way to evaluate the relative importance of the crosssectional versus time-series components of the prots of momentum strategies is to note that there are only two instances in which these strategies gain from continuations in asset prices, that is, the P (k )s are positive. These are (obviously) the same two cases mentioned above. However, an advantage of evaluating the relative contribution of P (k ) is that we can also determine the statistical signicance of any prots to trading strategies due to predictable time-series patterns in asset prices. The evidence shows that even in the two cases which benet from price continuations, the resulting prots are statistically indistinguishable from zero. Using our particular method of decomposing prots, the statistical signicance of medium-horizon momentum prots appears to emanate from the statistical signicance of the 2 (k )s. Given that this empirical decomposition is affected by measure ment errors in mean returns, however, our inferences at this stage should be treated with caution. 2.3 Contrarian strategies The importance of the cross-sectional dispersion in mean returns in determining the protability of trading strategies is again observed in cases where a contrarian strategy appears to work. Note that barring the weekly and the 3-month strategies, the 2 (k )s lead to substantial losses to contrarian strategies. For example, even in the seven long-term strategies that yield statistically signicant prots to a contrarian strategy, the losses due to cross-sectional dispersion in mean returns are larger than the net prots. The important role of 2 (k ) is also exemplied by the fact that there are statistically signicant prots due to the price reversals in stock prices, 504 An Anatomy of Trading Strategies especially at longer horizons, yet only a few strategies yield statistically signicant net contrarian prots. Specically, the P (k )s are statistically signicantly negative for all long-term (18- to 36-month) strategies. Yet only in less than half the cases (7 of the 15 long-term strategies) are the price reversals able to overwhelm the losses from the cross-sectional variance in mean returns and lead to statistically signicant net prots. All of this evidence appears to be an outcome of severe and unusual price movements during the 19261947 subperiod. 3. Robustness Tests: Some Simulations8 Our analysis, based on the decomposition of the prots of trading strategies, suggests that the main determinant of the prots of return-based trading strategies is the cross-sectional variation in mean returns. Contrary to the commonly held belief that forms the basis of return-based strategies, the evidence suggests that time-series patterns in security returns are unlikely to result in statistically signicant net prots to trading strategies. The decomposition of the trading prots in Table 2 is based, however, on two assumptions. First, the mean returns of individual securities are assumed to be constant over the period in which the trading strategies are implemented. Second, the cross-sectional distribution of the in-sample mean returns accurately measure the true cross-sectional variation in the mean returns. While we do not allow for time-varying mean returns that could potentially explain predictability in returns, we do attempt to address the potentially serious effects of measurement errors in in-sample mean returns by conducting several simulation exercises and providing additional evidence about the potential role of the cross-sectional differences in mean returns. The main purpose of the simulations is to analyze the protability of trading strategies using simulated returns that are devoid of any time-series patterns that may be present in the real data, while maintaining the crosssectional characteristics of each security. Conducting simulations of any trading strategy, however, involves a great deal of time and computer resources, since the returns of several thousand individual securities need to be simulated. Consequently, we chose to simulate the prots of medium-term trading strategies during the 19641989 period. We chose the medium-term strategies because they are usually protable in the real data we focus on the 19641989 period because momentum strategies are most protable during this subperiod. We rst implement the medium-term trading strategies on real data during the 19641989 period. The second column of Table 3 contains the av - 8 We thank Ravi Jagannathan for recommending the use of simulations as a robustness check for our empirical decomposition. 505 The Review of Financial Studies / v 11 n 3 1998 erage prots, with their heteroscedasticity - and autocorrelation-consistent z - statistics in parentheses, for the 3- to 12-month strategies. Not surprisingly, the prot estimates are virtually identical to the prots for the 19621989 sample period in Table 2, panel A. 3.1 Bootstrap results To gauge whether the cross-sectional variance in mean returns alone can generate the prots to medium-horizon strategies, we rst conduct bootstrap simulations in which the returns of individual securities are scrambled in an attempt to eliminate any time-series relations that may be present in the real data see Efron (1979). Specically, we generate a sample of 301 monthly returns for each stock in the sample by resampling with replacement from the actual monthly returns between (December) 1964 and (December) 1989. This bootstrap sample should eliminate any time-series properties