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Developing Robust Asset Allocations1
Working Paper
First Version: February 17, 2006 Current Version: April 18, 2006

Thomas M. Idzorek, CFA Director of Research Ibbotson Associates 225 North Michigan Avenue Suite 700 Chicago, Illinois 60601-7676 312-616-1620 (Main) 312-616-0404 (Fax) tidzorek@ibbotson.com

Abstract
Over the last 50 years, Markowitz’s mean-variance optimization framework has become the asset allocation model of choice. Unfortunately the model often leads to highly concentrated asset allocations, the primary reason that practitioners haven’t fully embraced this Nobel Prize winning idea. Two relatively new techniques that help practitioners develop robust, well-diversified asset allocations are the BlackLitterman model and resampled mean-variance optimization. The first approach focuses on building capital market expectations that behave better within an optimizer while the second approach is an attempt to build a better optimizer. In addition to providing practitioner friendly overviews of the two approaches, this article contributes to the literature by comparing / contrasting empirical examples of both approaches as well as the first empirical example of how the Black-Litterman model and resampled mean-variance optimization can be used together to develop robust asset allocations. Key Words: Robust asset allocation, mean-variance optimization, Black-Litterman, resampling.

© 2006 Ibbotson Associates

Robust Asset Allocation

Page 1

Introduction
In their seminal and extremely influential work, Brinson, Hood, and Beebower [1986] estimates that over time 90% of the variance in returns of a typical portfolio is explained by the variance of the portfolio’s asset allocation. Ibbotson and Kaplan [2000], among others, confirms this important finding supporting the notion that strategic asset allocation (SAA) is the most important decision in the investment process. Strategic asset allocation is both a process and a result. The strategic asset allocation focuses on how to invest assets to maximize the probability of achieving one’s long-term goals at an appropriate level of risk. It is the process of determining the target long-term allocations to the available asset classes. The process results in a set of long-term target allocations to applicable investable asset classes (proxied by market indices). The resulting long-term target asset allocations are often formalized into a strategic policy benchmark (policy benchmark for short) or model asset allocation. Using today’s popular alphabeta vernacular, strategic asset allocation is the beta decision, and as such, investment vehicles like mutual funds and hedge funds are not part of the discussion. 2 The most widely used quantitative strategic asset allocation framework is Harry Markowitz’s meanvariance optimization, an idea that resulted in a Nobel Prize for Markowitz (see Markowitz [1952, 1959]). Mean-variance optimization is one of the cornerstones of modern portfolio theory and over the last half century has become the dominant asset allocation model. The procedure maximizes expected return for a given level of risk, or equivalently, minimizes risk for a given return. The traditional textbook approach to asset allocation is as follows. Step 1 – Estimate the returns, risks, and correlations of the relevant asset classes based on capital market conditions. Step 2 – Use mean-variance optimization to create an efficient frontier. Step 3 – Select a point on the efficient frontier or select a mix of the risk-free asset and the optimum risky asset allocation based on an estimated risk tolerance level. By almost all accounts, the maximization of return per unit of risk is a logical and worthwhile objective. However, the Markowitz framework may be too powerful for its own good. Common issues or criticisms of traditional mean-variance optimization include: 1. Mean-variance optimization usually leads to asset allocations in which the majority of the...
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