Portfolio Risk Models Research Articles

How Do Hedge Funds Manage Portfolio Risk?

We investigate the determinants and effectiveness of several methods that hedge funds use to manage portfolio risk. We find that levered funds are more likely to use formal models to evaluate portfolio risk (i.e., value at risk, stress testing, and scenario analysis) and funds with higher levels of proprietary capital are more likely to have a dedicated chief risk officer who has no trading authority. With respect to effectiveness, funds in our sample that use formal models performed better in the down months of 2008 and, in general, lower exposures to systematic risk than sample funds that did not. Moreover, funds employing value at risk and stress testing had more accurate expectations of how they would perform in a short-term equity bear market. Overall, our results suggest that models of portfolio risk increase the accuracy of managers' expectations and assist managers in reducing systematic risk exposures.

Granularity Adjustment for Mark-to-Market Credit Risk Models

The impact of undiversified idiosyncratic risk on value-at-risk and expected shortfall can be approximated analytically via a methodology known as granularity adjustment (GA). In principle, the GA methodology can be applied to any risk-factor model of portfolio risk. Thus far, however, analytical results have been derived only for simple models of actuarial loss, i.e., credit loss due to default. We demonstrate that the GA is entirely tractable for single-factor versions of a large class of models that includes all the commonly used mark-to-market approaches. Our approach covers both finite ratings-based models and models with a continuum of obligor states. We apply our methodology to CreditMetrics and KMV Portfolio Manager, as these are benchmark models for the finite and continuous classes, respectively. Comparative statics of the GA with respect to model parameters in CreditMetrics reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.

Measuring the Credit Risk of Synthetic CDOs with CDS-Implied Ratings

Market price-based measures of credit risk have become commonplace in single-name risk management, but they are lacking for structured credit instruments such as CDOs. In this article, the authors demonstrate how CDS-implied ratings for corporate reference entities, together with an analytic portfolio risk model, can be used to derive CDS-implied tranche ratings for corporate synthetic CDOs (CSOs). It is an experiment in which one key variable is changed—the ratings of the portfolio of reference entities—while holding other data and model assumptions constant. The authors create two parallel rating histories for the CDO tranches, one using Moody’s corporate ratings for the reference entities and one using CDS-implied ratings for the same entities, and measure and compare how the derived tranche ratings perform. They find that CDS-implied tranche ratings lead changes in Moody’s ratings, are no more volatile than Moody’s-based ratings, more accurately rank order default losses by rating, and exhibit higher loss prediction accuracy ratios for the riskiest tranches. <b>TOPICS:</b>CLOs, CDOs, and other structured credit, credit default swaps, information providers/credit ratings

The Empirical Relation between Credit Quality, Recovery, and Correlation

The majority of industry credit portfolio risk models, as well as recent scientific results, are based on isolated modules for default probabilities and recoveries in the event of default. This paper shows that these common methods lead to various econometric drawbacks when the parameters are interpreted and aggregated for risk capital allocation and pricing purposes. This paper provides a top down approach in which individual credit risk parameters are derived analytically from a single model. This model allows for a i) dynamic, ii) consistent, and iii) unbiased modeling of credit portfolio risks. An empirical analysis provides evidence for the inferred relationship between credit quality, recovery and correlation.

Beyond Value at Risk: Forecasting Portfolio Loss at Multiple Horizons

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 distributional asymmetry, heavy tails, heteroscedasticity, and serial correlation. Loss distributions are time aggregated by taking products of characteristic functions. We test loss-surface-implied forecasts of value at risk and expected shortfall out of sample on a diverse set of portfolios and we compare our forecasts to industry-standard risk forecasts that are based on asset and factor covariance matrices. The empirical results make a compelling case for the application and further development of our approach.

Capital Allocation for Credit Portfolios with Kernel Estimators

Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.

Capital allocation for credit portfolios with kernel estimators

Determining the contributions of sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often, economic capital is measured as the Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR contributions then have to be estimated from Monte Carlo samples. In the context of a partly continuous loss distribution (i.e. continuous except for a positive point mass on zero), we investigate how to combine kernel estimation methods with importance sampling to achieve more efficient (i.e. less volatile) estimation of VaR contributions.

On the Use of Portfolio Risk Models and Capital Requirements in Emerging Markets: The Case of Argentina

A portfolio based model (Credit Risk of Credit Suisse First Boston) and recent Central Bank of Argentina credit bureau data are used to estimate whether current capital and provisioning regulations match actual risks. Arguing that provisions should cover expected losses and that capital requirements should cover potential losses beyond expected losses subject to some statistical level of tolerance, the article assesses how well actual capital and provisioning requirements match the estimated requirements given by the model. Actual provisioning requirements were found to be close to implied levels of expected losses. The estimate of potential losses was found to be highly sensitive to the assumptions of the model, especially the parameter relating the volatility of a loan's rate of default to its mean value. This volatility parameter cannot be estimated accurately with the credit bureau data because of the short time span covered, so proxy data were used to estimate it, and two values around that estimate were tried. The difficulty of estimating this critical parameter implies that the results should only be regarded as suggestive. Moreover, the methodology only does not seek to estimate credit risk and not interest rate risk or exchange rate risk, nor does it fully take into account the indirect effects of interest rates and exchange rates on credit risk. As recent events in Argentina have demonstrated, estimating credit risk along these lines should be thought of as just one tool in attempting to assess the appropriate level of bank provisions and capital.

Risk Control Techniques for Social Investing

Plan sponsors can use industry standard risk management tools to achieve more consistent and competitive results in their socially constrained mandates. Multiple-factor risk models and portfolio optimization tools are especially valuable in the management of portfolios with social constraints. Plan sponsors can apply risk management tools and concepts in at least three different ways. They can use portfolio risk models to help construct the lists of socially excluded securities; identify portfolio managers who can use optimization models and risk measurement tools to offset, at least partially, the gaps created by the exclusion of particular securities; and use manager optimization tools to build a team of managers who will have the opportunity to achieve targeted levels of value-added and active risk similar to unconstrained mandates.

Evaluating Credit Risk Models: A Critique And A Proposal (New Version)

Evaluating the quality of credit portfolio risk models is an important issue for both banks and regulators. Lopez and Saidenberg (2000) suggest cross-sectional resampling techniques in order to make efficient use of available data. We show that their proposal disregards cross-sectional dependence in resampled portfolios, which renders standard statistical inference invalid. We proceed by suggesting the Berkowitz (1999) procedure, which relies on standard likelihood ratio tests performed on transformed default data. We simulate the power of this approach in various settings including one in which the test is extended to incorporate cross-sectional information. To compare the predictive ability of alternative models, we propose to use either Bonferroni bounds or the likelihood-ratio of the two models. Monte Carlo simulations show that a default history of ten years can be sufficient to resolve uncertainties currently present in credit risk modeling.