in each securitys returns, while maintaining all the other characteristics. Specically, the cross-sectional distribution of the individual-security mean returns should be preserved. In re-creating the bootstrap sample, we preserve the missing observations because that helps us retain the exact sample size used in the actual trading strategy.9 All medium-term (3- to 12-month) strategies are implemented on the bootstrap sample, and this exercise is replicated on 500 bootstrapped samples. Table 3, panel A, contains the results from the bootstrap simulations. The rst column of panel A contains the average prots of the trading strategies, the second column contains the average t - statistics of the 500 replications, and the last column shows the p - values which measure the proportion of times the simulated mean returns are greater than the mean returns of the actual strategies shown in the second column of Table 3. The bootstrap results conrm the ndings of our decomposition analysis. The mean prots of the bootstrap strategies are always greater than the corresponding estimates in panel A and the p - values are large, ranging between 0.69 and 1.00. Moreover, the average t - statistics of all the medium-term bootstrap strategies are greater than 10 and each of the t values are signicant for each strategy in all the 500 replications.10 These results suggest that the cross-sectional properties of the returns observed 9 To maintain the cross-sectional correlation in the returns, in one of our bootstrap experiments we attempted to scramble entire vectors of returns. This created a substantial mismatch between the number of securities used in the actual trading strategy and the simulated strategy, since the resampling of vectors scrambled the missing values as well. The substantial reduction in the number of securities in the simulated sample rendered the simulated and the actual samples incomparable. Consequently, we chose to preserve the placement of missing values in scrambling the individual security returns and thus maintain the same set of securities in the simulations that are used in the actual strategy. 10 The average t - values in Table 3, panel A, are always substantially larger than the corresponding t - values of the prots of the actual strategies because of a lack of cross-sectional correlation in the bootstrapped sample. 506 0.3512 (4.52) 0.7199 (5.83) 0.7183 (4.63) 6 months 9 months 12 months t 1.4704 0.8411 0.3775 0.0988 p 24.20 1.00 21.21 0.88 17.53 0.69 11.19 1.00 Panel A E t (k ) t 1.5944 0.9220 0.4041 0.1026 p 20.06 1.00 17.96 0.88 15.56 0.82 10.93 1.00 Panel B E t (k ) t 1.4345 0.8093 0.3655 0.0935 p 22.44 1.00 20.34 0.80 16.90 0.60 10.92 1.00 Panel C E t (k ) t 1.1956 0.6608 0.2913 0.0721 1.00 p 21.93 1.00 18.96 0.24 14.81 0.07 8.87 Panel D E t (k ) t 0.0144 0.0127 0.0069 0.0015 0.07 0.00 0.07 0.00 0.26 0.00 1 1 R (k ). The where t (k ) is the dollar prot at time t from a k - period trading strategy, wit 1 (k ) N Rit 1 (k ) Rmt 1 (k ) and Rmt 1 (k ) N i 1 it 1 second column contains estimates of average prots of medium-term momentum strategies implemented on the real data from December 1964 to December 1985. The numbers in parentheses are z-statistics that are asymptotically N (0, 1) under the null hypothesis that true prots are zero and are robust to heteroscedasticity and autocorrelation. The table also contains results of several simulations, each with 500 replications. Panel A contains a bootstrap simulation in which we generate 1-month returns from the sample with replacement and then implement the four medium-term (3- to 12-month) momentum strategies. The panel also contains the t-statistics average of the 500 simulated t-values and the p-values, where these values denote the proportion of times the 500 simulated mean returns are greater than the sample mean prots of the actual strategy shown in the second column. Panels BE contain Monte Carlo simulations. In Panel B we show average prots, average t-values, and the p-values of implementing the trading strategies on randomly sampled 1-month individual security returns from normal distributions that have moments (means and variances) that match the monthly moments of the securities in the sample. Panels C and D contain estimates for trading strategies implemented on randomly sampled monthly returns generated from normal distributions that exclude the extreme 1 and 5, respectively, of the high - and low-mean securities. Panel E provides the average prots, average t-values, and p-values of trading strategies implemented on randomly sampled rms from normal distributions with identical means but variances that match the sample counterparts. All prot estimates are multiplied by 100. N p 0.16 0.05 Panel E E t (k ) This table contains average actual and average simulated prots to zero-cost trading strategies that buy NYSE/AMEX winners and sell losers based on their past N w (k ) Rit (k ) i 1. N. performance relative to the performance of an equal-weighted index of all stocks. The dollar prots are given by t (k ) i 1 it 1 0.0217 (0.60) E t (k ) 3 months Strategy Interval Table 3 Average prots of actual and simulated medium-term trading strategies An Anatomy of Trading Strategies 507 The Review of Financial Studies / v 11 n 3 1998 between 1964 and 1989 alone have the potential to explain the prots of momentum strategies.11 An interesting and important aspect of the bootstrap results is the relation between the average prots of the momentum