The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given...

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...

We investigate the impact of shrinkage estimation techniques for the moments of asset returns on risk-parity portfolios. In contrast to mean-variance portfolios, the risk contributions of individual assets in risk-parity portfolios are fixed a priori. This additional restriction stabilizes...

Investors sometimes have strong convictions that a distinctive economic regime will prevail in the period ahead and therefore would like to form a portfolio that reflects the expected returns, standard deviations, and correlations of assets during such a regime. To do so, they typically isolate...

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 d + 2 and number of assets d 4. 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...

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...

Unstable fluctuations in financial markets caused by the 2008 financial crisis and currently by the Covid-19 crisis have generated greater concern among investors regarding their capital protection. In view of this situation, the consideration of alternative investments has taken a relevant...

We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP). The GMVP weights are the population coefficients of a linear regression of a benchmark return on a vector of return differences. This representation enables us to derive a consistent loss...

We propose a novel dynamic approach to forecast the weights of the global minimum variance portfolio (GMVP). The GMVP weights are the population coefficients of a linear regression of a benchmark return on a vector of return differences. This representation enables us to derive a consistent loss...