Mean-variance optimization provides a framework for constructing portfolios that have minimum risk for a given level of expected return. The required inputs are the expected asset returns, the asset covariance matrix, and a set of investment constraints. While portfolio optimization always leads...

A key to deeper understanding of factor models lies in the concept of factor-mimicking portfolios, whose returns exactly replicate the payoffs to the factors. Simple factor portfolios are obtained by considering each factor in isolation, whereas pure factor portfolios are constructed by treating...

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...

While performance analysis is typically conducted on a benchmark-relative basis, risk analysis is often presented on an absolute-return basis. This mismatch between sources of risk and return leads to the pitfall that active management decisions cannot be evaluated on a risk-adjusted basis. In...