strategies and their holding periods. Specically, consistent with the prediction of the random walk model, the prots increase geometrically with the holding period, k see Equation (8) and the discussion in Section 2.2. Given the mean returns for the basic monthly measurement interval (i. e. for k 1), the relation between the average prots of the 3-month versus the 6-month and 12month strategies is virtually identical to the predictions of the random walk model: starting with an average prot of 0.099 for the 3-month strategy, there is a geometric increase to 0.378, 0.841, and 1.470 for the 6-, 9-, and 12-month strategies, respectively. This is in sharp contrast for the average prots for the real strategies reported in the second column, which increase with the holding period, but less than geometrically, and eventually exhibit no change between the 9- and 12-month strategies. This behavior in turn suggests the presence of price reversals, and not momentum, in the real data. The bootstrap results appear to conrm the ndings of the empirical decomposition of the real prots presented in Table 2. Since we do not estimate any parameters of individual-security returns in the bootstrap tests, these results should be devoid of measurement errors in mean returns present in the empirical decomposition. 3.2 Monte Carlo evidence We also conduct Monte Carlo simulations in which returns of individual securities are sampled from normal, independent, and identical distributions with moments that match the moments of the securities used in the trading strategy. We conduct these experiments for two reasons: (i) to ensure that individual security returns do not contain any time-series correlations, and (ii) to check the sensitivity of the empirical decomposition in Table 2 to measurement errors in mean returns (or specically to the extreme mean returns observed in the real data). 11 Note that all estimates in Tables 2 and 3 are prots and not returns because the strategies are zeroinvestment strategies see Equation (2a). Under the null hypothesis that stock returns follow random walks, however, the prots from the actual and simulated strategies are directly comparable. This follows because the expected value of dollar investment long (or short) see Equation (2b) is the same since it depends on the unconditional means of the returns which, in turn, are the same in the actual and each of the simulated strategies. Karolyi and Kho (1993) also conduct bootstrap and Monte Carlo experiments on momentum strategies. They simulate or shufe monthly returns to examine 6-month strategies and, like Jegadeesh and Titman (1993), rank stocks on the basis of past returns and buy (sell) equal-weighted decile portfolios of the highest (lowest) return securities. Although this portfolio method differs from ours, their results also suggest that cross-sectional variation in mean returns is importantthey nd that the average prots of the simulated zero-investment strategy, though less than the actual prots, still constitute about 80 of prots in the real data. Recall that we do not implement the Jegadeesh and Titman (1993) strategy because it does not lend itself readily to the decomposition analysis that is our main focus see the discussion in Section 1. 508 An Anatomy of Trading Strategies In the Monte Carlo simulations we generate 1-month individual security returns from independent and identical normal distributions that have means and variances that are identical to those observed in the real data. We simulate 500 such monthly series and implement the momentum trading strategy for the 3- to 12-month intervals for each set of returns. Table 3, panel B, contains the average prots, the average t - statistics, and the p - values denoting the proportion of times the 500 simulated mean returns are greater than the corresponding sample mean returns in the second column of the table. The results of this Monte Carlo experiment are similar to the bootstrap evidence in panel A. The mean prots are all greater than those witnessed in the real data, and the p - values range between 0.82 and 1.00, suggesting that the cross-sectional characteristics of the data could generate the prots of the momentum strategies. And again, the difference between the average prots of the simulated and real strategies increases signicantly with an increase in the holding period, implying that there are reversals in the real data at least at the 9- and 12-month horizons. The Monte Carlo simulations therefore suggest that in-sample crosssectional differences in individual security returns can account for the profitability of medium-term momentum strategies. To determine the robustness of the protability of the simulated strategies to extreme mean returns observed in the data, we conduct two additional Monte Carlo experiments. In these two simulations, we exclude individual securities that have extreme means (both positive and negative) from the entire simulated samples, that is, we exclude 1 and 5, respectively, of the securities based on the magnitudes of their estimated mean returns. This has the effect of reducing the estimated cross-sectional variance of mean returns of individual securities. It also provides a means of checking the sensitivity of our results to estimation error in the mean returns, since it is possible that the extreme means of individual security returns observed in the real data are an outcome of measurement errors rather than being true extreme means. Ideally