Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T07:19:34.682Z Has data issue: false hasContentIssue false
  • English
  • Français

Parameter Uncertainty in Multiperiod Portfolio Optimization with Transaction Costs

Published online by Cambridge University Press:  20 January 2016

Victor DeMiguel,
Alberto Martín-Utrera and
Francisco J. Nogales
Victor DeMiguel
Affiliation:
avmiguel@london.edu, London Business School, London NW1 4SA, United Kingdom
Alberto Martín-Utrera*
Affiliation:
a.martinutrera@lancaster.ac.uk, Lancaster University Management School, Lancaster LA1 4YX, United Kingdom
Francisco J. Nogales
Affiliation:
fcojavier.nogales@uc3m.es, Universidad Carlos III de Madrid, Getafe (Madrid) 28903, Spain.
*
*Corresponding author: a.martinutrera@lancaster.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We study the impact of parameter uncertainty on the expected utility of a multiperiod investor subject to quadratic transaction costs. We characterize the utility loss associated with ignoring parameter uncertainty, and show that it is equal to the product between the single-period utility loss and another term that captures the effects of the multiperiod mean-variance utility and transaction cost losses. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios and demonstrate with simulated and empirical data sets that they substantially outperform portfolios that ignore parameter uncertainty, transaction costs, or both.

Information

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 50 , Issue 6 , December 2015, pp. 1443 - 1471
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2016 

