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

Kerstin Bergk, Mario Brandtner and Wolfgang Kürsten

Chapter 9 in Modern Finance and Risk Management:Festschrift in Honour of Hermann Locarek-Junge, 2022, pp 197-218 from World Scientific Publishing Co. Pte. Ltd.

Abstract: 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.

Keywords: Finance; Risk Management; Commodities; Energy Finance; Risk; Cryptocurrencies; Asset Management; Banking; Behavioral Finance; Behavioural Finance; Markowitz; Portfolio Selection; Asset Allocation; Crowdfunding; COVID; Pandemic; Corona; Investment Strategies; Low-Risk Investments; Social Banks; Excess Liquidity; Cost of Capital; Utilities; Network Industries; Private Equity; Small and Medium-Sized Enterprises; Black Swan; Statistical Inference; Maximum Likelihood; Bayesian Methods; Tail Risks; Conditional Value-at-Risk; Tail Nonlinearly Transformed Risk; Capital Constraints; Bank Regulation; Subjective Risk Assessment; Expert Knowledge; Model Risk; Risk Factors; Option Pricing; Volatility; Resilience; Supply Chains; Disruption; Systemic Risk; Oil; Renewable Energies; Corporate Risk Management; Power Purchase Agreements; Gold; Precious Metals; Dynamic Correlation; Mixed Data Sampling (search for similar items in EconPapers)
JEL-codes: G11 G3 G32 G4 (search for similar items in EconPapers)
Date: 2022
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