a calibration of the underlying cross-sectional distribution of mean returns should be determined by an asset pricing model. However, given the lack of success of theoretical asset pricing models like the CAPM to explain the cross-section of required returns, we do not attempt such an exercise. Our simulation analysis is similar in spirit to the work of Knez and Ready (1997), who show that the size effect can be explained by 1 of the outliers in the data. The evidence from the Monte Carlo experiments that exclude 1 and 5 of the extreme-mean securities is shown in Table 3, panels C and D, respectively. These results show that excluding 1 and 5 of the extreme-mean securities from the simulation lowers the average prots at all horizons, but it does not change the basic conclusion that the success of the momentum strategies can be accounted for by cross-sectional differences in mean re - 509 The Review of Financial Studies / v 11 n 3 1998 turns of individual securities. In panel C, none of the mean prots are less than the corresponding real numbers reported in the second column of the table, and the p - values remain large, ranging from 0.60 to 1.00. In panel D, the mean prots are about 20 and 10 lower than the real prots for the 6- and 9-month strategies, respectively, but the p - values remain relatively high at 0.07 and 0.24. For the 3- and 12-month strategies the average simulated prots are substantially higher than the corresponding real prots, with p - values of 1.00. Finally, we attempt to determine whether there are any biases inherent in the Monte Carlo simulations by simulating individual security returns that have the same variances as the real data, but have identical (zero) means and no time-series relations. We again simulate 500 series of monthly returns for all the securities in our sample and implement the medium-term momentum strategies. The results of this experiment are shown in Table 3, panel E. The prots are invariably positive due to noise, but the magnitudes of the average prots are small: 0.0015, 0.0069, 0.0127, and 0.0144 for the 3- to 12-month strategies, respectively. Also, the p - values are all close to zero. These estimates are between 0.90 and 1.71 of the corresponding Monte Carlo estimates in panel B, which reect all the in-sample cross-sectional variation in mean returns. Moreover, the average t-statistics are also small, ranging between 0.073 and 0.259. Hence, the biases in the simulations appear to have a minor effect on the inferences because the protability of trading strategies is very small if there is no cross-sectional variation in the mean returns of individual securities.12 3.3 Some additional evidence and interpretation The empirical decomposition and the simulation evidence suggest that cross-sectional differences in mean returns could play an important role in determining the protability of return-based trading strategies. In this section, we provide some additional evidence and interpretation that may shed more light on this issue. The problem with the empirical decomposition is that it is based on estimates of the mean returns of individual securities that are measured with error in nite samples (see Appendix). The small-sample bias is potentially important, especially for longer horizons because we use k - period returns 12 We conduct another set of tests to check the robustness of our ndings. Specically we sort securities based on their betas before implementing the trading strategies. The prots of strategies implemented on securities sorted by beta should reduce the cross-sectional variation in mean returns, 2 (k ), and should also simultaneously increase our ability to highlight or emphasize the role (if any) of price continuations or reversals in generating prots for trading strategies. The most important general nding for the beta-sorted strategies is that, although there is a substantial reduction in the point estimates of the cross-sectional dispersion in mean returns for most holding periods, 2 (k ) continues to have an important effect on the prots of trading strategies. The contribution of 2 (k ) is again always statistically different from zero. Moreover, as in Table 2, 2 (k ) contributes high percentages of the prots of momentum strategies and it also continues to result in large losses to contrarian strategies. 510 An Anatomy of Trading Strategies to calculate the k - period mean returns (that is, 12-month returns are used to calculate 12-month mean returns). To assess the effects of small samples on the empirical decomposition of trading prots presented in Table 2, we now provide estimates of the cross-sectional variance in mean returns for all horizons in italics by alternative estimates of the cross-sectional variance in weekly mean returns. Since the number of weekly observations are large (up to 1,434 for the 19621989 period), the effects of measurement errors in mean returns on estimates of the cross-sectional variance in mean returns should be small (see Appendix). The implied estimate of the cross-sectional variance in mean returns for different horizons are calculated using the following formula see Equation (8): 2 (k ) n 2 2 (weekly) (9) where n is the number of weeks in the holding period, k. of the trading strategy (k 3 months. 