Factor analysis of security returns aims to decompose a return covariance matrix into systematic and specific risk components. To date, most commercially successful factor analysis has been based on fundamental models, although there is a large academic literature on statistical models. While...

Wrong way risk can be incorporated in Credit Value Adjustment (CVA) calculations in a reduced form model. Hull and White (2012) introduced a CVA model that captures wrong way risk by expressing the stochastic intensity of a counterparty's default time in terms of the financial institution's...

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...

Factor models are standards in investment management. For decades, Barra factor models have provided valuable risk forecasts and inputs for the portfolio construction process. Most uses of factor models have targeted longer horizons of months or years. However, we demonstrate in this paper 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...

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...