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Does the Market Anticipate? Can it? Should it?

Kangda Ken Wren

Abstract

We explore a nuance to 'no arbitrage' in relation to 'informational efficiency': acting immediately on an arbitrage is sometimes suboptimal; in such cases optimised trading can suppress the anticipation of predictable risk-outcomes, thereby creating an apparent Status Quo Bias, with Momentum and Low-Risk effects. This is shown in continuous time under model- or event-risk, where, unlike existing approaches, pre-horizon risk-resolution and Risk-Neutral Equivalent pricing are allowed, with the technical challenges overcome through results from the 'weak viability' and 'side-inside information' literature. The 'tension' between 'no arbitrage', 'informational efficiency' and 'risk-anticipation' is thus exposed and treated in a practically relevant setting.

Does the Market Anticipate? Can it? Should it?

Abstract

We explore a nuance to 'no arbitrage' in relation to 'informational efficiency': acting immediately on an arbitrage is sometimes suboptimal; in such cases optimised trading can suppress the anticipation of predictable risk-outcomes, thereby creating an apparent Status Quo Bias, with Momentum and Low-Risk effects. This is shown in continuous time under model- or event-risk, where, unlike existing approaches, pre-horizon risk-resolution and Risk-Neutral Equivalent pricing are allowed, with the technical challenges overcome through results from the 'weak viability' and 'side-inside information' literature. The 'tension' between 'no arbitrage', 'informational efficiency' and 'risk-anticipation' is thus exposed and treated in a practically relevant setting.
Paper Structure (30 sections, 6 theorems, 39 equations)

This paper contains 30 sections, 6 theorems, 39 equations.

Table of Contents

  1. Setup
  2. A Classical Starting Point: the Essential Standard Model
  3. Adding Model-Risk the Standard Way
  4. Adding Consistent Model-Risk Resolvable by Predictive Data
  5. The Risk-Neutral Approach to Model-Risk Pricing
  6. Some Constraints for Asset-Pricing under Model-Risk
  7. FTAP-Viable Asset-Pricing under Model-Risk
  8. NUPBR Viability at Risk-Resolution
  9. The Dominance of Non-Anticipation
  10. A Market of Heterogeneous Beliefs: Status Quo vs Change
  11. Status Quo Wins
  12. Bias and Risk-Pricing Measurement via Price Anomalies
  13. The Joint-Hypothesis Problem
  14. Bias and Risk-Pricing Parameters under Model-Uncertainty
  15. An Ideal Model-Risk Driven Market
  16. ...and 15 more sections

Key Result

Proposition 1

Under model-risk $B$ and reference model-risk beliefs $\{\pi^B_t\}$, based on reference law $\pi^B_0\cdot\mathbf{W}^{t_D}_B$ of data $\{\mathbf{D}_t\}$ on $(0,t_D]$, any FTAP-viable asset-pricing must be of the form: where $\langle{Y}\rangle_t^{\hat{\pi}}$ is its model-risk only version, the RNE law of which is of the form $\hat{\pi}^B_0\cdot\hat{W}^D_B\times{W}_B|_{t_D}$, with $\hat{\pi}^B_0\sim

Theorems & Definitions (19)

  • Remark 1
  • Remark 2
  • Remark 3
  • Proposition 1
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 9 more