Utility-Weighted Forecasting and Calibration for Risk-Adjusted Decisions under Trading Frictions

TL;DR

This paper tackles the mismatch between forecasting accuracy and real-world trading performance by modeling forecasting as an input to a frictionful, constrained decision problem. It introduces a utility-weighted calibration (UWC) criterion that weights calibration errors by their marginal impact on the friction-adjusted decision objective, and proves a dominance result: calibrated forecasts yield lower expected decision loss than uncalibrated or standard-calibrated alternatives under a broad set of regularity conditions. The empirical study uses a pre-committed nested walk-forward protocol on liquid equity-index futures, showing that UWC reduces turnover, lowers constraint-binding frequency, and improves risk-adjusted performance during drawdowns, with a t-statistic of -30.31 on loss differentials. The findings advocate a shift in financial econometrics toward decision-focused calibration and provide a rigorous governance framework with stress-testing, multiple-testing control, and replication-ready data pipelines. The work lays groundwork for further decision-focused learning by integrating calibration with end-to-end policy optimization under real-world frictions.

Abstract

Forecasting accuracy is routinely optimised in financial prediction tasks even though investment and risk-management decisions are executed under transaction costs, market impact, capacity limits, and binding risk constraints. This paper treats forecasting as an econometric input to a constrained decision problem. A predictive distribution induces a decision rule through a utility objective combined with an explicit friction operator consisting of both a cost functional and a feasible-set constraint system. The econometric target becomes minimisation of expected decision loss net of costs rather than minimisation of prediction error. The paper develops a utility-weighted calibration criterion aligned to the decision loss and establishes sufficient conditions under which calibrated predictive distributions weakly dominate uncalibrated alternatives. An empirical study using a pre-committed nested walk-forward protocol on liquid equity index futures confirms the theory: the proposed utility-weighted calibration reduces realised decision loss by over 30\% relative to an uncalibrated baseline ($t$-stat -30.31) for loss differential and improves the Sharpe ratio from -3.62 to -2.29 during a drawdown regime. The mechanism is identified as a structural reduction in the frequency of binding constraints (from 16.0\% to 5.1\%), preventing the "corner solution" failures that characterize overconfident forecasts in high-friction environments.

Figures (11)

• Figure 1: Forecast Error Sensitivity under Frictions. The loss function (Eq. 11) flattens as frictions ($\eta$) increase. In high-friction states (blue dashed), the decision is less sensitive to forecast precision, implying a lower utility-weight $\omega_t$ for small errors.
• Figure 2: Geometry of Dominance (Theorem 1). The contours represent the friction-adjusted decision loss $\mathcal{L}(Q)$. The Uncalibrated forecast $\tilde{Q}_t$ (red) lies on a high-loss contour. The Calibration Projection $\Pi(\tilde{Q}_t)$ (green) maps this forecast onto the manifold of calibrated distributions. By orthogonality of the projection under the decision-relevant norm $d_t$, the calibrated forecast necessarily lies on a lower loss contour, closer to the true DGP $P_t$ (star).
• Figure 3: Corner Solution Mechanism. When turnover constraints are present (Eq. 19), the realised trade (red) becomes insensitive to the forecast signal once the cap $\tau$ is hit. Uncalibrated forecasts that overshoot this boundary waste "signal budget" without altering the decision, generating zero marginal value.
• Figure 4: Finite-Sample Convergence. Simulation of the utility-weighted calibration discrepancy $\hat{d}_T$ as a function of sample size $T$. The calibrated estimator (green) converges systematically to a lower error floor than the uncalibrated baseline (red), validating the stability bound in Lemma 1.
• Figure 5: Limits of the Quadratic Approximation. Comparison of decision rules (Left) and sensitivities (Right) under Quadratic vs. Fixed costs. The quadratic weight (blue) provides a constant, smooth approximation to the discontinuous true sensitivity (red), avoiding the numerical instability of vanishing/exploding gradients in the no-trade and jump zones.

Theorems & Definitions (21)

• Definition 1: Information set
• Definition 2: Predictive distribution
• Definition 3: Admissible decision
• Definition 4: Friction operator
• Definition 5: Decision objective
• Definition 6: Decision loss
• Definition 7: Calibration
• Definition 8: Utility-weighted calibration criterion
• Proposition 1: Canonical quadratic-case utility-weight
• Lemma 1: Sensitivity of the induced decision to miscalibration