Multihorizon Sharpe Ratios

Abstract

Wavelet analysis represents a new approach to investigating the empirical relationship between the Sharpe ratio and the investment horizon for portfolios of small stocks, large stocks, and intermediate–term and long–term bonds. A wavelet multiscale approach decomposes a given time series on a scale–by–scale basis. Empirical results indicate that the wavelet variance declines as the wavelet scale increases, implying that an investor with a short investment horizon must respond to every fluctuation in realized returns, while an investor with a much longer horizon faces much less significant long–run risk associated with unknown expected returns. The long scale Sharpe ratio is much higher than the short scale, implying that the Sharpe ratio is not time–consistent. Finally, stock portfolios have higher Sharpe ratios than bond portfolios, except in certain–length periods, indicating that evaluation of the performance of stock and bond portfolios should account for investment horizon.