Portfolio Selection Models Based on Interval-Valued Conditional Value-at-Risk (ICVaR) and Case Study on the Data from Stock Markets

Abstract

Risk management is very important for individual investors or companies. There are several ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a good tool to describe uncertainty including both randomness and imprecision. Considering the uncertainty of financial market, we employ random intervals to describe returns of a risk asset and define an interval-valued risk measurement, which considers the tail risk. It is called the interval-valued conditional value-at-risk (ICVaR, for short). Similar to the classical conditional value-at-risk, ICVaR satisfies the sub-additivity. Under the new risk measure ICVaR, as a manner similar to the classical Mean-CVaR portfolio model, two optimal interval-valued portfolio selection models are built. The sub-additivity of ICVaR guarantees the global optimal solution to the Mean-ICVaR portfolio model. Based on the real data from mainland Chinese stock markets and international stock markets, the case study shows that our models are interpretable and consistent with the practical scenarios.