36 months). The implied cross-sectional variances in Equation (9) are obtained under the assumption that returns follow stationary processes. We use three alternative samples to calculate the weekly cross-sectional variance in mean returns used in Equation (9). The rst sample is the survivor-sample of 512 rms that have no missing weekly returns during the entire 19621989 period. The cross-sectional variance in mean returns of these rms is likely to have little bias since each rms mean return is calculated using 1,434 observations (see Appendix). The weekly estimate of the cross-sectional variance reported in Table 4 is 0.000087, which is virtually identical to the estimate of 0.00009 reported in Lo and Mackinlay (1990) based on a sample of 551 survived rms for the 19621987 period, each with 1,330 observations. Although the cross-sectional variance of the mean returns of rms in this sample is likely to be measured with reasonable accuracy, it is also likely to provide a lower bound on the cross-sectional variance of the mean returns of the rms used in our trading strategies. Firms that survive the entire sample are likely to be large rms with similar mean returns and, in any event, a real time trading strategy could not be implemented on such a set of survived rms. The second sample of rms used to calculate the weekly cross-sectional variance in mean returns is the limited sample of 2,111 rms that have transaction prices for at least half (that is, 717 weeks) of the sample period. The bias in the cross-sectional variance of the mean returns of the individual securities in this sample should also be relatively small. On the other hand, however, the true cross-sectional variance in mean returns in this sample should again be less than the sample of rms used in the trading strategies. The estimated cross-sectional variance in mean returns of this sample (see Table 4) is 0.000140, which is 60 larger than the corresponding estimate for the survived sample. Some of this increase may be due to the increased effects of measurement errors, 511 The Review of Financial Studies / v 11 n 3 1998 Table 4 Implied cross-sectional variation in mean returns for different horizons based on weekly estimates Strategy interval 1 week 3 months 6 months 9 months 12 months Survivor rms ( N 512) Limited rms ( N 2,111) All rms ( N 6,524) 0.000087 0.014703 (21,56) 0.058812 (16,40) 0.132327 (19,48) 0.235248 (34,119) 0.000140 0.023660 (34,89) 0.094640 (26,64) 0.212940 (30,77) 0.378560 (54,191) 0.000535 0.090415 (129,333) 0.361660 (100,246) 0.813735 (115,295) 1.446640 (207,732) This table contains the implied cross-sectional variation in mean returns for trading strategies of different horizons based on weekly estimates for three alternative samples. The weekly cross-sectional variation of the survivor-rm sample is based on a set of 512 rms that have no missing returns during the 19621989 period, and each individual-securitys mean return is calculated using 1,434 observations. The cross-sectional variation of the limited-rm sample is based on a set of 2,111 rms that had a minimum of 717 returns during the 19621989 period, while the estimate for the all rm sample is based on all 6,524 rms that are included in the trading strategy reported in Table 1. The implied estimates of the cross-sectional variation in mean returns are obtained as 2 (k ) n 2 2 (week), where n is the number of weeks in the holding period, k. of the trading strategy. All estimates of the cross-sectional variation in weekly mean returns are multiplied by 100. The numbers in parentheses below the implied estimates of the cross-sectional variation in mean returns are the minimum and maximum percentages of the prots of trading strategies reported in Table 1 for different time periods that can be explained by the implied estimates. but some of it is likely to be due to larger differences in the true means of individual securities. The third weekly estimate of the cross-sectional variance in mean returns is 0.000535, which is for the all-rm sample of 6,524 rms used in the actual weekly trading strategy reported in Table 1. This estimate is six (four) times larger than the corresponding estimate for the survived sample (limited sample). Table 4 contains the implied cross-sectional variances in mean returns for all three samples of rms for the medium horizons (3 to 12 months). We do not report the implied estimates for the long horizons (18 to 36 months) because, even without adjusting for the cross-sectional variation in mean returns, there appear to be reversals in the long run. The numbers in parentheses below the implied cross-sectional variance in mean returns are the minimum and maximum percentages of the actual prots of trading strategies reported in Table 1 that can be explained by them. For example, the implied cross-sectional variances of 0.094640 at the 6-month horizon for the limited-rm sample can explain a minimum of 26 of the prots of the 512 An Anatomy of Trading Strategies 6-month momentum strategy in the 19621989 period, and a maximum of 64 of the prots of the 6-month trading strategy in the 19261989 period. The results in Table 4 shed some light on the relative importance of the cross-sectional variance in mean returns in determining the protability of trading strategies. Consider the most conservative estimates of the crosssectional variation in mean returns based on the survived sample. The implied cross-sectional variance can explain between 16 and 119 of medium horizon strategies implemented over the various time periods. The corresponding percentages are 26 and 191 for the limited-rms sample. Finally, the implied cross-sectional variation in mean returns for the all-rms sample is sufcient to explain the prots of all medium-horizon strategies. Hence, even if we rely solely on the most conservative estimates in Table 4, the evidence suggests that cross-sectional differences in the mean returns of securities included in trading strategies could play a nontrivial role in determining the protability of these strategies. 