Paper: arXiv 2601.07852

Authors: Craig S Wright

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework linking probabilistic forecast calibration directly to downstream decision loss under market frictions. Its empirical methodology is highly disciplined, utilizing a pre-committed nested walk-forward protocol on liquid futures to yield statistically strong, economically meaningful results.

Research Flowchart

  flowchart TD
    A["Research Question: Minimize Decision Loss<br/>under Trading Frictions & Constraints?"] --> B["Input Data: Liquid Equity Index Futures<br/>(Pre-committed Nested Walk-Forward)"]
    B --> C["Forecast & Friction Modeling:<br/>Utility Objective + Cost & Feasible Constraints"]
    C --> D["Utility-Weighted Calibration:<br/>Aligns Predictive Distribution to Decision Loss"]
    D --> E["Outcomes: Realized Loss Reduced >30%<br/>Sharpe Ratio: -3.62 to -2.29 in Drawdowns"]
    D --> F["Mechanism: Binding Constraint Frequency<br/>Dropped from 16.0% to 5.1%"]

Cited References (48)

  1. Arbitrage Theory in Continuous Time (2019)
  2. Stochastic Integration and Differential Equations (2005)
  3. Dynamic Asset Pricing Theory (2010)
  4. Optimal Execution of Portfolio Transactions (2001) — link
  5. Bayesian forecasting in economics and finance: A modern review (2024) — link
  6. Evaluating Density Forecasts Using Weighted Multivariate Scores in a Risk Management Context (2024) — link
  7. Multivariate probabilistic CRPS learning with an application to day-ahead electricity prices — → 2303.10019
  8. Markowitz portfolios under transaction costs (2025) — link
and 40 more
  1. Constrained portfolio strategies in a regime-switching economy (2023) — link
  2. End-to-end, decision-based, cardinality-constrained portfolio optimization (2025) — link
  3. Markowitz portfolios under transaction costs (2025) — link
  4. Efficient estimation of bid–ask spreads from open, high, low, and close prices (2024) — link
  5. Quantifying Long-Term Market Impact (2022) — link
  6. Do price trajectory data increase the efficiency of market impact estimation? (2024) — link
  7. The risk of falling short: Implementation Shortfall variance in portfolio construction (2025) — link
  8. Capacity Constraints in Hedge Funds: The Relation Between Fund Performance and Cohort Size (2022) — link
  9. Uncertain mean- CVaR model for portfolio selection with transaction cost and investors’ preferences (2024) — link
  10. End-to-end, decision-based, cardinality-constrained portfolio optimization (2025) — link
  11. The risk of falling short: Implementation Shortfall variance in portfolio construction (2025) — link
  12. Regression diagnostics meets forecast evaluation: conditional calibration, reliability diagrams, and coefficient of determination (2023) — link
  13. Tail calibration of probabilistic forecasts (2025) — link
  14. Probabilistic forecasts, calibration and sharpness (2007) — link
  15. A modified Diebold–Mariano test for equal forecast accuracy with clustered dependence (2021) — link
  16. Conditional Superior Predictive Ability (2022) — link
  17. GARCH density and functional forecasts (2023) — link
  18. Forecasting Value-at-Risk Using Deep Neural Network Quantile Regression (2024) — link
  19. Multivariate dynamic mixed-frequency density pooling for financial forecasting (2024) — link
  20. Decision-focused linear pooling for probabilistic forecast combination (2025)
  21. Strictly Proper Scoring Rules, Prediction, and Estimation (2007) — link
  22. Forecast Evaluation (2006) — link
  23. Decision-based Methods for Forecast Evaluation (2002)
  24. Forecasting and Decision Theory (2006) — link
  25. Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules (2011) — link
  26. Public Policy in an Uncertain World: Analysis and Decisions (2013)
  27. The Model Confidence Set (2011) — link
  28. A Test for Superior Predictive Ability (2005)
  29. Dynamic Trading with Predictable Returns and Transaction Costs (2013)
  30. Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? (2009)
  31. Making and Evaluating Point Forecasts (2011)
  32. The Role of the Information Set for Forecasting Functionals (2014)
  33. Empirical Asset Pricing via Machine Learning (2020)
  34. Can Machines ‘Learn’ Finance? (2020)
  35. Price Volatility, Trading Volume, and Market Depth: Evidence from Futures Markets (1993)
  36. Issues in Assessing Trade Execution Costs (2003)
  37. Do Liquidity Measures Measure Liquidity? (2009)
  38. Task-based End-to-End Model Learning in Stochastic Optimization (2017)
  39. Melding the Data-Decision Pipeline: Decision-Focused Learning for Combinatorial Optimization (2019)
  40. Differentiable Convex Optimization Layers (2019)

1 of 48 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.