A number of papers have solved for the optimal dynamic portfolio strategy when expected returns are time-varying and trading is costly, but only for agents with myopic utility. Non-myopic agents benefit from hedging against future shocks to the investment opportunity set even when transaction costs are zero (Merton, 1969, 1971). In this paper, we propose a solution to the dynamic portfolio allocation problem for non-myopic agents faced with a stochastic investment opportunity set when trading is costly. We show that the agent’s optimal policy is to trade toward an “aim” portfolio, the makeup of which depends both on transaction costs and on each asset’s correlation with changes in the investment opportunity set. The speed at which the agent should trade towards the aim portfolio depends both on the shock’s persistence and on the extent to which the shock can be effectively hedged. We illustrate the differences in portfolio makeup that result from considering hedging demands of a long-horizon investor using a set of simplified examples, and using a daily trading strategy based on the estimated relation between retail order imbalance and future returns.
Authors
- Acknowledgements & Disclosure
- We thank Agostino Capponi, Darrell Duffie, Julien Huggonier, Kevin Webster and the participants of the Workshop on Non-Standard Investment Choice at ESSEC, the Princeton University Stochastic Control and Financial Engineering Conference, the Peking University Math Finance seminar, and the 2022 Financial Management Association Meetings for helpful discussions and comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. Kent D. Daniel The author declares that he consults for financial firms, and serves on the academic advisory boards of several financial firms, but has no relevant or material financial interests that bear upon the research described in this paper.
- DOI
- https://doi.org/10.3386/w33058
- Pages
- 62
- Published in
- United States of America
Table of Contents
- NBER WORKING PAPER SERIES 1
- OPTIMAL DYNAMIC ASSET ALLOCATION WITH TRANSACTION COSTS THE ROLE OF HEDGING DEMANDS 1
- Pierre Collin-Dufresne Kent D. Daniel Mehmet 1
- Sağlam 1
- Working Paper 33058 httpwww.nber.orgpapersw33058 1
- NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge MA 02138 October 2024 1
- At least one co-author has disclosed additional relationships of potential relevance for this research. Further information is available online at httpwww.nber.orgpapersw33058 1
- Sağlam 1
- Optimal Dynamic Asset Allocation with Transaction Costs The Role of Hedging Demands Pierre Collin-Dufresne Kent D. Daniel and Mehmet NBER Working Paper No. 33058 October 2024 JEL No. G11 G12 2
- Sağlam 2
- Pierre Collin-Dufresne Ecole Polytechnique Federale de Lausanne CDM SFI SFI-PCD EXTRA 209 CH-1015 Lausanne Switzerland pierre.collin-dufresneepfl.ch 2
- Kent D. Daniel Columbia Business School Kravis Hall 722 655 West 130th St. New York NY 10027 United States and NBER kd2371columbia.edu 2
- Mehmet Associate Professor of Finance Carl H. Lindner College of Business University of Cincinnati 408 Lindner Hall Cincinnati OH 45221 mehmet.saglamuc.edu 2
- Sağlam 2
- 2 The continuous time model with a finite horizon 7
- 3 The stationary model with a random horizon 13
- 4 Hedging Demand and Transaction Costs Numerical Example 17
- 4.1 The one asset and one predictor case 17
- 4.2 The two asset and one predictor case 22
- 5 Empirical Application with Retail Order Imbalance 24
- 5.1 Predictability model 25
- 5.2 Average utility and calibration of main parameters 26
- 5.3 Calibration of the Price Impact Matrix 27
- 5.4 Insights from the one-asset and one-predictor experiments 29
- 5.5 Numerical experiments with multiple assets and predictors 31
- 6 Conclusion 35
- References 39
- APPENDIX 42
- A Stochastic Differential Utility of Terminal Wealth 42
- B Source-Dependent SDU with Vanishing Risk Aversion to Ex- 43
- C Recursive Construction of the Source-Dependent Stochastic 44
- Differential Utility of Terminal Wealth 44
- D Source-dependent SDU with a random horizon 45
- E Finite horizon solution without transaction costs 46
- . . 47
- . . 48
- F Finite horizon solution with transaction costs 49
- . . . . . 50
- . . . . . 50
- . . 51
- . . 51
- G The finite horizon solution with CMV preferences 52
- H The infinite horizon portfolio problem without transaction costs 54
- I The infinite horizon portfolio problem with transaction costs 57
- J The one asset one factor case 59
- J.1 The infinite horizon no-transaction-cost case 59
- J.2 The infinite horizon with tcost 59
- K The infinite horizon solution CMV preferences 60
