We use the Barra Extreme Risk (BxR) model to analyze a US dollar-denominated corporate bond portfolio consisting of 2142 distinct issues. As in the case of equities, we find that the BxR proprietary extreme risk forecasts, xShortfall and xVaR, are higher than value-at-risk and expected-shortfall...

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...

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...

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...

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...

The principle of indifference states that events should be assigned equal probabilities if no reason can be given for regarding one event as more likely than another. This paper provides a normative argument for the principle of indifference based on a new formal model of decision under...