Controlling risk through diversification in portfolio selection with non-historical information

We deal with the portfolio selection problem for investors having information on the expected returns of the assets based not only on historical data. In the absence of a way of measuring the risk of non-historical information, the investor may try to adjust it through the consideration of a suitable set of diversification constraints. With this aim, we relate the concept of value of information (recently introduced by Kao and Steuer) to a qualitative subjective measure of the investor’s level of confidence in his/her non-historical information. As an illustration, we analyze the behavior of the proposed indicator in the Spanish IBEX35 index for risk, upper bound, semicontinuous variable and cardinality constraints.