The paper studies the design of optimal (bond) portfolios taking into account various possible utility functions of an investor. The most prominent model for portfolio optimization was introduced by Markowitz. A real solution in this model can be achieved by quadratic programming routines for meanvariance analysis. Of course, there are many reasons for an investor to prefer other utility criteria than returnlvariance of return in the Markowitz model. In the last few years, many efficient multiple purpose optimization heuristics have been invented for the needs in optimizing telephone nets, chip layouts, job shop scheduling etc. Some of these heuristics have essential advantages: they are extremely flexible and very easy to implement on computers. One example of such an algorithm is the threshold-accepting algorithm (TA). TA is able to optimize portfolios under nearby arbitrary constraints and subject to nearly every utility function. In particular, the utility functions need neither to be convex, differentiable nor 'smooth' in any sense. We implemented TA for bond portfolio optimization with different utility criteria. The algorithms and computational results are presented. Under various utility functions, the 'best' portfolios look surprisingly different and have quite different qualities. Thus, for a portfolio manager it might be useful to provide himself with such a 'multiple-taste' optimizer in order to be able easily to readjust it according to his own personal utility considerations.
KEY WORDS Optimization Threshold accepting Portfolio optimization 1. INTRODUCTION
In his pioneering work Markowitz presented the standard model of mean-variance analysis in portfolio choice. In this model, an investor seeks a 'best' compromise between (high) return of his assets and (low) risk. The risk of a portfolio is measured in terms of variance of the return. The Markowitz model is smooth enough to allow the evaluation of efficient portfolios in practice. Nowadays, many software tools are available to compute the so-called efficient frontier of specific mean-variance models. These algorithms are essentially based on quadratic programming routines.
Of course, there are many reasons for an investor to prefer utility criteria other than returnlvariance of return. Meanwhile, there exists a fully exploited theory of utility and preference. Many different useful utility functions have been suggested. The drawback of several useful utility functions is that it is not possible to practically get solutions with common standard software. Utility functions of individuals representing preferences other than suggested by the mean-variance approach may look poor from a computer programmer's point of view. In this case, it may be very hard to compute efficient portfolios.