Exploring the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings

Purpose - This paper aims to explore the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings and investment strategies. Design/methodology/approach - A novel multi-objective portfolio model is proposed to assess investment decisions under sectoral diversification, where the objective functions and constraints are interval-valued. The objective functions used are risk minimization (through the semi-absolute deviation measure of risk), maximization of liquidity (using turnover as a proxy) and the maximization of logarithmic return. Besides coherence constraints (imposing that the sum of the percentages of investment assigned to each stock should be equal to 100%), constraints regarding the maximum proportion of capital that can be invested (ensuring a minimum level of diversification) and cardinality constraints (to account for transaction costs) are also imposed. Findings - Besides the trade-off between return and risk, the study findings highlight a trade-off between liquidity and return and a positive relationship between risk and liquidity. Under an economic crisis scenario, the trade-off between return and liquidity is reduced. With the economic recovery, the levels of risk increase when contrasted with the setting of the economic crisis. The highest liquidity levels are reached with the economic boom, whereas the highest returns are obtained with the economic recession. Originality/value - This paper suggests a new modeling approach for assessing the trade-offs between liquidity, risk and return under different scenarios and investment strategies. A new interactive procedure inspired on the reference point approach is also proposed to obtain possibly efficient portfolios according to the investor's preferences. Regarding previous approaches suggested in the literature, this new procedure allows obtaining both supported and unsupported efficient solutions when cardinality constraints are included.