Credit cycles and macro fundamentals

We use an intensity-based framework to study the relation between macroeconomic fundamentals and cycles in defaults and rating activity. Using Standard and Poor's U.S. corporate rating transition and default data over the period 1980–2005, we directly estimate the default and rating cycle from micro data. We relate this cycle to the business cycle, bank lending conditions, and financial market variables. In line with earlier studies, the macro variables appear to explain part of the default cycle. However, we strongly reject the correct dynamic specification of these models. The problem is solved by adding an unobserved dynamic component to the model, which can be interpreted as an omitted systematic credit risk factor. By accounting for this latent factor, many of the observed macro variables loose their significance. There are a few exceptions, but the economic impact of the observed macro variables for credit risk remains low. We also show that systematic credit risk factors differ over transition types, with risk factors for downgrades being noticeably different from those for upgrades. We conclude that portfolio credit risk models based only on observable systematic risk factors omit one of the strongest determinants of credit risk at the portfolio level. This has obvious consequences for current modeling and risk management practices.     

Firm heterogeneity and credit risk diversification

This paper examines the impact of neglected heterogeneity on credit risk. We show that neglecting heterogeneity in firm returns and/or default thresholds leads to underestimation of expected losses (EL), and its effect on portfolio risk is ambiguous. Once EL is controlled for, the impact of neglecting parameter heterogeneity is complex and depends on the source and degree of heterogeneity. We show that ignoring differences in default thresholds results in overestimation of risk, while ignoring differences in return correlations yields ambiguous results. Our empirical application, designed to be typical and representative, combines both and shows that neglected heterogeneity results in overestimation of risk. Using a portfolio of U.S. firms we illustrate that heterogeneity in the default threshold or probability of default, measured for instance by a credit rating, is of first order importance in affecting the shape of the loss distribution: including ratings heterogeneity alone results in a 20% drop in loss volatility and a 40% drop in 99.9% VaR, the level to which the risk weights of the New Basel Accord are calibrated.     

Unobserved systematic risk factor and default prediction

We conduct a thorough analysis on the role played by the unobserved systematic risk factor in default prediction. We find that this latent factor outweighs the observed systematic risk factors and can substantially improve the in-sample predictive accuracy at the firm, rating group, and aggregate levels. Thus it might be helpful to include the unobserved systematic risk factor when simulating portfolio credit losses. However, we also find that this factor only marginally improves out-of-sample model performance. Therefore, although the models we investigated all show reasonably good ability to rank order firms by default risk, accurate prediction of default rate remains challenging even when the unobserved systematic risk factor is considered.     

Validation of default probability models: A stress testing approach

This study aims to evaluate the techniques used for the validation of default probability (DP) models. By generating simulated stress data, we build ideal conditions to assess the adequacy of the metrics in different stress scenarios. In addition, we empirically analyze the evaluation metrics using the information on 30,686 delisted US public companies as a proxy of default. Using simulated data, we find that entropy based metrics such as measure M are more sensitive to changes in the characteristics of distributions of credit scores. The empirical sub-samples stress test data show that AUROC is the metric most sensitive to changes in market conditions, being followed by measure M. Our results can help risk managers to make rapid decisions regarding the validation of risk models in different scenarios.     

Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation

Consider a portfolio of n obligors subject to possible default. We propose a new structural model for the loss given default, which takes into account the severity of default. Then we study the tail behavior of the loss given default under the assumption that the losses of the n obligors jointly follow a multivariate regular variation structure. This structure provides an ideal framework for modeling both heavy tails and asymptotic dependence. Multivariate models involving Archimedean copulas and mixtures are revisited. As applications, we derive asymptotic estimates for the value at risk and conditional tail expectation of the loss given default and compare them with the traditional empirical estimates.     

A mean/variance approach to long-term fixed-income portfolio allocation

Abstract

Long-term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default spread, measuring the difference between the yield when no default occurs and the expected yield. For zero-coupon bonds and for actual market data, the default spread is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default spread. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be built following a mean/variance utility function. Straightforward computations allow us to obtain the optimal portfolio, depending on a pre-set risk-aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default spread allows us to obtain simple expressions for the value, yield and risk of the optimal portfolio.     