4. Conclusion We present an analysis of trading strategies that rely on time-series patterns in security returns. We implement the two most commonly suggested strategiesmomentum and contrarianat eight different horizons and during several different time periods. We show that less than 50 of the 120 strategies implemented in this article yield statistically signicant prots and, unconditionally, momentum and contrarian strategies are equally likely to be successful. However, there are two systematic patterns that emerge. First, the momentum strategy usually nets positive and statistically significant prots at medium horizons, except during the 19261947 subperiod. Second, the contrarian strategy is successful at long horizons, but the profits to these strategies are statistically signicant only during the 19261947 subperiod. We nd that an important determinant of the protability of trading strategies is the estimated cross-sectional dispersion in the mean returns of individual securities comprising the portfolios used to implement these strategies. This cross-sectional variance is not related to the time-series patterns in returns that form the basis of return-based trading strategies. Specically, the cross-sectional dispersion in mean returns witnessed during different time periods can potentially generate the observed prots of the most consistently protable strategy, the momentum strategy implemented at medium horizons. Our ndings, based on the empirical decomposition of prots, bootstrap and Monte Carlo simulations, and alternative estimates based on weekly returns, suggest that cross-sectional differences in mean returns play a nontrivial role in determining the protability of momentum strategies. On the other hand, although there is substantial and statistically reliable evidence of price reversals, the net prots to contrarian strategies are statis - 513 The Review of Financial Studies / v 11 n 3 1998 tically signicant primarily during one subperiod: 19261947. In all other subperiods, the consistently signicant prots from price reversals are (statistically) neutralized at least in part by the losses due to the cross-sectional dispersion in the mean returns of securities included in the strategy. These losses again appear to have no relation to time-series patterns in security returns that form the basis of trading strategies they occur because a contrarian strategy on average involves the purchase of low-mean securities from the proceeds of the sale of high-mean securities. The results of our article are clearly dependent on the assumption that the mean returns of individual securities are constant during the periods in which the trading strategies are implemented. However, our results raise the intriguing possibility that the cross-sectional variation in mean returns can simultaneously account for the prots of momentum strategies and the typical lack of success of contrarian strategies. This nding in itself may raise questions about the protability of trading strategies and the related, and more signicant, issue about the informational efciency of stock prices. Obviously, different specications of the model for unconditional required returns could affect the conclusions of our analysis. Several recent attempts at explaining the momentum effect are being made along these lines, but with mixed results see, e. g. Fama and French (1996) and Moskowitz (1997). It is also possible that more plausible models of time-varying expected returns could provide deeper insights into the potential sources of the prots of momentum strategies see, e. g. Grundy and Martin (1997) and Karolyi and Kho (1993). Appendix A.1 Estimation of the components of prots The components of total prots see Equation (4) are estimated by allowing serial covariances (both own and cross) and the cross-sectional variance of mean returns of individual securities to be time dependent. Specically, C1 (k ) T (k ) 1 C1t (k ), T (k ) 1 t (k )2 where C1t Rmt (k ) Rmt 1 (k ) 2 1 (k ) mt O1 (k ) 514 1 2 N N i 1 Rit (k ) Rit 1 (k ) it 1 (k ) 2 T (k ) 1 O1t (k ), T (k ) 1 t (k )2 An Anatomy of Trading Strategies where O1t N 1 N2 N i 1 Rit (k ) Rit 1 (k ) it()1 (k ) 2 k and 2 (k ) T (k ) 1 2 (k ), T (k ) 1 t (k )2 t where t2 (k ) 1 N N it 1 (k ) mt 1 (k )2 i 1 and T (k ) total number of overlapping returns in the sample period for a trading strategy based on holding period k. For ease of exposition, we do not have a security-related subscript on T (k ), but each security in the trading strategy will have a different number of observations. In calculating the components of the prots to trading strategies, we assume that individual security returns are mean stationary, and we calculate all sample means of security returns for each holding period k. i (k ), us ing overlapping data over the entire sample period. The t 1 subscript on it 1 (k ) and mt 1 (k ) simply denotes that these are the sample means of securities available at time t 1 to form the trading strategy portfolios see Equation (1). The only reason the mean returns of individual securities change at each portfolio formation time t 1 