Journal of Mathematical Finance, 2012, 2, 96-104 http://dx.doi.org/10.4236/jmf.2012.21012 Published Online February 2012 (http://www.SciRP.org/journal/jmf) Analytical Hierarchy Process and Goal Programming Approach for Asset Allocation Komlan Sedzro 1 , Arif Marouane 2 , Tov Assogbavi 3 1 Finance Department, School of Business and Management, University of Quebec, Montreal, Canada 2 Business Development Bank of Canada, Montreal, Canada 3 School of Commerce and Administration, Laurentian University, Sudbury, Canada Email: sedzro.k@uqam.ca, Marouane.arif@bdc.ca, tassogbavi@laurentian.ca Received September 27, 2011; revised November 29, 2011; accepted December 8, 2011 ABSTRACT Asset allocation in portfolio construction must simultaneously consider market conditions and investors’ specific pref- erences. Therefore, it is a multi-criteria decision that goes beyond the scope of the two-criteria, mean and variance of the portfolio returns, optimization method that traditionally prevails in the financial literature. This article suggests a pro- cedure that makes integrated asset management possible, based on the Analytic Hierarchy Process combined with a mean variance and goal programming model. We illustrate this procedure with data from Canadian mutual funds over a total period of five years and three months, from September 2002 to November 2007. The results obtained are encour- aging, as the portfolios constructed in this manner perform better than the S&P/TSX 60 index, which is the reference portfolio for the Canadian market. Keywords: Asset Allocation; Goal Programming; Analytic Hierarchy Process 1. Introduction We apply the Analytic Hierarchy Process (AHP), com- bined with a mean variance optimization and goal progra- mming model to allocate assets within a portfolio, consid- ering both market conditions and investors’ preferences. Asset allocation is one of the most deciding tasks that influence portfolio performance. Brinson, Hood and Bee- bower [1] and Brinson, Singer and Beebower [2] show that investment policy accounts for an average of 93.6% of ove- rall return variations, whereas selectivity and market tim- ing only contribute slightly. Ibboston and Kaplan [3] con- firms these results. They observe that asset allocation ex- plains 90% of the variability of mutual funds overtime, 40% of variations between funds, and an average of 100% of a fund’s returns. To aid managers in this exercise of decisive importance for portfolio performance, Sharpe [4] suggests an integrated approach to asset allocation that considers both market conditions, and the investor’s goals and wealth. Figure 1 below illustrates the major steps of this asset allocation process. Quadrant C 1 represents the current capital market con- ditions. Certain techniques must be used (quadrant C 2 ) to translate these market conditions into asset return predic- tions (quadrant C 3 ). Figure 1. Integrated asset allocation. Adapted from [4]. The investor’s wealth (quadrant I 1 ) usually determines his degree of risk tolerance (quadrant I 3 ) through a risk tolerance function (quadrant I 2 ). Based on the degree of risk tolerance (quadrant I 3 ) and asset return predictions (quadrant C 3 ), an Optimizer (qua- drant M 1 ) can be used to determine the most suitable asset mix (quadrant M 2 ) for the investor. Quadrant M 3 repre- Copyright © 2012 SciRes. JMF