RISK MEASUREMENT USING EXTENDED GINI SHORTFALL WHILE CONSIDERING RISK-AVERSION PARAMETER

Abstract

Risk is an uncertainty that may occur in the future and cause a loss. To minimize the loss, a risk measure is needed to predict future losses. Corrado Gini (1912) invented a risk measure known as Gini Shortfall (GS). GS is coherent and provide information about variability of the distribution tail. However, GS generalizes that everyone has the same tendency to take risks, when in reality they do not. Therefore, Yitzhaki (1983) developed GS into Extended Gini Shortfall (EGS). EGS is a generalization of GS by taking risk-aversion into consideration. Risk-aversion is a tendency to take minimum risk. EGS is a coherent risk measure under certain conditions and can calculate average severity and variability of losses in the distribution tail with Tail Extended Gini functional, a variability measure based on the Extended Gini functional. Furthermore, the explicit formula of EGS for exponential, Pareto, and logistic distributions and the example of EGS calculation are presented. This calculation uses monthly loss of PT Unilever Indonesia Tbk stock from November 2010 to November 2020. Assuming a constant risk-aversion parameter, EGS tends to increase with the increasing prudence level. Meanwhile, with a constant prudence level, EGS tends to decrease with the increasing risk-aversion parameter.