Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T06:19:19.177Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Portfolio Choice with Linear Rebalancing Rules

Published online by Cambridge University Press:  15 June 2017

Ciamac C. Moallemi  and
Mehmet Sağlam
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution and show that it achieves near optimal performance. We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 52 , Issue 3 , June 2017 , pp. 1247 - 1278
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

We are grateful for helpful comments from an anonymous referee, David Brown, Stephen Brown (the editor), Sylvain Champonnois (discussant), Michael Sotiropoulos, and conference participants at the 2011 Annual Conference on Advances in the Analysis of Hedge Fund Strategies at Imperial College London. Moallemi acknowledges the support of National Science Foundation (NSF) grant CMMI-1235023. Sağlam acknowledges support from the Eugene M. Lang Doctoral Student Grant.

References

Almgren, R. F., and Chriss, N.. “Optimal Execution of Portfolio Transactions.” Journal of Risk, 3 (2000), 5–39.Google Scholar
Balduzzi, P., and Lynch, A. W.. “Transaction Costs and Predictability: Some Utility Cost Calculations.” Journal of Financial Economics, 52 (1999), 47–78.Google Scholar
Basak, S., and Chabakauri, G.. “Dynamic Mean-Variance Asset Allocation.” Review of Financial Studies, 23 (2010), 2970–3016.Google Scholar
Ben-Tal, A.; Golany, B.; Nemirovski, A.; and Vial, J.. “Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach.” Manufacturing and Service Operations Management, 7 (2005), 248–271.Google Scholar
Ben-Tal, A.; Goryashko, A.; Guslitzer, E.; and Nemirovski, A.. “Adjustable Robust Solutions of Uncertain Linear Programs.” Mathematical Programming, 99 (2004), 351–376.CrossRefGoogle Scholar
Bertsekas, D. P. Dynamic Programming and Optimal Control, 2nd ed. Belmont, MA: Athena Scientific (2000).Google Scholar
Bertsimas, D., and Goyal, V.. “On the Power and Limitations of Affine Policies in Two-Stage Adaptive Optimization.” Mathematical Programming, 134 (2012), 491–531.CrossRefGoogle Scholar
Bertsimas, D.; Iancu, D. A.; and Parrilo, P. A.. “Optimality of Affine Policies in Multistage Robust Optimization.” Mathematics of Operations Research, 35 (2010), 363–394.Google Scholar
Bertsimas, D., and Lo, A.. “Optimal Control of Execution Costs.” Journal of Financial Markets, 1 (1998), 1–50.Google Scholar
Boyd, S.; Mueller, M. T.; O’Donoghue, B.; and Wang, Y.. “Performance Bounds and Suboptimal Policies for Multi-Period Investment.” Foundations and Trends in Optimization, 1 (2014), 1–72.Google Scholar
Boyd, S., and Vandenberghe, L.. Convex Optimization. Cambridge, UK: Cambridge University Press (2004).Google Scholar
Brandt, M. W.; Goyal, A.; Santa-Clara, P.; and Stroud, J. R.. “A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning about Return Predictability.” Review of Financial Studies, 18 (2005), 831–873.CrossRefGoogle Scholar
Brandt, M. W., and Santa-Clara, P.. “Dynamic Portfolio Selection by Augmenting the Asset Space.” Journal of Finance, 61 (2006), 2187–2217.CrossRefGoogle Scholar
Brandt, M. W.; Santa-Clara, P.; and Valkanov, R.. “Parametric Portfolio Policies: Exploiting Characteristics in the Cross-Section of Equity Returns.” Review of Financial Studies, 22 (2009), 3411–3447.CrossRefGoogle Scholar
Brown, D. B., and Smith, J. E.. “Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds.” Management Science, 57 (2011), 1752–1770.Google Scholar
Calafiore, G. C.“An Affine Control Method for Optimal Dynamic Asset Allocation with Transaction Costs.” SIAM Journal on Control and Optimization, 48 (2009), 2254–2274.Google Scholar
Campbell, J. Y., and Viceira, L. M.. Strategic Asset Allocation. Oxford, UK: Oxford University Press (2002).Google Scholar
Chen, N.; Roll, R.; and Ross, S. A.. “Economic Forces and the Stock Market.” Journal of Business, 59 (1986), 383–403.CrossRefGoogle Scholar
Chen, X.; Sim, M.; and Sun, P.. “A Robust Optimization Perspective on Stochastic Programming.” Operations Research, 55 (2007), 1058–1071.Google Scholar
Chen, X.; Sim, M.; Sun, P.; and Zhang, J.. “A Linear Decision-Based Approximation Approach to Stochastic Programming.” Operations Research, 56 (2008), 344–357.Google Scholar
Constantinides, G. M.“Capital Market Equilibrium with Transaction Costs.” Journal of Political Economy, 94 (1986), 842–862.Google Scholar
