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...

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...

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...