Three concepts: stochastic discount factors, multi-beta pricing and mean-variance efficiency, are at the core of modern empirical asset pricing. This chapter reviews these paradigms and the relations among them, concentrating on conditional asset-pricing models where lagged variables serve as...

We introduce a methodology for dynamic modelling and forecasting of realized covariance matrices based on generalization of the heterogeneous autoregressive model (HAR) for realized volatility. Multivariate extensions of popular HAR framework leave substantial information unmodeled in residuals....

Risk decomposition is a standard tool for analyzing investment portfolio risk. The portfolio is divided into notional parts—e.g., individual securities, holdings by sector or region, factor exposures—whose contributions to net risk are estimated and reported. Convention regards the...

Ever since Harry Markowitz published his seminal paper on portfolio selection, investors have incorporated estimates of future volatilities and correlations into their asset allocation process. While portfolio construction methods continue to evolve, many investors continue to forecast...

To examine the familiar tradeoff between risk and return in financial investments, we use a rolling two-stage stochastic program to compare mean-risk optimization models with time series momentum strategies. In a backtest of allocating investment between a market index and a risk-free asset, we...

Many electricity markets exhibit an oligopolistic structure with market participants whose individual trading activities may shift prices essentially. In this context, the question of how to optimally liquidate an existing electricity futures portfolio over a fixed time horizon under the...