This paper develops a shrinkage model for portfolio choice. It places a layer on a conventional portfolio problem where the optimal portfolio is shrunk towards a reference portfolio. The model can accommodate a wide range of portfolio problems with various objectives and constraints, and its implementation is simple and straightforward. A data-driven method to determine the shrinkage level is offered. A comprehensive comparative study suggests the proposed model substantially enhances the performance of its underlying model and outperforms existing shrinkage models as well as the naïve strategy. The naïve strategy serves better as the reference portfolio than the current portfolio.

In this article, we propose an LGD model that is solely based on legal and internal debt collection actions. Our model is supported by empirical tests in which it performs better than a usual firm specific model. This result is noteworthy when we recall that the model has only binary variables that indicate whether an action was taken. Our model can be applied to update the LGD of distressed firms in a timely manner reflecting the actions taken during the debt collection period. It also can be used to assess the effect of a recovery action and to determine whether to apply an action to certain types of debt.

Employing methods of differential geometry, we propose a new framework for covariance dynamics modeling. Our approach respects the intrinsic geometric properties of the space of covariance matrices and allows their natural evolution. We develop covariance models that exploit either asset returns or realized covariances and propose a new estimation method that minimizes the length of the geodesic between the forecast and the realization. The geodesic length is equivalent to the Fisher information metric under the Gaussian assumption and is deemed a proper measure of similarity between two covariance matrices. Empirical studies involving three data samples and various performance metrics suggest that our models outperform existing ones.