Robust Asset Allocation with Benchmarked Objectives

37 Pages Posted: 23 Aug 2011

See all articles by Andrew Lim

Andrew Lim

National University of Singapore (NUS) - Department of Decision Sciences; National University of Singapore (NUS) - Department of Finance; National University of Singapore (NUS) - Institute for Operations Research and Analytics

J. George Shanthikumar

Purdue University - Krannert School of Management

Thaisiri Watewai

Chulalongkorn University - Department of Banking & Finance

Multiple version iconThere are 2 versions of this paper

Date Written: October 2011

Abstract

In this paper, we introduce a new approach for finding robust portfolios when there is model uncertainty. It differs from the usual worst‐case approach in that a (dynamic) portfolio is evaluated not only by its performance when there is an adversarial opponent (“nature”), but also by its performance relative to a stochastic benchmark. The benchmark corresponds to the wealth of a fictitious benchmark investor  who invests optimally given knowledge of the model chosen by nature, so in this regard, our objective has the flavor of min–max regret. This relative performance  approach has several important properties: (i) optimal portfolios seek to perform well over the entire range of models and not just the worst case, and hence are less pessimistic than those obtained from the usual worst‐case approach; (ii) the dynamic problem reduces to a convex static optimization problem under reasonable choices of the benchmark portfolio for important classes of models including ambiguous jump‐diffusions; and (iii) this static problem is dual to a Bayesian  version of a single period asset allocation problem where the prior on the unknown parameters (for the dual problem) correspond to the Lagrange multipliers in this duality relationship. This dual static problem can be interpreted as a less pessimistic alternative to the single period worst‐case Markowitz problem. More generally, this duality suggests that learning and robustness are closely related when benchmarked objectives are used.

Keywords: ambiguity, model uncertainty, relative performance measure, relative regret, regret, robust portfolio selection, robust control, convex duality, Bayesian models

Suggested Citation

Lim, Andrew E. B. and Shanthikumar, J. George and Watewai, Thaisiri, Robust Asset Allocation with Benchmarked Objectives (October 2011). Mathematical Finance, Vol. 21, Issue 4, pp. 643-679, 2011, Available at SSRN: https://ssrn.com/abstract=1914919 or http://dx.doi.org/10.1111/j.1467-9965.2010.00448.x

Andrew E. B. Lim (Contact Author)

National University of Singapore (NUS) - Department of Decision Sciences ( email )

NUS Business School
Mochtar Riady Building, 15 Kent Ridge
Singapore, 119245
Singapore

National University of Singapore (NUS) - Department of Finance ( email )

Mochtar Riady Building
15 Kent Ridge Drive
Singapore, 119245
Singapore

National University of Singapore (NUS) - Institute for Operations Research and Analytics ( email )

Singapore

J. George Shanthikumar

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Thaisiri Watewai

Chulalongkorn University - Department of Banking & Finance ( email )

Thailand

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