Tail Nonlinearly Transformed Risk Measure as a Capital Constraint — A Better Choice for Bank Regulation Than Conditional Value-at-Risk?

The purpose of this chapter is to compare regulatory capital constraints based on tail nonlinearly transformed risk measure (TNT) and conditional value-at-risk (CVaR). TNT extends CVaR by additionally transforming financial positions’ outcomes by means of a concave transformation function and, as such, it results that the TNT constraint is stricter than the corresponding CVaR constraint for any given confidence level. In a setting with n risky assets and one risk-free asset, we analyse the implications from imposing a TNT constraint on a bank’s (μ, σ)-portfolio selection problem and compare them with those arising from imposing a CVaR constraint. We find two major outcomes: First, due to its strictness, the (convex) TNT constraint is more effective than the (linear) CVaR constraint to induce slightly risk-averse banks to select a portfolio with smaller standard deviation. Second, the benefits of using a TNT constraint may come at a price, causing highly risk-averse banks to select a portfolio with larger standard deviation. We further derive the intersections of the (μ, σ)-efficient frontier and the TNT constraint analytically.