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...

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 reliable...

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...

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...