# “Spectral Risk Measures: Properties and Limitations”: Comment on Dowd, Cotter, and Sorwar

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## Abstract

In their paper “Spectral Risk Measures: Properties and Limitations”, Dowd et al. (J Financ Serv Res 341:61–75, 2008) introduce exponential and power spectral risk measures as subclasses of spectral risk measures (SRMs) to the literature, and claim that they are subject to three serious limitations: First, for these subclasses, the spectral risk may be counterintuitively decreasing when the user’s risk aversion is increasing. Second, these subclasses, and power SRMs in particular, become completely insensitive to market volatility when the respective parameters of risk aversion tend to their lower and upper boundaries. Third, exponential SRMs exhibit constant absolute risk aversion, while constant relative risk aversion better meets the empirical evidence. Consequently, “users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.” (p. 61). In this comment, we show that the findings of Dowd et al. (J Financ Serv Res 341:61–75, 2008) suffer from misinterpretations and wrong conclusions.

## Keywords

Spectral risk measures Exponential risk spectrum Power risk spectrum Comparative risk aversion## JEL Classification

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