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-
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