Validez Del Supuesto De Neutralidad Del Horizonte De Tiempo En El CAPM Y La Metodología Del Rango Reescalado: Aplicación a Colombia (Validity of the Time Horizon Neutrality Assumption in the CAPM Model and the Rescaled Range Method)

Abstract

Long-term memory in financial time series implies that today assets’ returns may affect future returns beyond the short term. Peters (1989 and 1992), Mandelbrot (1972), León and Vivas (2010), among others, find evidence of long-term dependence in financial time series. This document extends the analysis to the investment horizon neutrality assumption in the CAPM by quantifying long-term dependence effects in the model, as developed by Greene and Fieltz (1980). Results for Colombian and American stocks suggest that CAPM systemic risk measure (beta) is statistically different when taking in account long-term dependence, as a result expected returns are significantly different.

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Keywords: CAPM, Hurst exponent, long-term dependence, fractional brownian motion, rescaled range analysis