Portfolio Selection from Multiple Benchmarks: A Goal Programming Approach to an Actual Case

This paper deals with benchmark-based portfolio choice for buy-and-hold strategies of investing. Multiple benchmarks for returns are considered, which is more realistic than taking a unique benchmark – a unique aspiration difficult to select in practice among the various aspirations for returns that the investor has in mind. Portfolio selection with multiple benchmarks leads to a multi-objective problem, which is addressed by mean value – stochastic goal programming. In particular, two benchmarks are considered, which involves two goals. Weights for goals depend on investor's preferences and Arrow's absolute risk aversion coefficients. An efficient frontier of portfolios is obtained. Advantages of this stochastic method in our context are as follows: (i) Mean value-stochastic goal programming relies on classical utility theory under uncertainty and Arrow's absolute risk aversion, which ensures soundness and strictness, and (ii) the numerical model is easily solved by using available software such as mean–variance software. Numerical results are tabulated and discussed.