In the context of modern portfolio theory, we compare the out-of-sample performance of 8 investment strategies which are based on statistical methods with the out-of-sample performance of a family of trivial strategies. A wide range of approaches is considered in this work, including the...

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...

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 are derived. The presented results hold for any number of observations n = d 2 and number of assets d = 4. The...

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...

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...

Ellsberg's famous thought experiments demonstrate that most people prefer less ambiguous alternatives to more ambiguous ones. This apparently violates Savage's Sure-thing Principle. I provide a solution to Ellsberg's paradox. More precisely, I demonstrate that ambiguity aversion can be readily...

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...

Traditional portfolio optimization has often been criticized for not taking estimation risk into account. Estimation risk is mainly driven by the parameter uncertainty regarding the expected asset returns rather than their variances and covariances. The global minimum variance portfolio has been...