Equivalent Risky Allocation: The New ERA of Risk Measurement for Heterogeneous Investors

Abstract

This paper introduces an investor-specific risk measure derived from the linear-exponential (linex) utility function. It combines the notions of risk perception and risk aversion. To make this measure interpretable and comparable with others like variance or value-at-risk, it is translated into an Equivalent Risky Allocation (ERA), where the risk value is matched with the one of a selected benchmark. We demonstrate that portfolio allocations are sensitive to risk perception. The linex risk measure provides more stable allocations and is closer to the target risk profile than the variance, while it provides better consistency of risk exposures over time than the value-at-risk.