is because the securities included in each strategy in each period themselves change and, consequently, the mean return of the portfolio of all these securities, m (k ), also changes. Therefore, although we require mean stationarity, estimates of all components of the prots/losses of trading strategies are time dependent. The use of the entire sample period to calculate the mean returns of individual securities, as opposed to calculating the means based on a rolling sample of data up to time t 1, should reduce the estimates of the cross-sectional variance in mean returns because each mean is estimated more precisely. The assumption of mean stationarity does not appear to affect our main inferences because they are robust across different sample periods. Finally, note that the minor differences between the population parameters C1 (k ) and O1 (k ) in Equation (4) and their sample counterparts are reected above in the last element of C1t (k ) and the NN 21 factor in O1t (k ). The estimators are calculated slightly differently so that C1 (k ) depends en tirely on cross-serial covariances, while O1 (k ) depends solely on own-serial covariances see also Lo and MacKinlay (1990). 515 The Review of Financial Studies / v 11 n 3 1998 A.2 Small-sample biases in estimators of the components of prots It can be shown that since sample means are estimated with error in small samples, covariance estimators are downward biased see Fuller (1976). Consequently, the estimators of the components of total prots see Equation (4) are biased in small samples. Specically, E C1 (k ) C1 (k ) E O1 (k ) O1 (k ) and E 2 (k ) 2 mt 1 (k ). T (k ) N 2 i 1 it 1 (k ) 1 N 2 (k ) T (k ) 1 N. N i 1 2 2 it 1 (k ) mt 1 (k ) . T (k ) T (k ) where T (k ) is the number of returns of holding period k used to calculate trading prots, i2 is the population variance of an individual securitys 2 return, and m is the population variance of the return of the equal-weighted portfolio of all securities used in the trading strategy portfolio. Finally, it is important to note that all the small-sample biases noted above are derived under the null hypothesis that returns are independently and identically distributed. An interesting aspect of the above analysis is that the biases in the com ponents offset each other. Also, note that C1 (k ) and O1 (k ) are downward N 1 2 2 biased, but since N i 1 it 1 ampgt mt 1. the downward bias in O1 (k ) 1 (k ). For a momentum strategy, is greater than the downward bias in C therefore, in small samples 2 (k ) will be upward biased while the predictability-protability index, P (k ), will be downward biased by the same magnitude. This bias could be nontrivial in small samples which, in turn, could materially affect inferences about the relative importance of the sources of prots to trading strategies. Since the bias disappears as T (k ) , however, we use overlapping holding period returns at the monthly frequency for each trading strategy (except the 1-week strategy). It is important to note that the entire discussion of the small-sample biases is based on the assumption that true returns are serially uncorrelated. This assumption will result in an over - (or under-) estimate of the bias if returns are negatively (positively) serially correlated. Since measurement errors are likely to have some effects on our references even using overlapping data, we address this issue in several alternative ways in Section 3 of the article. References Alexander, S. 1961, Price Movements in Speculative Markets: Trends or Random Walks, Industrial Management Review, 2, 726. Alexander, S. 1964, Price Movements in Speculative Markets: Trends or Random Walks, number 2, Industrial Management Review, 5, 2546. 516 An Anatomy of Trading Strategies Allen, F. and R. Karjalainen, 1993, Using Genetic Algorithms to Find Technical Trading Rules, working paper, University of Pennsylvania. Asness, C. 1994, The Power of Past Stock Returns to Explain Future Stock Returns, working paper, University of Chicago. Ball, R. S. Kothari, and J. Shanken, 1995, Problems in Measuring Portfolio Performance: An Application to Contrarian Investment Strategies, Journal of Financial Economics, 38, 79107. Bernard, A. 1984, How to Use the Value Line Investment Survey: A Subscribers Guide, Value Line, New York. Bessembinder, H. and K. Chan, 1994, Do the Prots from Technical Trading Rules Reect Inefciencies, working paper, Arizona State University, Tempe, Arizona. Boudoukh, J. M. Richardson, and R. Whitelaw, 1994, A Tale of Three Schools: Insights on Autocorrelations of Short-Horizon Stock Returns, Review of Financial Studies, 7, 539573. Brock, W. J. Lakonishok, and B. LeBaron, 1992, Simple Technical Trading Rules and the Stochastic Properties of Stock Returns, Journal of Finance, 47, 17311764. Brown, S. W. Goetzmann, and S. Ross, 1995, Survival, Journal of Finance, 50, 853873. Campbell, J. Y. S. J. Grossman, and J. Wang, 1993, Trading Volume and Serial Correlation in Stock Returns, Quarterly Journal of Economics, 108, 905939. Chan, K. C. 1988, On Contrarian Investment Strategy, Journal of Business, 61, 147163. Chopra, N. J. Lakonishok, and J. Ritter, 1992, Measuring Abnormal Returns: Do Stocks OverreactJournal of Financial Economics, 31, 235268. Conrad, J. M. Gultekin, and G. Kaul, 1997, Protability of Short-Term Contrarian Portfolio Strategies: Implications for Market Efciency, Journal of Business and Economic Statistics, 15, 379386. Conrad, J. A. Hameed, and C. Niden, 