We present a simple and powerful approach to create meaningful stress scenarios for risk management and investment analysis of multi-asset portfolios, which effectively combines economic forecasts and ‘expert’ views with portfolio simulation methods. Expert scenarios are typically described in terms of a small number of key economic variables or factors. However, when applied to a portfolio, they are incomplete — they generally do not describe what occurs to all relevant market risk factors that affect the portfolio. We need to understand how these market risk factors behave, conditional on the outcome of the economic factors. The key insight to our approach is that the conditional expectation, and more generally the full conditional distribution of all the factors, and of the portfolio profit and loss (P&L), can be estimated directly from a pre-computed simulation using least squares regression. We refer to this approach as least squares stress testing (LSST). LSST is a simulation-based conditional scenario generation method that offers many advantages over more traditional analytical methods. Simulation techniques are simple, flexible and provide very transparent results, which are auditable and easy to explain. LSST can be applied to both market and credit risk stress testing with a large number of risk factors, which can follow completely general stochastic processes, with fat-tails, non-parametric and general co-dependence structures, autocorrelation, etc. LSST further produces explicit risk factor P&L contributions. We demonstrate the methodology in detail with the practical example of a multi-asset investment portfolio and economic scenarios from an industry report.

We address the problem of allocating the counterparty-level credit valuation adjustment (CVA) to the individual trades composing the portfolio. We show that this problem can be reduced to calculating contributions of the trades to the counterparty-level expected exposure (EE) conditional on the counterparty's default. We propose a methodology for calculating conditional EE contributions for both collateralized and non-collateralized counterparties. Calculation of EE contributions can be easily incorporated into exposure simulation processes that already exist in a financial institution. We also derive closed-form expressions for EE contributions under the assumption that trade values are normally distributed. Analytical results are obtained for the case when the trade values and the counterparty's credit quality are independent as well as when there is a dependence between them (wrong-way risk).

We address the problem of allocating counterparty-level credit valuation adjustment to individual trades comprising a portfolio. We show that this problem can be reduced to calculating contributions of the trades to the counterparty-level expected exposure (EE) conditional on the counterparty's default. We propose a methodology for calculating conditional EE contributions for both collateralized and non-collateralized counterparties. The calculation of EE contributions can be easily incorporated into exposure simulation processes that already exist in a financial institution. We also derive closed-form expressions for EE contributions under the assumption that trade values are normally distributed. Analytical results are obtained for the case when the trade values and the counterparty's credit quality are independent and the case when there is a dependence between them (wrong-way risk).

Determining contributions to overall portfolio risk is an important topic in risk management. For positions (instruments and sub-portfolios), this problem has been well studied, and a significant theory built, around the calculation of marginal contributions. We consider the problem of determining the contributions to portfolio risk of risk factors. This cannot be addressed through an immediate extension of techniques for position contributions, since the portfolio loss is a nonlinear function of the risk factors. We employ the Hoeffding decomposition of the portfolio loss into a sum of terms depending on the factors. This decomposition restores linearity, but includes terms arising from joint effects of groups of factors. These cross-factor terms provide information to risk managers, since they can be viewed as best hedges of the portfolio loss involving instruments of increasing complexity. We illustrate the technique on multi-factor portfolio credit risk models, where systematic factors represent industries, geographical sectors, etc.

The current financial crisis has highlighted the need for transparent and robust methods for valuing and hedging structured credit portfolios. First-generation models such as Gaussian copula-based methods have documented practical and theoretical limitations well. In this paper we demonstrate the practical application of the weighted Monte Carlo methodology for valuing and computing sensitivities and risk statistics for collateralized loan obligation (CLO) portfolios and CLOsquared structures. The model extends the full bottom-up approach of Rosen and Saunders for pricing bespoke collateralized debt obligations to include cancelability and stochastic losses given default in a natural way. The performance of the model is analyzed across a three-month period in 2008 during the credit crisis. The model calibrates very well to observed prices for the CDX.HY and LCDX indices, and provides stable implied distributions for the systematic factor. Furthermore, it gives robust, consistent prices and sensitivities for CLOs and CLO-squared transactions, even during this very volatile period.

