In the present work I derive the risk functions of 5 standard estimators for expected asset returns which are frequently advocated in the literature, viz the sample mean vector, the James-Stein and Bayes-Stein estimator, the minimum-variance estimator, and the CAPM estimator. I resolve the...

In this paper, we derive two shrinkage estimators for the global minimum variance portfolio that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of observations n ≥ d + 2 and number of assets d ≥...

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm....

We introduce a measure of diversification for portfolios comprising d risky assets. This measure relates the smallest possible return variance among these d assets to the overall portfolio return variance, yielding the portion of non-diversifiable risk. In the context of normally distributed...

In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets d =4 and number of observations n =d 2. The...

A portfolio-resampling procedure invented by Richard and Robert Michaud is the subject of a highly controversial discussion and big scientific dispute. It has been evaluated in many empirical studies and Monte Carlo experiments. Apart from the contradictory findings, the Michaud approach still...

In recent publications standard methods of random matrix theory have been applied to principal components analysis of high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory in the light of the stylized facts of empirical finance. It...

In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices...

Traditional approaches to Arbitrage Pricing Theory (APT) propose a factor model, whereas empirical applications of APT nowadays are based on seemingly unrelated regression. I drop the factor model and assume only that the market is ergodic. This enables me to apply the theory of Hilbert spaces...