Scaling portfolio volatility and calculating risk contributions in the presence of serial cross-correlations

TL;DR

This paper addresses the failure of the square-root-of-time rule for scaling portfolio volatility and risk contributions when serial cross-correlations are present, proposing alternative methods for accurate risk measurement over various holding periods.

Contribution

It introduces new procedures for scaling volatility and calculating risk contributions that account for serial cross-correlations and non-synchronous trading effects.

Findings

Standard scaling fails with serial cross-correlations.

Proposed methods improve accuracy of risk contributions.

Applicable to arbitrary holding periods.

Abstract

In practice daily volatility of portfolio returns is transformed to longer holding periods by multiplying by the square-root of time which assumes that returns are not serially correlated. Under this assumption this procedure of scaling can also be applied to contributions to volatility of the assets in the portfolio. Close prices are often used to calculate the profit and loss of a portfolio. Trading at exchanges located in distant time zones this can lead to significant serial cross-correlations of the closing-time returns of the assets in the portfolio. These serial correlations cause the square-root-of-time rule to fail. Moreover volatility contributions in this setting turn out to be misleading due to non-synchronous correlations. We address this issue and provide alternative procedures for scaling volatility and calculating risk contributions for arbitrary holding periods.