Sample covariance matrices tend to underestimate the risk of optimized portfolios. In this article, we identify special portfolios, termed “eigenportfolios,” that capture these systematic biases. Further, we present a methodology for estimating eigenportfolio biases and for adjusting the...

Risk analysis involves gaining deeper insight into the sources of risk, and evaluating whether these risks accurately reflect the views of the portfolio manager. In this paper, we show how to extend standard volatility analytics to shortfall, a measure of extreme risk. Using two examples, we...

The authors present an exact methodology for decomposing cross-sectional volatility into contributions from various factors. Treating country, industry, and style factors equally, they used their framework to investigate several relevant issues in the global equity markets, including the...

Measurement uncertainty is as important as measurement in metrology and industry. The GUM and its supplements provide a widely accepted framework for evaluating measurement uncertainty; but don't provide a reasonable assessment method for some special circumstances, especially for dynamic...