Conditional Expected Loss as a Measure of Risk: Implications for Portfolio Selection

Abstract

In this paper, we analyze the economic implications arising from imposing a Conditional Expected Loss (CEL) constraint in the portfolio selection problem of a fund manager, and compare them with those arising from the imposition of a Value-at-Risk (VaR) constraint. For a given confidence level and bound, a CEL constraint is tighter than a VaR constraint. Consequently, a CEL constraint is more effective than a VaR constraint as a tool to control aggressive (i.e., slightly risk-averse) fund managers. However, there is a perverse side effect of the CEL constraint in that it may force conservative (i.e., highly risk-averse) fund managers to select portfolios with larger standard deviations. While this result is also true with the use of VaR as a risk management tool, it is even more perverse with CEL. Hence, the benefits of using CEL instead of VaR come at a price.