References

Almgren, R. “Execution Costs.” In Encyclopedia of Quantitative Finance. Chichester, England: John Wiley & Sons (2010), 612–616.Google Scholar
Almgren, R., and Chriss, N.. “Optimal Execution of Portfolio Transactions.” Journal of Risk, 3 (2001), 5–39.CrossRefGoogle Scholar
Bertsimas, D., and Lo, A. W.. “Optimal Control of Execution Costs.” Journal of Financial Markets, 1 (1998), 1–50.CrossRefGoogle Scholar
Best, M. J., and Grauer, R. R.. “Positively Weighted Minimum-Variance Portfolios and the Structure of Asset Expected Returns.” Journal of Financial and Quantitative Analysis, 27 (1992), 513–537.Google Scholar
Brown, S. J. “The Portfolio Choice Problem: Comparison of Certainty Equivalence and Optimal Bayes Portfolios.” Communications in Statistics—Simulation and Computation, 7 (1978), 321–334.CrossRefGoogle Scholar
Constantinides, G. M. “Multiperiod Consumption and Investment Behavior with Convex Transactions Costs.” Management Science, 25 (1979), 1127–1137.Google Scholar
Cornuejols, G., and Tutuncu, R.. Optimization Methods in Finance. Cambridge, MA: Cambridge University Press (2007).Google Scholar
Davis, M. H. A., and Norman, A. R.. “Portfolio Selection with Transaction Costs.” Mathematics of Operations Research, 15 (1990), 676–713.CrossRefGoogle Scholar
DeMiguel, V.; Garlappi, L.; Nogales, F. J.; and Uppal, R.. “A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms.” Management Science, 55 (2009), 798–812.CrossRefGoogle Scholar
DeMiguel, V.; Garlappi, L.; and Uppal, R.. “Optimal versus Naïve Diversification: How Inefficient Is the 1/N Portfolio Strategy?” Review of Financial Studies, 22 (2009), 1915–1953.Google Scholar
DeMiguel, V.; Martín-Utrera, A.; and Nogales, F. J.. “Size Matters: Optimal Calibration of Shrinkage Estimators for Portfolio Selection.” Journal of Banking and Finance, 37 (2013), 3018–3034.Google Scholar
Engle, R., and Ferstenberg, R.. “Execution Risk.” Journal of Portfolio Management, 33 (2007), 34–44.Google Scholar
Engle, R.; Ferstenberg, R.; and Russell, J.. “Measuring and Modeling Execution Cost and Risk.” Journal of Portfolio Management, 38 (2012), 14–28.Google Scholar
Garlappi, L.; Uppal, R.; and Wang, T.. “Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach.” Review of Financial Studies, 20 (2007), 41–81.CrossRefGoogle Scholar
Garleanu, N., and Pedersen, L. H.. “Dynamic Trading with Predictable Returns and Transaction Costs.” Journal of Finance, 68 (2013), 2309–2340.Google Scholar
Goldfarb, D., and Iyengar, G.. “Robust Portfolio Selection Problems.” Mathematics of Operations Research, 28 (2003), 1–38.Google Scholar
Greenwood, R. “Short- and Long-Term Demand Curves for Stocks: Theory and Evidence on the Dynamics of Arbitrage.” Journal of Financial Economics, 75 (2005), 607–649.CrossRefGoogle Scholar
Haff, L. R. “An Identity for the Wishart Distribution with Applications.” Journal of Multivariate Analysis, 9 (1979), 531–544.Google Scholar
Jagannathan, R., and Ma, T.. “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps.” Journal of Finance, 58 (2003), 1651–1684.Google Scholar
Kan, R., and Zhou, G.. “Optimal Portfolio Choice with Parameter Uncertainty.” Journal of Financial and Quantitative Analysis, 42 (2007), 621–656.Google Scholar
Kirby, C., and Ostdiek, B.. “It’s All in the Timing: Simple Active Portfolio Strategies That Outperform Naïve Diversification.” Journal of Financial and Quantitative Analysis, 47 (2012), 437–467.CrossRefGoogle Scholar
Klein, R. W., and Bawa, V. S.. “The Effect of Estimation Risk on Optimal Portfolio Choice.” Journal of Financial Economics, 3 (1976), 215–231.Google Scholar
Kyle, A. S. “Continuous Auctions and Insider Trading.” Econometrica, 53 (1985), 1315–1335.Google Scholar
Ledoit, O., and Wolf, M.. “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices.” Journal of Multivariate Analysis, 88 (2004), 365–411.Google Scholar
Ledoit, O., and Wolf, M.. “Robust Performance Hypothesis Testing with the Sharpe Ratio.” Journal of Empirical Finance, 15 (2008), 850–859.Google Scholar
Lillo, F. J.; Farmer, J. D.; and Mantegna, R. N.. “Master Curve for Price-Impact Function.” Nature, 421 (2003), 129–130.Google Scholar
Liu, H. “Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets.” Journal of Finance, 59 (2004), 289–338.Google Scholar
MacKinlay, A. C., and Pástor, L.. “Asset Pricing Models: Implications for Expected Returns and Portfolio Selection.” Review of Financial Studies, 13 (2000), 883–916.Google Scholar
Markowitz, H. “Portfolio Selection.” Journal of Finance, 7 (1952), 77–91.Google Scholar
Pástor, L. “Portfolio Selection and Asset Pricing Models.” Journal of Finance, 55 (2000), 179–223.Google Scholar
Pástor, L., and Stambaugh, R. F.. “Comparing Asset Pricing Models: An Investment Perspective.” Journal of Financial Economics, 56 (2000), 335–381.Google Scholar
Politis, D., and Romano, J.. “The Stationary Bootstrap.” Journal of the American Statistical Association, 89 (1994), 1303–1313.CrossRefGoogle Scholar
Rustem, B.; Becker, R. G.; and Marty, W.. “Robust Min-Max Portfolio Strategies for Rival Forecast and Risk Scenarios.” Journal of Economic Dynamics and Control, 24 (2000), 1591–1621.Google Scholar
Schottle, K., and Werner, R.. “Towards Reliable Efficient Frontiers.” Journal of Asset Management, 7 (2006), 128–141.CrossRefGoogle Scholar
Tu, J., and Zhou, G.. “Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty.” Journal of Financial and Quantitative Analysis, 45 (2010), 959–986.Google Scholar
Tutuncu, R. H., and Koeing, M.. “Robust Asset Allocation.” Annals of Operations Research, 132 (2004), 157–187.Google Scholar
Wang, Z. “A Shrinkage Approach to Model Uncertainty and Asset Allocation.” Review of Financial Studies, 18 (2005), 673–705.Google Scholar