One of the critical issues in the Basel II internal ratings based method for counterparty credit risk (CCR) is the calculation of exposure at default, which requires estimation of a parameter called the alpha multiplier A major challenge in calculating the alpha multiplier is the modeling of wrong way risk (ie, correlation between exposures and defaults in a credit portfolio). We present a computationally efficient approach to modeling wrong way risk and estimating CCR capital and alpha. The methodology fully leverages existing counterparty exposure simulations used for risk management and credit limits, and preserves the joint distribution of counterparty exposures. Although the methodology can be applied with general integrated market-credit risk models, we show that a simplified model to correlate directly the (precomputed) exposures with credit events leads to a parsimonious, computationally tractable approach, which is easy to implement and consistent with the Basel II definition and credit portfolio model. To assess the impact of wrong way risk and for regulatory applications, alpha is defined and plotted as a function of the correlation between exposures and defaults. This leads to an intuitive numerical solution for the inverse problem of finding the level of market-credit correlation that hits the regulatory floor of 1.2. Several market factors driving counterparty exposures can also be considered to stress the market-credit dependence structure. An analysis of a realistic trading book is used to demonstrate the methodology and its application within the regulatory framework.

This paper presents a robust and practical collateralized debt obligation (CDO) valuation framework based oil the application of multi-factor credit models in conjunction with weighted Monte Carlo techniques used in options pricing. The genera factor framework produces arbitrage-free prices and call be used to value consistently CDOs of bespoke portfolios, CDO-squared and cash CDOs. The quoted prices of individual name credit default swaps as well as various credit portfolio instruments, such as CDO tranches, are used to imply the "risk-neutral" distributions for the underlying systematic risk factors, which drive joint obligor defaults. We solve numerically the inverse problem of implying the factors' joint distribution, defined over a discrete set of scenarios oil the factors. Multi-factor models allow the inclusion of sector and geographical concentrations, deals that refer simultaneously to multiple indexes and potentially other risk factors such as recoveries and prepayments. We describe various numerical techniques for effectively sampling factor scenarios and obtaining well-behaved implied factor distributions, and illustrate the use of the method oil several bespoke synthetic deals.

Multi-factor credit portfolio models are used widely today for managing economic capital and pricing collateralized debt obligations (CDOs) and asset-backed securities. Commonly, practitioners allocate capital to the portfolio components (sub-portfolios, counterparties, or transactions). The hedging of credit risk is generally also focused on the ‘deltas’ of underlying names. We present analytical results for hedging portfolio credit risk with linear combinations of systematic factors, based on the minimization of systematic variance of portfolio losses. We solve these problems within a multi-factor Merton-type credit portfolio model, and apply them to hedge systematic credit default losses of loan portfolios and CDOs.

Economic capital (EC) acts as a buffer for financial institutions to absorb large unexpected losses, thereby protecting depositors and other claim holders and providing confidence to external investors and rating agencies on the financial health of the firm. Once the amount of capital has been determined, it must be allocated equitably among the various components of a portfolio (e.g., activities, business units, obligors or individual transactions). Capital allocation is an important management decision support and business planning tool, required for pricing, profitability assessment and limits, building optimal risk-return portfolios and strategies, performance measurement and risk based compensation.This chapter provides a practical overview of the measurement of economic credit capital contributions and their application to capital allocation. We discuss the advantages and disadvantages of various risk measures and models, the interpretation of various allocation strategies as well as the numerical issues associated with this task. We stress four key points. First, marginal risk contributions provide a useful basis for allocating EC since they are additive and reflect the benefits of diversification within a portfolio. Second, the choice of the risk measure can have a substantial impact on capital allocation. In particular, Value at Risk (VaR) and expected shortfall (ES) contributions avoid the inconsistencies, and potentially inefficient allocations, associated with the widely-used volatility-based methods. The quantile level chosen for measuring risk can also have a significant impact on the relative amount of capital allocated to portfolio components. Third, VaR and ES contributions can be calculated analytically under certain simple models. These methods provide fast calculations and can be used to understand capital allocation strategies better, but they present important practical limitations, as well. Finally, Monte Carlo methods may be required to compute risk contributions in more realistic credit models. Computing VaR and ES contributions is challenging, especially at the extreme quantiles typically used for credit capital definition. The quality of contribution estimates can be improved by exploiting the conditional independence framework underlying the most common models, through the use of more sophisticated quantile estimators (especially for VaR) and through the use of variance reduction techniques, such as Importance Sampling.