1994, Volume and Autocovariances in Short-Horizon Individual Security Returns, Journal of Finance, 49, 13051329. Conrad, J. and G. Kaul, 1988, Time-Variation in Expected Returns, Journal of Business, 61, 409425. Conrad, J. and G. Kaul, 1989, Mean Reversion in Short-Horizon Expected Returns, Review of Financial Studies, 2, 225240. Cootner, P. (ed.), 1964, The Random Character of Stock Market Prices, MIT Press, Cambridge, Mass. Copeland, T. and D. Mayers, 1982, The Value Line Enigma (19651978): A Case Study of Performance Evaluation Issues, Journal of Financial Economics, 10, 289321. DeBondt, W. and R. Thaler, 1985, Does the Stock Market Overreact Journal of Finance, 40, 793805. Efron, B. 1979, Bootstrap Methods: Another Look at the Jackknife, The Annals of Statistics, 7, 126. Fama, E. 1965, The Behavior of Stock Market Prices, Journal of Business, 38, 34105. Fama, E. 1970, Efcient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance, 25, 383417. Fama, E. 1991, Efcient Capital Markets: II, Journal of Finance, 46, 15751617. Fama, E. and M. Blume, 1966, Filter Rules and Stock market Trading Prots, Journal of Business, 39, 226241. 517 The Review of Financial Studies / v 11 n 3 1998 Fama, E. and K. French, 1988, Permanent and Temporary Components of Stock Prices, Journal of Political Economy, 96, 246273. Fama, E. and K. French, 1992, The Cross-Section of Expected Stock Returns, Journal of Finance, 47, 427465. Fama, E. and K. French, 1996, Multifactor Explanations of Asset Pricing Anomalies, Journal of Finance, 51, 5584. Fuller, W. 1976, Introduction to Statistical Time Series, John Wiley ampamp Sons, New York. Grinblatt, M. and S. Titman, 1989, Mutual Fund Performance: An Analysis of Quarterly Portfolio Holdings, Journal of Business, 62, 394415. Grinblatt, M. S. Titman, and R. Wermers, 1994, Momentum Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior, working paper, University of Colorado, Boulder. Grundy, B. and J. S. Martin, 1997, Momentum: Fact or Factor Momentum Investing When Returns Have a Factor Structure working paper, University of Pennsylvania. Hansen, L. 1982, Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50, 10291054. Hendricks, D. J. Patel, and R. Zeckhauser, 1993, Hot Hands in Mutual Funds: Short-Run Persistence of Relative Performance, 19741988, Journal of Finance, 48, 93130. James, F. 1968, Monthly Moving AveragesAn Effective Investment Tool, Journal of Financial and Quantitative Analysis, 3, 315326. Jegadeesh, N. 1990, Evidence of Predictable Behavior of Security Returns, Journal of Finance, 45, 881898. Jegadeesh, N. and S. Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efciency, Journal of Finance, 48, 6591. Jegadeesh, N. and S. Titman, 1995a, Overreaction, Delayed Reaction, and Contrarian Prots, Review of Financial Studies, 8, 973993. Jegadeesh, N. and S. Titman, 1995b, Short-Horizon Return Reversals and the Bid-Ask Spread, Journal of Financial Intermediation, 4, 116132. Jensen, M. and G. Bennington, 1970, Random Walks and Technical Theories: Some Additional Evidence, Journal of Finance, 25, 469482. Jones, C. 1994, Transaction Costs and Short-Term Return Predictability, working paper, Princeton University. Karolyi, G. and B. Kho, 1993, Time-Varying Risk Premia and the Returns to Buying Winners and Selling Losers: Caveat Emptor et Veditor, working paper, Ohio State University. Kaul, G. 1997, Predictable Components in Stock Returns, Handbook of Statistics, 14, 269296. Keynes, J. M. 1936, The General Theory of Employment, Interest, and Money, Harcourt, Brace ampamp Co. New York. Kim, M. C. Nelson, and R. Startz, 1991, Mean Reversion in Stock Prices A Reappraisal of the Empirical Evidence, Review of Economic Studies, 58, 515528. Knez, P. J. and M. J. Ready, 1997, On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions, Journal of Finance, 52, 13551382. 518 An Anatomy of Trading Strategies Lehmann, B. 1990, Fads, Martingales and Market Efciency, Quarterly Journal of Economics, 105, 128. Levich, R. and L. Thomas, 1993, The Signicance of Technical Trading-Rule Prots in the Foreign Exchange Market: A Bootstrap Approach, Journal of International Money and Finance, 12, 451474. Levy, R. 1967, Relative Strength as a Criterion for Investment Selection, Journal of Finance, 22, 595610. Lo, A. and C. MacKinlay, 1988, Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specication Test, Review of Financial Studies, 1, 4166. Lo, A. and C. MacKinlay, 1990, When are Contrarian Prots due to Stock Market Overreaction, Review of Financial Studies, 3, 175206. Moskowitz, T. J. 1997, Industry Factors as an Explanation for Momentum in Stock Returns, working paper, University of California, Los Angeles. Poterba, J. and L. Summers, 1988, Mean Reversion in Stock Prices: Evidence and Implications, Journal of Financial Economics, 22, 2579. Richardson, M. 1993, Temporary Components of Stock Prices: A Skeptics View, Journal of Business and Economic Statistics, 11, 199207. Samuelson, P. A. 1965, Proof that Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review, 6, 4149. Stickel, S.,1985, The Effect of Value Line Investment Survey Rank Changes on Common Stock Prices, Journal of Financial Economics, 14, 121144. Sweeney, R. 1988, Some New Filter Rule Tests: Methods and Results, Journal of Financial and Quantative Analysis, 23, 285300. Van Horne, J. and G. Parker, 1967, The Random Walk Theory: An Empirical Test, Financial Analyst Journal, 23, 8792. 519. 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