Multihorizon sharpe ratios

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.