Portfolio selection on the Madrid Exchange: a compromise programming model

Abstract

As a contribution to portfolio selection analysis, we develop a compromise programming approach to the investor's utility optimum on the Madrid Online Market. This approach derives from linkages between utility functions under incomplete information, Yu's compromise set, and certain biased sets of portfolios on the efficient frontier. These linkages rely on recent theorems in multi–criteria literature, which allow us to approximate the investor's utility optimum between bounds which are determined either by linear programming models or graphic techniques. Returns on 104 stocks are computed from capital gains and cash–flows, including dividends and rights offerings, over the period 1992–1997. The first step consists in normalizing the mean–variance efficient frontier, which is defined in terms of two indexes, profitability and safety. In the second step, interactive dialogues to elicit the investor's preferences for profitability and safety are described. In the third step, the utility optimum for each particular investor who pursues a buy–&–hold policy is bounded on the efficient frontier. From this step, a number of portfolios close to the investor's utility optimum are obtained. In the fourth step, compromise programming is used again to select one ‘satisficing’ portfolio from the set already bounded for each investor. This step is new with respect to previous papers in which compromise/utility models are employed. Computing processes are detailed in tables and figures which also display the numerical results. Extensions to active management policies are suggested.

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