Bear Miss Rates for Downside Forecast Evaluation: Materiality, Empirical Evidence and Research Direction

Aggregate forecast-error measures do not directly show how often a point forecast is too optimistic when a loss occurs. This research note develops the Bear Miss Rate formulation, originating in an MSc dissertation, as an integrated three-part diagnostic design: $BMR$ for optimistic errors on realised loss days, BMRₜₒₗ for errors exceeding a materiality threshold, and BMRZ for missed severe-return events defined from training data. It establishes BMRₜₒₗ's relationship to a conditional optimistic-error survival profile and the fixed-cutoff BMRZ ratio's identity with one minus event recall, while retaining the complete robust z-tail construction as part of the author-developed design. A corrected reproducible illustration compares three forecasts on a common panel of 1,575 observations for five UK-listed energy securities. Median Quantile Regression has the best pooled squared-error accuracy; HuPin LSTM records fewer optimistic loss-day misses but worse aggregate accuracy; and all three forecasts miss all 115 realised severe-return events. The note proposes an accuracy-qualified secondary-use rule for same-functional forecasts and a research programme on comparative evaluation, dependence-aware inference, threshold selection, conservatism, and prospective decision relevance. The evidence is exploratory and establishes neither statistical superiority nor trading profitability.