Annual Risk Measures and Related Statistics

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Annual Risk Measures and Related Statistics
Arno E. Weber, CIPM, Ortec Finance

A common method to annualize monthly risk measures is to multiply the outcome by 12 or the square root of 12. Paul D. Kaplan has shown that for one particular measure, the standard deviation, this approach is incorrect, given that returns are compounded over time rather than summed. Kaplan has also presented a method to calculate the annual standard deviation correctly. This article expands on Kaplan’s work. It shows for a wide palette of risk measures and related statistics how the annual variants can be calculated correctly, under the assumption of compounded returns.

Annual Risk Measures and Related Statistics
Arno E. Weber, CIPM, Ortec Finance

A common method to annualize monthly risk measures is to multiply the outcome by 12 or the square root of 12. Paul D. Kaplan has shown that for one particular measure, the standard deviation, this approach is incorrect, given that returns are compounded over time rather than summed. Kaplan has also presented a method to calculate the annual standard deviation correctly. This article expands on Kaplan’s work. It shows for a wide palette of risk measures and related statistics how the annual variants can be calculated correctly, under the assumption of compounded returns.

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