Portfolio risk forecasts are commonly evaluated using test statistics that are sums of random variables. We study the distributional properties of these test statistics for value at risk, expected shortfall, and volatility. For a diverse collection of 74 US equity portfolios, risk forecasts...

We develop a portfolio risk model that uses high-frequency data to forecast the loss surface, which is the set of loss distributions at future time horizons. Our model uses a fully automated, semi-parametric fitting procedure that has its basis in extreme value statistics. We take account of...

We examine the efficacy of the I-squared incomplete information credit model in a broad context that is relevant to fund and asset managers.Using a rigorous statistical analysis, we show that I-squared is a powerful forecaster of the following events:- Rating agency downgrades- Investment grade...

Extreme value statistics provides a practical, flexible, mathematically elegant framework in which to develop financial risk management tools that are consistent with empirical data. In this introductory survey, we discuss some of the basic tools including power law distributions, the peaks over...

We propose a multi-firm first-passage credit model in which investors have incomplete information. In this model, investors observe neither a firm's value nor its default barrier. The model accounts for the short term risk inherent in default events, the market-wide impact of defaults on...

Given a collection of single-market covariance matrix forecasts for different markets, we describe how to embed them into a global forecast of total risk.We do this by starting with any global covariance matrix forecast that contains information about cross-market correlations, and revising it...

Recent high-profile defaults of investment grade bond issuers have demonstrated the weakness of conventional ratings in rapidly changing circumstances. We propose a simple method to derive market-based ratings from spread data, and show that classifying bonds using such ratings provides a more...

We give an empirical assessment of I^2, a structural credit model based on incomplete information. In this model, investors cannot observe a firm's default barrier. As a consequence, I^2 exhibits both the economic appeal of a structural model and the tractable pricing formulae and empirical...

We present a generalization of the two sample t-test for the equality of means to the case where the sample values have unequal weights. This is a natural situation in financial risk modelling where some samples are considered more reliable than others in predicting a common mean. We describe...

The Modigliani-Miller theorem describes conditions under which the value of a firm is independent of its leverage ratio. It is one of the cornerstones of finance. A history of this result along with a modern perspective on its derivation is given in Rubinstein (2003). We extend this history by...