The accurate evaluation of a risk measure employed by a financial institution is of high importance in view of that institution's minimum capital requirement. Having a sensitive reaction to breaks in the volatility of the profit-and-loss process is a desirable property of the underlying measure. This paper proposes a loss function-based framework for the comparative measurement of the sensitivity of quantile downside risk measures to breaks in volatility or distribution. We do this by extending the model comparison approach introduced by Lopez in 1998. Value-at-risk and expected shortfall (ES) are contrasted over realistic evaluation horizons within a broad simulation study, in which numerous settings involving volatility breaks of different intensities and several data-generating processes are checked by employing a magnitude-type loss function. As a result, it can generally be noted that ES appears to be the superior measure in terms of its ability to identify breaks in the volatility. In addition, an empirical study, in which data from six stock market indexes are used, demonstrates the applicability of this procedure and reconfirms the findings from the simulation study.