substantial impact of doing so. In short, the risk climate can and should be incorporated in a stress test. Second, we provide a … to a trade-off between the competing objectives of minimizing risk and maximizing return. We achieve this with a scenario …-constrained mean-variance optimization that can incorporate extreme risk and other non-Gaussian effects. We illustrate our methods in …

that enables investors to envision and administer extreme scenarios. The risk model is integral to the stress test. They …

An extended history of market returns reveals aspects of financial risk that are not evident over short timescales. The … most enduring risk measure is variance, which quantifies short-term regularities in return dispersion. An alternative … measure, shortfall, quantifies the risk of extreme market moves, and calls for a deep history to inform its forecasts. Both …

Risk analysis involves gaining deeper insight into the sources of risk, and evaluating whether these risks accurately … measure of extreme risk. Using two examples, we show how shortfall provides a more complete and intuitive picture of risk than … value at risk. In two subsequent examples we illustrate the additional perspective offered by analyzing shortfall and …

Theorems. Subsequently, we explore the gap between the normal distribution and financial risk. This can be traced to a failure …

We give an explicit algorithm and source code for extracting equity risk factors from dead (a.k.a. "flatlined" or …

We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk … factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in … quant trading with much shorter holding horizons is suboptimal: 1) longer horizon risk factors (value, growth, etc …

We discuss how to build ETF risk models. Our approach anchors on i) first building a multilevel (non …-)binary classification/taxonomy for ETFs, which is utilized in order to define the risk factors, and ii) then building the risk models based … on these risk factors by utilizing the heterotic risk model construction of https://ssrn.com/abstract=2600798 (for binary …

We discuss a practical and effective extension of portfolio risk management and construction best practices to account … value-at-risk limit is breached. Shortfall is the most basic measure of extreme risk, and unlike volatility and value at … risk, it probes the tails of portfolio return and profit/loss distributions. Consequently, shortfall is (in principle) a …

Risk-only investment strategies have been growing in popularity as traditional investment strategies have fallen short … of return targets over the last decade. However, risk-based investors should be aware of four things. First, theoretical … considerations and empirical studies show that apparently distinct risk-based investment strategies are manifestations of a single …