Scaling Portfolio Risk with Serial Cross-Correlations

Summary

This paper examines how to estimate portfolio volatility and asset risk contributions over holding periods longer than one day. The familiar square-root-of-time scaling assumes returns are not serially correlated. Under that assumption, volatility contributions can also be scaled in the same way.

The authors explain why the assumptions can fail when portfolios combine assets traded in distant time zones: close-to-close returns may show serial cross-correlations because the markets close at different times. These asynchronous correlations can make both scaled volatility estimates and asset-level risk contributions misleading. The paper proposes alternative procedures for arbitrary holding periods. The supplied description does not specify the formulas or empirical tests, so it establishes the problem and scope of the proposed methods rather than their detailed implementation or performance.

Key ideas

• Square-root-of-time scaling relies on returns having no serial correlation.
• Distant market closing times can produce serial cross-correlations in close-to-close portfolio returns.
• These correlations can invalidate standard volatility scaling and distort estimated asset risk contributions.
• The paper proposes alternative procedures for volatility scaling and risk contributions across arbitrary holding periods.

Tags

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


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









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.