The Temporal Dimension of Risk

Journal of Risk, Forthcoming

23 Pages Posted: 9 Jan 2015 Last revised: 23 Jun 2016

See all articles by Ola Mahmoud

Ola Mahmoud

University of Basel; University of California, Berkeley

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Date Written: June 22, 2016


Multi-period measures of risk account for the path that the value of an investment portfolio takes. In the context of probabilistic risk measures, the focus has traditionally been on the magnitude of investment loss and not on the dimension associated with the passage of time. In this paper, the concept of temporal path-dependent risk measure is mathematically formalized to capture the risk associated with the temporal dimension of a stochastic process and its theoretical properties are analyzed. We then study the temporal dimension of investment drawdown, its duration, which measures the length of excursions below a running maximum. Its properties in the context of risk measures are analyzed both theoretically and empirically. In particular, we show that duration captures serial correlation in the returns of two major asset classes. We conclude by discussing the challenges of path-dependent temporal risk estimation in practice.

Keywords: temporal risk measure, path-dependent risk measure, drawdown, duration, liquidation stopping time, serial correlation

Suggested Citation

Mahmoud, Ola, The Temporal Dimension of Risk (June 22, 2016). Journal of Risk, Forthcoming. Available at SSRN: or

Ola Mahmoud (Contact Author)

University of Basel ( email )

Petersplatz 1
Basel, CH-4003

University of California, Berkeley ( email )

Center for Risk Management Research
Evans Hall
Berkeley, CA 94720
United States

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