Multi-period measures of risk account for the path that the value of an investment portfolio takes. The most widely used such path-dependent indicator of risk is drawdown, which is a measure of decline from a historical peak in cumulative returns. In the context of probabilistic risk measures, the focus has been on one particular dimension of drawdown, its magnitude , and not on its temporal dimension , its duration . In this paper, the concept of temporal path-dependent risk measure is introduced to capture the risk associated with the temporal dimension of a stochastic process. We analyze drawdown duration, which measures the length of excursions below a running maximum , and liquidation stopping time, which denotes the first time drawdown duration exceeds a subjective liquidation threshold, in the context of coherent temporal path-dependent risk measures and show that they, unlike drawdown magnitude, do not satisfy any of the axioms for coherent risk measures. Despite its non-coherence, we illustrate through an empirical example some of the insights gained from analyzing drawdown duration in the investment process and discuss the challenges of path-dependent  risk estimation in practice.
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. We discuss the properties of temporal measures of risk and show that they can never be coherent. 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.
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The most widely used such path-dependent indicator of risk is drawdown, which is a measure of decline from a historical peak in cumulative returns.
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been on one particular dimension of drawdown, its magnitude ,
traditionally been on the magnitude of investment loss
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its temporal dimension , its duration
the dimension associated with the passage of time
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introduced
mathematically formalized
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analyze drawdown
discuss the properties of temporal measures of risk and show that they can never be coherent. We then study the temporal dimension of investment drawdown, its
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, and liquidation stopping time, which denotes the first time drawdown duration exceeds a subjective liquidation threshold,
. Its properties
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coherent temporal path-dependent risk measures and show that they, unlike drawdown magnitude, do not satisfy any of the axioms for coherent risk measures. Despite its non-coherence, we illustrate through an empirical example some of the insights gained from analyzing drawdown duration in
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
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investment process and discuss the
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temporal