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

Nikolaus Rab and Richard Warnung

Abstract

ABSTRACT

In practice, the 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 scaling procedure can also be applied to contributions to the volatility of the assets in the portfolio. Close prices are often used to calculate the profit and loss of a portfolio. rading 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 nonsynchronous correlations. We address this issue and provide alternative procedures for scaling volatility and calculating risk contributions for arbitrary holding periods.