Price Information Is Not Enough: Ordering and Decision Rules in Storage Bidding

Abstract

Price forecasts are evaluated in EUR/MWh of error, while storage earns euros; their link depends on the decision rule. We separate the optimal value of a signal V(S|C) from the revenue J(g,S) achieved by an implemented policy. For a price-taking asset with daily throughput bound L and a conditionally sub-Gaussian price law of scale s, the optimal gain over climatology is at most L s sqrt(2 I(S;Pi|C)). This is a square-root envelope, not a prediction for an individual policy. On 939 French day-ahead days the tested bound sits at least two orders of magnitude above the reference uplift. Along a nested Gaussian garbling family, however, plug-in policy revenue is non-monotone even though signal information is monotone: at the residual-noise scale the best Gaussian-shrinkage rule achieves -46% of the uplift, below climatology. The mechanism is ordinal. On a relaxation, optimal schedules depend on interval ordering and profitable-pair tests. A constructed rank-only bid captures 90% of the uplift; exchanging the cheapest and dearest entries of an otherwise exact price vector cuts total revenue by 53%. Within the designed sweep, rank agreement has in-sample R^2 = 0.99, against 0.34 for the information upper bound. Climatology already earns 78% of perfect-foresight revenue. Information quantity alone therefore does not value a forecast-driven policy; realised schedules and ordering must be evaluated explicitly.