The optimized portfolio that is calculated by a covariance matrix has large sensitivities to small eigen values of the covariance matrix. Estimation of sampling errors for small eigen values is quite important for fund managers who construct their portfolios from estimated covariance matrixes....

Bei der Kreditrisikobewertung müssen die Parameter Ausfallwahrscheinlichkeit und korrelation geschätzt werden. Diese Schätzung erfolgt unter Unsicherheit. In der Literatur werden asymptotische Konfidenzregionen diskutiert, um diese Unsicherheit bei der simultanen Schätzung beider Parameter...

The use of probability of default estimates to assess the risks of a credit portfolio should not ignore estimation uncertainty. The latter can be quantified by confidence intervals. But assumptions about dependencies of these intervals are inconsistent with assumptions of conventional credit...

This paper examines optimal portfolio selection using quantile-based risk measures such as Valueat-Risk (VaR) and Conditional Value-at-Risk (CVaR). We address the case of a singular covariance matrix of asset returns, which leads to an optimization problem with infinitely many solutions. An...

Investors often adopt mean-variance efficient portfolios for achieving superior risk-adjusted returns. However, such portfolios are sensitive to estimation errors, which affect portfolio performance. To understand the impact of estimation errors, I develop simple and intuitive formulas of the...