Adjusting covariance matrix for risk management

The covariance matrix of asset returns can change drastically and generate huge losses in portfolio value under extreme conditions such as market interventions and financial crises. Estimation of the covariance matrix under a chaotic market is often a call to action in risk management. Nowadays, stress testing has become a standard procedure for many financial institutions to estimate the capital requirement for their portfolio holdings under various stress scenarios. A possible stress scenario is to adjust the covariance matrix to mimic the situation under an underlying stress event. It is reasonable that when some covariances are altered, other covariances should vary as well. Recently, Ng et al. proposed a unified approach to determine a proper correlation matrix which reflects the subjective views of correlations. However, this approach requires matrix vectorization and hence it is not computationally efficient for high dimensional matrices. Besides, it only adjusts correlations, but it is well known that high correlations often go together with high standard deviations during a crisis period. To address these limitations, we propose a Bayesian approach to covariance matrix adjustment by incorporating subjective views of covariances. Our approach is computationally efficient and can be applied to high dimensional matrices.