The Divergence of the High and Low Frequency Estimation: Causes and Consequences

Abstract

Financial analysts typically estimate volatilities and correlations from monthly or higher frequency returns when determining the optimal composition of a portfolio. Although it is widely acknowledged that these measures are not necessarily stationary across samples, most analysts assume implicitly that, within sample, volatilities scale with the square root of time and correlations estimated from high-frequency returns are similar to correlations estimated from low-frequency returns. Evidence does not support this view. Instead, evidence shows that relative asset values often evolve through time in ways that are highly inconsistent with their high-frequency volatilities and correlations. As a consequence, portfolios that are optimal based on high-frequency returns often lead to significantly sub-optimal results for investors with long horizons. We analyze the causes and consequences of this discrepancy, and we present a framework for constructing portfolios that balance short-horizon and long-horizon optimality.

Keywords: Auto-correlation, Comparative statics, Cross-correlation, Excess dispersion, High-frequency estimation, Independent and identically distributed, Iso-expected return curve, Low-frequency estimation, Tracking error, Triannualized, Variance ratio

JEL Classification: C10, C11, C13, C32, C50, C53, C61, G11, G12