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...

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...

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...

We gauge the return-generating potential of four investment strategies: value weighted, 60/40 fixed mix, unlevered and levered risk parity. We have three main findings. First, even over periods lasting decades, the start and end dates of a backtest can have a material effect on results; second,...

Since the nineteenth century investors have incorporated social or ethical values into their portfolios, an approach described over time with such labels as SRI (socially responsible investing), ESG (environmental, social, governance), or MRI (mission-related investing). Among investment...

Purpose – The purpose of this paper is to describe a generalization of the familiar two‐sample t ‐test for equality of means to the case where the sample values are to be given unequal weights. This is a natural situation in financial risk modeling when some samples are considered more...