Integrated measures of household risk in financial plans optimized under a consumption rate constraint

Abstract

Measures of risk suited to the life-long financial plan of a household differ from other popular risk measures. When discussing a risk variable that would incorporate exposures to all significant types of risk, a natural choice for a financial institution would be value (e.g. of a portfolio), and, for enterprises, it would be, for instance, net income or cash flow. Based on these natural risk variables, integrated risk measures for financial institutions and investors are thus Value at Risk (VaR) or Expected Shortfall (ES) or related measures. For enterprises, these may be Earnings at Risk (EaR) and Cash Flow at Risk (CFaR). A measure of risk suited to the specificity of a household should, in turn, address threats to the accomplishment of its life objectives (to be more precise – life objectives of its members) and must take into account its life cycle. In this article, we present some proposals of new downside risk measures that fulfill these conditions. The measures are suited to the household financial planning framework proposed in other works by the authors of this paper and their concept is presented within this framework, but the very idea of the measures is much more universal and should be possible to be applied (maybe after some adjustments) in many other optimization models of financial plans.