Asset Allocation Under the Basel Accord Risk Measures

Abstract

Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank's trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks to take into account the constraint of capital requirement when they make asset allocation decisions. In this paper, we propose a new asset allocation model that incorporates the regulatory capital requirements under both the Basel 2.5 Accord, which is currently in effect, and the Basel III Accord, which was recently proposed and is currently under discussion. We propose an unified algorithm based on the alternating direction augmented Lagrangian method to solve the model; we also establish the first-order optimality of the limit points of the sequence generated by the algorithm under some mild conditions. The algorithm is simple and easy to implement; each step of the algorithm consists of solving convex quadratic programming or * We are grateful to Steven Kou for his insightful comments to the paper. Zaiwen Wen was partially supported by the NSFC grant 11101274 and research fund (20110073120069)

Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems

“…Nevertheless, it has been observed by many researchers that the ADMM works extremely well for various applications involving nonconvex objectives, such as the nonnegative matrix factorization [37,38], phase retrieval [39], distributed matrix factorization [40], distributed clustering [41], sparse zero variance discriminant analysis [42], polynomial optimization [43], tensor decomposition [44], matrix separation [45], matrix completion [46], asset allocation [47], sparse feedback control [48] and so on. However, to the best of our knowledge, existing convergence analysis of ADMM for nonconvex problems is very limited -all known global convergence analysis needs to impose uncheckable conditions on the sequence generated by the algorithm.…”

“…However, to the best of our knowledge, existing convergence analysis of ADMM for nonconvex problems is very limited -all known global convergence analysis needs to impose uncheckable conditions on the sequence generated by the algorithm. For example, references [43,[45][46][47] show global convergence of the ADMM to the set of stationary solutions for their respective nonconvex problems, by making the key assumptions that the limit points do exist, and that the successive differences of the iterates (both primal and dual) converge to zero. However such assumption is nonstandard and overly restrictive.…”

Three essays on the financial analysis of the political actions of the Chinese National Social Security Fund

“…CVaR refers to the conditional expectation of the loss above VaR. Based on VaR, Basel Accords propose the Basel II risk measure to calculate the capital requirements for a bank's trading book (Wen et al, 2013).…”

“…During the financial crisis, the Basel II risk measure was considered to be not sufficiently conservative and procyclical (Wen et al, 2013). Hence, Basel Accords revised the Basel II risk measure to the Basel 2.5 risk measure (stressed VaR) in 2009, and further to the Basel III (Stressed CVaR) in 2012 (Wen et al, 2013).…”

“…Hence, Basel Accords revised the Basel II risk measure to the Basel 2.5 risk measure (stressed VaR) in 2009, and further to the Basel III (Stressed CVaR) in 2012 (Wen et al, 2013). Recently, alternative downside risk measures, such as nonlinearly weighted ES (Chen and Yang, 2011) and generalized quantiles risk measures (Bellini et al, 2014), have been identified.…”