Value-at-Risk Capital Requirement Regulation, Risk Taking and Asset Allocation: A Mean-Variance Analysis

In this study, the mean-variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders' welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.

[1]  Susanne Emmer,et al.  Optimal Portfolios with Bounded Downside Risks , 2002 .

[2]  Matthew Pritsker,et al.  The Hidden Dangers of Historical Simulation , 2001 .

[3]  J. Vicente,et al.  Social Welfare Analysis in a Financial Economy with Risk Regulation , 2010 .

[4]  Anthony M. Santomero,et al.  Regulation of Bank Capital and Portfolio Risk , 1980 .

[5]  Alexandre M. Baptista,et al.  Reducing estimation risk in optimal portfolio selection when short sales are allowed , 2009 .

[6]  Philippe Jorion,et al.  Risk2: Measuring the Risk in Value at Risk , 1996 .

[7]  Internal Models-Based Capital Regulation and Bank Risk-Taking Incentives , 2002 .

[8]  Philippe Jorion,et al.  Portfolio Optimization with Constraints on Tracking Error , 2002 .

[9]  Raghuram G. Rajan,et al.  Liquidity Risk, Liquidity Creation, and Financial Fragility: A Theory of Banking , 1999, Journal of Political Economy.

[10]  Douglas W. Diamond,et al.  Liquidity Shortages and Banking Crises , 2002 .

[11]  Turan G. Bali,et al.  The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR , 2008 .

[12]  Shu Yan,et al.  Mean¿variance portfolio selection with ¿at-risk¿ constraints and discrete distributions. , 2007 .

[13]  Basel ’ s value-at-risk capital requirement regulation : An efficiency analysis q , 2007 .

[14]  Arnoud Boot,et al.  The Economics of Bank Regulation , 1995 .

[15]  F. Nogales,et al.  Optimal Portfolios with Minimum Capital Requirements , 2010 .

[16]  Ka Fai Cedric Yiu.  Optimal portfolios under a value-at-risk constraint , 2004 .

[17]  Douglas W. Diamond,et al.  A Theory of Bank Capital , 1999 .

[18]  João A. C. Santos.  Bank Capital Regulation in Contemporary Banking Theory: A Review of the Literature , 2000 .

[19]  Suleyman Basak,et al.  Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices , 1999 .

[20]  Phhilippe Jorion.  Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[21]  Asli Demirgüç-Kunt,et al.  Regulations, Market Structure, Institutions, and the Cost of Financial Intermediation , 2003 .

[22]  R. Maller,et al.  On the performance of the minimum VaR portfolio , 2011 .

[23]  Jonathan B. Berk,et al.  Necessary Conditions for the CAPM , 1997 .

[24]  H. Levy,et al.  Asset Return Distributions and the Investment Horizon , 2004 .

[25]  Alexandre M. Baptista,et al.  A comparison of the original and revised Basel market risk frameworks for regulating bank capital , 2013 .

[26]  Traian A. Pirvu.  Portfolio optimization under the Value-at-Risk constraint , 2007 .

[27]  J. Tobin.  Liquidity Preference as Behavior towards Risk , 1958 .

[28]  Turan G. Bali,et al.  Does Systemic Risk in the Financial Sector Predict Future Economic Downturns? , 2012 .

[29]  Estimating economic capital allocations for market and credit risk , 2004 .

[30]  B. Giancarlo.  Are banks really special? A note on the theory of financial intermediaries , 2004 .

[31]  Miguel A. Lejeune,et al.  A VaR Black–Litterman model for the construction of absolute return fund-of-funds , 2011 .

[32]  Douglas W. Diamond,et al.  Money in a Theory of Banking , 2003 .

[33]  Turan G. Bali.  An Extreme Value Approach to Estimating Volatility and Value at Risk , 2003 .

[34]  Gordon J. Alexander,et al.  From Markowitz to modern risk management , 2009 .

[35]  Alexandre M. Baptista,et al.  Active portfolio management with benchmarking: Adding a value-at-risk constraint , 2008 .

[36]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[37]  T. Vorst.  Optimal Portfolios under a Value at Risk Constraint , 2001 .

[38]  J. Lintner.  THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS , 1965 .

[39]  Markus Leippold,et al.  Equilibrium Impact of Value-at-Risk Regulation , 2002 .

[40]  H. M. Markowitz.  Approximating Expected Utility by a Function of Mean and Variance , 2016 .

[41]  Alexandre M. Baptista,et al.  Portfolio Selection With a Drawdown Constraint , 2006 .

[42]  M. Ma,et al.  FOUNDATIONS OF PORTFOLIO THEORY , 1990 .

[43]  Alexandre M. Baptista,et al.  Does the Basle Capital Accord reduce bank fragility? An assessment of the value-at-risk approach ☆ , 2006 .

[44]  R. Roll,et al.  A Mean/Variance Analysis of Tracking Error , 1992 .

[45]  V. Acharya.  Is the International Convergence of Capital Adequacy Regulation Desirable? , 2002 .

[46]  Alexandre M. Baptista,et al.  Active portfolio management with benchmarking: A frontier based on alpha. , 2010 .

[47]  Suleyman Basak,et al.  Risk Management with Benchmarking , 2001, Manag. Sci..

[48]  R. C. Merton,et al.  An Analytic Derivation of the Efficient Portfolio Frontier , 1972, Journal of Financial and Quantitative Analysis.

[49]  Philippe Jorion,et al.  Portfolio Optimization with Tracking-Error Constraints , 2003 .

[50]  Dwight M. Jaffee,et al.  On the Application of Portfolio Theory to Depository Financial Intermediaries , 1974 .

[51]  David H. Pyle.  ON THE THEORY OF FINANCIAL INTERMEDIATION , 1971 .

[52]  H. Levy,et al.  Efficiency analysis of choices involving risk , 1969 .

[53]  G. Chamberlain.  A characterization of the distributions that imply mean—Variance utility functions☆ , 1983 .

[54]  W. Sharpe.  CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK* , 1964 .

[55]  Claudia Klüppelberg,et al.  Optimal Portfolios with Bounded Capital at Risk , 2001 .

[56]  Anthony M. Santomero,et al.  Risk in Banking and Capital Regulation , 1988 .