Publisher Summary This chapter defines enterprise risk management (ERM), describes a conceptual framework for an ERM strategy, and touches upon organizational issues. Asset and liability management (ALM) is then identified as a core activity of ERM for financial institutions. It discusses ALM for various financial institutions, and provides an overview of tools to support ALM activities. Enterprise risk management aligns a firm's business strategy with the risk factors of its environment in pursuit of business objectives. It is considered a well-grounded management strategy for corporations. The management of assets and liabilities is at the core of ERM for financial institutions. In this chapter, we discuss the general framework for ERM, and the role of ALM within this broader strategy. From the general concepts, we proceed to focus on specific financial institutions, and conclude with a discussion of modelling issues that arise in the enterprise-wide management of assets and liabilities.

We present a simple adjustment to the single-factor credit capital model, which recognizes the diversification from a multifactor model. We introduce the concept of a diversification factor at the portfolio level, and show that it can be expressed as a function of two parameters that broadly capture the sector concentration and the average cross-sector correlation. The model further supports an intuitive capital allocation methodology through the definition of marginal diversification factors at the sector or obligor level. We estimate the diversification factor for a family of models, and show that it can be expressed in parametric form or tabulated for potential regulatory applications and risk management. As a risk management tool, it can be used to understand concentration risk, capital allocation and sensitivities, stress testing, as well as to compute "real-time" marginal risk.

27.1 IntroductionFinancial institutions worldwide have devoted much effort to developing systems that integrate information across their organizations to measure, monitor, and manage risk on an enterprise-wide basis. Beyond simply measuring risk, an effective risk management function first must help the firm to understand the sources of its exposures and to identify the major risk contributors. Second, it should indicate how changes in external (i.e., market) risk factors or in the portfolio itself (i.e., potential trades) affect the firm's risk. Finally, it must provide the means to optimally trade off risk and reward, both within and across various business lines.Risk management requires tools that construct a comprehensive picture of all types of risk faced by the firm and that permit the effective utilization of the wealth of financial products available in the markets to obtain the desired risk and reward profiles. A risk manager's toolkit includes risk analytics that decompose the overall portfolio risk, explain the effects of new trades, and identify potential hedges for individual instruments, as well as mathematical programming models that allow portfolios to be optimally restructured.The most widely used risk management tools extend the insights originally developed in [29] and [43] in modern portfolio theory. Thus, they assume that the underlying risk factor changes follow a joint normal (or, more generally, elliptic) distribution and that the asset values depend linearly on these risk factors. Essentially, this takes the implicit view that the variance (or standard deviation) of the portfolio's losses is an appropriate measure of risk.

This paper examines a new approach for credit risk optimization. The model is based on the Conditional Value-at-Risk (CVaR) risk measure, the expected loss exceeding Value-at-Risk. CVaR is also known as Mean Excess, Mean Shortfall, or Tail VaR. This model can simultaneously adjust all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints. The credit risk distribution is generated by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. The algorithm is very efficient; it can handle hundreds of instruments and thousands of scenarios in reasonable computer time. The approach is demonstrated with a portfolio of emerging market bonds.

In recent years, several methodologies for measuring portfolio credit risk have been introduced that demonstrate the benefits of using internal models to measure credit risk in the loan book. These models measure economic credit capital and are specifically designed to capture portfolio effects and account for obligor default correlations. An example of an integrated market and credit risk model that overcomes this limitation is given in Iscoe et al. [1999], which is equally applicable to commercial and retail credit portfolios. However, the measurement of portfolio credit risk in retail loan portfolios has received much less attention than the commercial credit markets. This article proposes a methodology for measuring the credit risk of a retail portfolio, based on the general portfolio credit risk framework of Iscoe et al. The authors discuss the practical estimation and implementation of the model. They demonstrate its applicability with a case study based on the credit card portfolio of a North American financial institution. They also analyze the sensitivity of the results to various assumptions.