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

Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.

Abstract

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.

Keywords:

• Decision support systems
• finance
• investment
• multi-objective

Notes

Please note this paper has been re-typeset by Taylor & Francis from the manuscript originally provided to the previous publisher.

1. In Figure 1, as always we provide numerical values for the risk of a portfolio, the shown value is not the variance provided by the risk function x^tVx, but the standard deviation $\sqrt{{\mathbf{x}}^{\mathbf{t}}\mathbf{Vx}}$, since it can be compared with the return more intuitively, as it can be interpreted as a kind of mean of the historical deviations from the mean return.

2. Those identified by the tickers ABE, ANA, ACS, AMS, BBVA, SAB, SAN, BKT, BME, CABK, DIA, ENG, ELE, FER, FCC, GAM, GAS, GRF, IBE, IDR, ITX, IAG, JAZ, MAP, TL5, OHL REE, REP, TRE, TEF.