In this article, we extend the standard paradigm for portfolio stress testing in two ways. First, we introduce a structured set of tools that enable investors to envision and administer extreme scenarios. We show how to take account of historical and hypothetical covariance matrices in scenario...

The authors extended the standard paradigm for portfolio stress testing in two ways. First, they introduced a toolkit that enables investors to envision and administer extreme scenarios. The risk model is integral to the stress test. They demonstrated the substantial impact of using historical...

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...

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...

Risk analysis involves gaining deeper insight into the sources of risk, and evaluating whether these risks accurately reflect the views of the portfolio manager. In this paper, we show how to extend standard volatility analytics to shortfall, a measure of extreme risk. Using two examples, we...

Systematic model bias has been implicated in the global recession that began in 2007, and this bias can be traced back to assumptions about the normality of data. Nonetheless, the normal distribution continues to play a foundational role in quantitative finance. One reason for this is that the...

We discuss a practical and effective extension of portfolio risk management and construction best practices to account for extreme events. The central element of the extension is (expected) shortfall, which is the expected loss given that a value-at-risk limit is breached. Shortfall is the most...