We model how investors allocate between asset managers, managers choose their portfolios of multiple securities, fees are set, and security prices are determined. The optimal passive portfolio is linked to the “expected market portfolio,” while the optimal active portfolio has elements of...

Equity basket correlation is an important risk factor. It characterizes the strength of linear dependence between assets and thus measures the degree of portfolio diversification. It can be estimated both under the physical measure from return series, and under the risk neutral measure from...

"We present a model in which some investors are prohibited from using leverage and other investors' leverage is limited by margin requirements. The former investors bid up high-beta assets while the latter agents trade to profit from this, but must de-lever when they hit their margin...

A flexible framework for the analysis of tail events is proposed. The framework contains tail moment measures that allow for Expected Shortfall (ES) estimation. Connecting the implied tail thickness of a family of distributions with the quantile and expectile estimation, a platform for risk...

Classical asset allocation methods have assumed that the distribution of asset returns is smooth, well behaved with stable statistical moments over time. The distribution is assumed to have constant moments with e.g., Gaussian distribution that can be conveniently parameterised by the first two...

Normal distribution of the residuals is the traditional assumption in the classical multivariate time series models. Nevertheless it is not very often consistent with the real data. Copulae allows for an extension of the classical time series models to nonelliptically distributed residuals. In...

Portfolio selection and risk management are very actively studied topics in quantitative finance and applied statistics. They are closely related to the dependency structure of portfolio assets or risk factors. The correlation structure across assets and opposite tail movements are essential to...

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A...