An Asset Allocation Distributionally Robust Optimization Model With Capital Adequacy Ratio Implemented

The modern portfolio theory represented by the Markowitz mean-variance model has been widely applied in bank optimal asset allocation. Uncertainty management is the key problem on this work. Changes in assets credit ratings could lead to the volatility of market value and ultimately result in changes of the bank's capital and the variations of the capital level in turn mirror the credit risk of rating migrations. Existing researches mainly focus on the influence of the uncertainty of deposits, financing cost and so on, but ignored the capital risk caused by the migration of assets credit ratings in bank investment decision-making.Furthermore, in methods, the classical mean-variance model just depend on the expectation and variance to depict the uncertainty of asset future returns, which may not entirely reflect the real information of future return and risk. In stochastic programming the full and accurate distribution information of random parameter is essential. Furthermore, calculation for this kind of model is often extremely complex. Nevertheless, distributional robust optimization model does not heavily dependent on the full probability distribution, but considers a distribution family which contains all possible distribution function, avoiding the decision biasness caused by the inaccuracy of the presumed distribution of random parameter. However, the existing distributional robust chance constraint optimization methods usually needs the expectation and covariance of uncertainty parameter which neglects the fact that the complete covariance matrix of random parameter is quiet hard to gain.This study models a distributionally robust asset allocation model with the chance constraint of capital adequacy ratio, supplying a guarantee that no matter how the credit ratings migrate it can always meet the regulation with great probability. Considering that it is hard to precisely quantify the joint variation of assets'future market value, this paper adopt less but more precise information to construct the uncertainty set, avoiding biasness led by the inaccurate estimation of the covariance. In algorithm, through the Lagrangian dual method, the optimization model is converted into a tractable semi-definite programming problem. In the end, we apply the model to a hypothetical bank, and simulate numerous scenarios of loans'credit migration to test bank's capital adequacy. The results show a practical appeal.