Covariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through...

Historical VaR, CVaR and ES (Expected Shortfall) to LIQUIDATION Software is a model characterized by its straightforwardness, allowing regulators measure risk using a standard database of primitive factors and portfolio positions only, leaving little error margin in comparing market risk for...

Asset allocation strategies which utilize stop-loss and stop-gain rules may dramatically decrease risk and even increase long-term return relative to passive investing. I introduce an asset allocation strategy which shifts portfolio weights based on simplistic stop rules. The two-asset (S&P...

We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and...

We consider an investor who faces parameter uncertainty in a continuous-time financial market. We model the investor's preference by a power utility function leading to constant relative risk aversion. We show that the loss in expected utility is large when using a simple plug-in strategy for...

This paper analyses and develops insights to systematic risk and diversification when random, imperfectly dependent, losses are aggregated. Systematic risk and diversification are shown to vary across layers of component losses according to local dependence and volatility structures. Systematic...

In this work, we have found a risk model that improves the performance of Risk Targeting. Risk Targeting in portfolio construction is implemented to improve capital utilization in growing markets and systematically step away from risk scenarios. However, the performance of risk targeting varies...

In this paper, we show empirically that Active Risk Budgeting is a superior portfolio construction methodology to the tangency portfolio method postulated by Mean Variance Optimization. We compare the performance of Active Risk Budgeting and Tangency Portfolio in a series of systematic...