The time aggregation of sharpe ratio

• Autor(a) principal: Pimentel, Sara Machado Ferreira
• Data de Publicação: 2008
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10071/692
• topic: Sharpe ratio; time aggregation; GARCH model; Theorem of Diebold; Índice de Sharpe; Agregação temporal; Modelos GARCH; Teorema de Diebold

More than four decades have passed and the Sharpe Ratio (SR) continues to be one of the most popular portfolio risk adjusted performance measures. We comment on Lo’s (2002) results for the time aggregation of SR considering a different approach to deal with the conditional heteroskedasticity of returns. Based on a theorem proposed by Diebold (1986, 1988) we verify, for the series of financial returns with no serial correlation, that the most common method for time aggregation, the product of the higher-frequency SR by the square root of the number of periods contained in the lower-frequency holding period, can still be used in the presence of heteroskedasticity, when higher-frequency returns have been generated by a GARCH process and aggregated returns converge to the normal distribution. In an empirical application based on 65 investment funds, the convergence to normality is illustrated, showing that in 70% of the cases the convergence is held at least when daily returns are aggregated into annual frequency. Moreover, we show that serial correlation tends to disappear when the number of periods in the aggregation process tends to infinity and the most common method of SR time aggregation should not be disregarded as a valid method. The results are in accordance with Lo (2002) who roughly states that when serial correlation is not significant, the time aggregation of SR should be performed with the most common method of time aggregation.