When Do Distributional Alarms Improve Downside Risk Control? Evidence from Four Equity Markets

A distributional alarm changes both when a portfolio cuts equity exposure and how much exposure it retains when only volatility signals stress. We replay allocation rules on the trading calendars of four equity markets and compare net returns at 10 basis points of one-way trading costs. Holding the other state weights fixed, cutting exposure by 25% on distributional-only dates raises mean net returns on common extreme dates by 0.061 percentage points relative to a fixed 22-session realized-volatility rule (95% interval 0.012 to 0.114). The corresponding certainty-equivalent difference is −0.123 percentage points, with an interval that spans zero. Against a volatility rule calibrated to the same historical exposure target, the overlay improves the mean of each policy’s own worst days by 0.022 percentage points and trails by 0.072 on common extreme dates. Both intervals span zero. The largest positive contribution to certainty equivalent in that comparison comes from retaining more equity on volatility-only dates. Fixed volatility and flat exposure yield higher certainty-equivalent point estimates across the trading-cost grid. The value of the additional signal therefore depends on the tail dates used to assess protection and on how the exposure budget is allocated across alarm states.