Managing surplus risk enables pension plans and endowments to align their asset allocations with their future obligations. BarraOne’s Correlation Risk Decomposition enables investors to identify the drivers of surplus risk, and to analyze the potentially subtle impact of specific hedges. In this case study, a term structure hedge using an interest rate swap substantially lowers surplus risk as expected. However, a credit hedge using a default swap elevates surplus risk. 

New currencies will emerge if the European Economic and Monetary Union (EMU) ruptures. Hypothetical forward rates are candidate proxies for exchange rates of new EMU currencies against the US dollar. The hypothetical forwards are generated by a formal application of covered interest rate parity to the euro/US dollar spot exchange rate and EMU sovereign interest rates.

In this paper, we present a daily factor model that forecasts daily volatility of variance for VIX Futures Contracts.

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 construction, and we provide examples that demonstrate the substantial impact of doing so. In short, the risk climate can and should be incorporated in a stress test. Second, we provide a means to...

This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance over minimizing variance, especially during down-markets, over the period 1985-2010. The outperformance of shortfall is due to intuitive tilts towards protective factors like...

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 show how shortfall provides a more complete and intuitive picture of risk than value at risk. In two subsequent examples we illustrate the additional perspective offered by analyzing shortfall and...

Extreme events are an important source of financial risk, but they present special challenges in quantitative forecasting.  In this paper we describe an empirical approach to forecasting extreme risk and evaluate its accuracy out-of-sample on a range of factor-based strategies and pair trades.  Our results show that for a large majority of strategies, our model is more consistent with market behavior than a conditional Normal model.

From the inception of the recent financial crisis in July 2007 to the turnaround in March 2009, the MSCI UK Value Investable Market Index (MSCI UK Value IMI) lost roughly 65% of its value, and then recovered half its losses during the remainder of 2009. In this Research Insight, we use the Barra Extreme Risk (BxR) model to understand the relationship between multi-faceted risk analysis and performance of the index.

Intensity based models of the portfolio loss process that are specified without reference to the portfolio constituents lead to tractable credit derivatives valuation formulae and accurate tranche market calibrations. We show how to complement these models with random thinning, which decomposes the portfolio loss process into single name loss processes. Random thinning facilitates consistent pricing and calibration of single- and multi-name securities and estimation of single name hedges.

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 moves, and calls for a deep history to inform its forecasts. Both variance and shortfall are convex, meaning that they tend to promote diversification and can be used in optimization. By offering a...

A portfolio credit derivative is a contingent claim on the aggregate loss of a portfolio of credit sensitive securities such as bonds and credit swaps. We propose an affine point process as a dynamic model of portfolio loss. The recovery at each default is random and events are governed by an intensity that is driven by affine jump diffusion risk factors. The portfolio loss itself is a risk factor so past defaults and their recoveries influence future loss dynamics. This specification...

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 normal often emerges, without prompting, as the distribution of sums or averages of large collections of random variables. Precise statements of this miracle are known as Central Limit Theorems, and...

Quantitative risk management relies on a constellation of tools that are used to analyze portfolio risk. We develop the standard toolkit, which includes betas, risk budgets and correlations, in a general, coherent, mnemonic framework centered around marginal risk contributions. We apply these tools to generate side-by-side analyses of volatility and expected shortfall, which is a measure of average portfolio excess of value-at-risk. We focus on two examples whose importance is highlighted by...

The credit risk premium is empirically documented to be a significant component of credit spreads. However, its determinants are not fully understood. We offer a structural model of the credit risk premium in which investors have incomplete information about a firm's default barrier. The premium has two components. One is standard and accounts for investors' aversion towards price volatility that is due to the diffusive fluctuation of the firm value. The other is an event premium...

We assess the effectiveness of the Barra Default Probability (BDP) model in explaining the cross-sectional variation of Credit Default Spreads. In order to establish the usefulness of the BDP model in forecasting real-world defaults, we test it against historical default experience. We find that the model shows good default discriminatory power relative to agency ratings.

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), Journal of Investment Management 1(2).  We extend this history by examining the relationship between the Modigliani-Miller theorem and quantitative models of creditrisk.  In the first part of the paper, we...

In our structural credit model based on incomplete information, investors cannot observe a firm's default barrier.  As a consequence, such a model has both the economic appeal of a structural model and the tractable pricing formulas and empirical plausibility of a reduced-form model.  A comparison of default probability and credit spread forecasts generated by this model and two well-known structural models indicates that it reacts more quickly to new information and, unlike the...

Most investment decisions are based on incomplete information.  This disquieting fact, whose origins range from the complex nature of our economic environment to sneaky corporate practices, flies in the face of the assumptions that underlie many credit models.  Nevertheless, a framework to model credit in the context of incomplete information is of surprisingly recent vintage - see for example, Duffie & Lando (2001), Giesecke (2001) and Cetin et al (2002).  There are two...

In recent years, the growth of the global credit market has been spectacular. From an investor perspective, this has created many new opportunities for higher returns and diversification, but a careful management of risk is more necessary than ever. In this context, measures of credit quality are becoming an increasingly important reference. Agency ratings are a standard measure of credit quality. The question of capital requirements and the recent collapse of several high-profile large...

We develop a structural model of default risk that incorporates the short-term uncertainty inherent in default events. It is based on the assumption of incomplete information: We take as a premise that bond investors are not certain about the true level of firm value that will trigger default. The coherent integration of structure and uncertainty is facilitated with compensators. Compensators form the infrastructure of a class of credit models that is broad enough to include traditional...

In recent years, the growth of the global credit market has been spectacular. From an investor perspective, this has created many new opportunities for higher returns and diversification, but a careful management of risk is more necessary than ever. In this context, measures of credit quality are becoming an increasingly important reference. Agency ratings are a standard measure of credit quality. The question of capital  requirements and the recent collapse of several high-profile large...

A global model that forecasts risk for portfolios with holdings across several markets will typically disagree with the predictions of a model specifically adapted to a single market. Given a global model and a collection of single market models, we describe an optimal, consistent way to embed the single market forecasts into the global model. The method involves framing the problem as an optimization over the ortogonal group O(n).