Portfolio optimisation with cardinality constraint based on expected shortfall

Assets diversification is a well-known strategy to reduce the investment risk and become a mathematical problem since Markowitz's work in 1952. In this paper, we investigated the portfolio selection method using expected shortfall (ES), which also known as expected tail loss (ETL) or conditional value-at-risk (CVaR), as a risk measure. A cardinality constraint was added to the model in order to help the investor choose k from n available assets into the portfolio, where k is higher than the lower bound L and smaller than the upper bound U. To solve this complex portfolio optimisation problem, we use the genetic algorithm method with binary chromosomes and obtain the optimal weight using exact method. A numerical case-study is provided using several stocks in Indonesia Stock Market.