A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR?
The Basel Committee on Banking Supervision (BCBS) (2013) recently proposed shifting the quantitative risk metrics system from Value-at-Risk (VaR) to Expected Shortfall (ES). The BCBS (2013) noted that “a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk” (p. 3). For this reason, the Basel Committee is considering the use of ES, which is a coherent risk measure and has already become common in the insurance industry, though not yet in the banking industry. While ES is mathematically superior to VaR in that it does not show “tail risk” and is a coherent risk measure in being subadditive, its practical implementation and large calculation requirements may pose operational challenges to financial firms. Moreover, previous empirical findings based only on means and standard deviations suggested that VaR and ES were very similar in most practical cases, while ES could be less precise because of its larger variance. In this paper we find that ES is computationally feasible using personal computers and, contrary to previous research, it is shown that there is a stochastic difference between the 97.5% ES and 99% VaR. In the Gaussian case, they are similar but not equal, while in other cases they can differ substantially: in fat-tailed conditional distributions, on the one hand, 97.5%-ES would imply higher risk forecasts, while on the other, it provides a smaller down-side risk than using the 99%-VaR. It is found that the empirical results in the paper generally support the proposals of the Basel Committee.
|Keywords||Stochastic dominance, Value-at-Risk, Expected Shortfall, Optimizing strategy, Basel III Accord|
|JEL||Financing Policy; Capital and Ownership Structure (jel G32), Portfolio Choice; Investment Decisions (jel G11), Financial Forecasting (jel G17), Forecasting and Other Model Applications (jel C53), Time-Series Models; Dynamic Quantile Regressions (jel C22)|
|Publisher||Erasmus University Rotterdam|
|Series||Econometric Institute Research Papers|
Chang, C-L, Jiménez-Martín, J.A, McAleer, M.J, & Pérez-Amaral, T. (2015). A Stochastic Dominance Approach to the Basel III Dilemma: Expected Shortfall or VaR? (No. EI2015-14). Econometric Institute Research Papers. Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/78155