Cvitanic, J.“Theory of Portfolio Optimization in Markets with Frictions.” In Handbooks in Mathematical Finance, Jouini, E., Cvitanic, J., and Musiela, M., eds. Cambridge, UK: Cambridge University Press (2001).Google Scholar
Davis, M. H. A., and Norman, A. R.. “Portfolio Selection with Transaction Costs.” Mathematics of Operations Research, 15 (1990), 676–713.Google Scholar
Desai, V. V.; Farias, V. F.; and Moallemi, C. C.. “Pathwise Optimization for Linear Convex Systems.” Working Paper, Columbia University (2011).Google Scholar
Detemple, J. B.; Garcia, R.; and Rindisbacher, M.. “A Monte Carlo Method for Optimal Portfolios.” Journal of Finance, 58 (2003), 401–446.CrossRefGoogle Scholar
Dumas, B., and Luciano, E.. “An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs.” Journal of Finance, 46 (1991), 577–595.Google Scholar
Fama, E. F., and French, K. R.. “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance, 51 (1996), 55–84.CrossRefGoogle Scholar
Gârleanu, N., and Pedersen, L. H.. “Dynamic Trading with Predictable Returns and Transaction Costs.” Journal of Finance, 68 (2013), 2309–2340.Google Scholar
Glasserman, P., and Xu, X.. “Robust Portfolio Control with Stochastic Factor Dynamics.” Operations Research, 61 (2013), 874–893.Google Scholar
Goetzmann, W. N., and Jorion, P.. “Testing the Predictive Power of Dividend Yields.” Journal of Finance, 48 (1993), 663–679.Google Scholar
Grant, M., and Boyd, S.. “CVX: Matlab Software for Disciplined Convex Programming, version 1.21.” Available at http://cvxr.com/cvx (2011).Google Scholar
Grinold, R. C., and Kahn, R. N.. Active Portfolio Management, 2nd ed. New York, NY: McGraw-Hill (1999).Google Scholar
Heston, S. L.; Korajczyk, R. A.; and Sadka, R.. “Intraday Patterns in the Cross-Section of Stock Returns.” Journal of Finance, 65 (2010), 1369–1407.Google Scholar
Hora, M.“The Practice of Optimal Execution.” Trading, 2006 (2006), 52–60.Google Scholar
Kuhn, D.; Wiesemann, W.; and Georghiou, A.. “Primal and Dual Linear Decision Rules in Stochastic and Robust Optimization.” Mathematical Programming, 130 (2011), 177–209.CrossRefGoogle Scholar
Liu, H.“Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets.” Journal of Finance, 59 (2004), 289–338.Google Scholar
Liu, H., and Loewenstein, M.. “Optimal Portfolio Selection with Transaction Costs and Finite Horizons.” Review of Financial Studies, 15 (2002), 805–835.Google Scholar
Lynch, A. W., and Balduzzi, P.. “Predictability and Transaction Costs: The Impact on Rebalancing Rules and Behavior.” Journal of Finance, 55 (2000), 2285–2309.Google Scholar
Lynch, A. W., and Tan, S.. “Multiple Risky Assets, Transaction Costs, and Return Predictability: Allocation Rules and Implications for U.S. Investors.” Journal of Financial and Quantitative Analysis, 45 (2010), 1015–1053.Google Scholar
Merton, R. C.“Optimum Consumption and Portfolio Rules in a Continuous-Time Model.” Journal of Economic Theory, 3 (1971), 373–413.CrossRefGoogle Scholar
Nemirovski, A.; Juditsky, A.; Lan, G.; and Shapiro, A.. “Stochastic Approximation Approach to Stochastic Programming.” SIAM Journal on Optimization, 19 (2009), 1574–1609.CrossRefGoogle Scholar
Shapiro, A.“Monte Carlo Sampling Methods.” In Handbooks in Operations Research and Management Science: Stochastic Programming, Vol. 10, Ruszczynski, A. and Shapiro, A., eds. Amsterdam, Netherlands: Elsevier (2003).Google Scholar
Shapiro, A., and Nemirovski, A.. “On Complexity of Stochastic Programming Problems.” In Applied Optimization: Continuous Optimization, Vol. 99, Pardalos, P. M., Hearn, D., Jeyakumar, V., and Rubinov, A., eds. New York, NY: Springer (2005).Google Scholar
Shreve, S. E., and Soner, H. M.. “Optimal Investment and Consumption with Transaction Costs.” Annals of Applied Probability, 4 (1994), 609–692.Google Scholar
Skaf, J., and Boyd, S. P.. “Nonlinear Q-Design for Convex Stochastic Control.” IEEE Transactions on Automatic Control, 54 (2009), 2426–2430.Google Scholar
Skaf, J., and Boyd, S. P.. “Design of Affine Controllers via Convex Optimization.” IEEE Transactions on Automatic Control, 55 (2010), 2476–2487.Google Scholar
Supplementary material: File

Moallemi and Sağlam supplementary material

Moallemi and Sağlam supplementary material

Download Moallemi and Sağlam supplementary material(File)
File 362.1 KB