Do measures of systemic risk predict U.S. corporate bond default rates?

Using univariate and multivariate Mixed Data Sampling (MIDAS) and LASSO estimation methodologies, we explore whether the U.S. annual average corporate bond default rate can be predicted by 12 monthly systemic risk measures proposed in the literature. We find that nearly all of the systemic risk indicators have predictive power for the default rate. Granger causality tests based on multivariate mixed frequency VAR models further support this conclusion. On the basis of MIDAS models, we illustrate that five of these indicators are able to forecast out-of-sample the 2009 corporate default crisis. Using a LASSO multivariate model, it is further shown that the systemic risk indicators can forecast out-of-sample both the 2009 default rate and the default rates during the buildup before the crisis and in the aftermath of the crisis. Institution-specific and volatility systemic risk measures are the most relevant for modeling U.S. corporate bond default rates, with the Conditional VaR measure of Adrian and Brunnermeier (2016) exhibiting the best performance.     

Biometric Solvency Risk for Portfolios of General Life Contracts. I. The Single-Life Multiple Decrement Case

Abstract

Solvency II splits life insurance risk into seven risk classes consisting of three biometric risks (mortality risk, longevity risk, and disability/morbidity risk) and four nonbiometric risks (lapse risk, expense risk, revision risk, and catastrophe risk). The best estimate liabilities for the biometric risks are valued with biometric life tables (mortality and disability tables), while those of the nonbiometric risks require alternative valuation methods. The present study is restricted to biometric risks encountered in traditional single-life insurance contracts with multiple causes of decrement. Based on the results of quantitative impact studies, process risk was deemed to be not significant enough to warrant an explicit calculation. It was therefore assumed to be implicitly included in the systematic/parameter risk, resulting in a less complex standard formula. For the purpose of internal models and improved risk management, it appears important to capture separately or simultaneously all risk components of biometric risks. Besides its being of interest for its own sake, this leads to a better understanding of the standard approach and its application extent. Based on a total balance sheet approach we express the liability risk solvency capital of an insurance portfolio as value-at-risk and conditional value-at-risk of the prospective liability risk understood as random present value of future cash flows at a given time. The proposed approach is then applied to determine the biometric solvency capital for a portfolio of general life contracts. Using the conditional mean and variance of a portfolio’s prospective liability risk and a gamma distribution approximation we obtain simple solvency capital formulas as well as corresponding solvency capital ratios. To account for the possibility of systematic/parameter risk, we propose either to shift the biometric life tables or to apply a stochastic biometric model, which allows for random biometric rates. A numerical illustration for a cohort of immediate life annuities in arrears reveals the importance of process risk in the assessment of longevity risk solvency capital.     

Endogenizing exogenous default barrier models: The MM algorithm

In this paper, we propose a Maximization–Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm’s assets by maximizing the log-likelihood function for the time series of equity prices; Step M2 updates the default barrier by maximizing the equity holders’ participation in the firm’s asset value. The main contribution of the method lies in the M2 step, which allows for ‘endogenizing’ the default barrier in light of actual data on equity prices. Using a large international sample of companies, we demonstrate that theoretical credit spreads based on the MM algorithm offer the lowest CDS pricing errors when compared to other, traditional default barrier specifications: smooth-pasting condition value, maximum likelihood estimate, KMV’s default point, and nominal debt.     

Contagion models a la carte: which one to choose?

We propose a copula contagion mixture model for correlated default times. The model includes the well-known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the default times of the underlying names in a reference portfolio to follow contagion intensity processes with exponential decay coupled with a copula dependence structure. We also model the default time of the counterparty and its dependence structure with the reference portfolio. Numerical tests show that correlation and contagion have an enormous joint impact on the rates of CDO tranches and the corresponding credit value adjustments are extremely high to compensate for the wrong-way risk.     

International diversification and risk of multinational banks: Evidence from the pre-crisis period

The recent financial crisis has clearly shown that the relationship between bank internationalization and risk is complex. Multinational banks can benefit from portfolio diversification, reducing their overall riskiness, but this effect can be offset by incentives going in the opposite direction, leading them to take on excessive risks. Since both effects are grounded on solid theoretical arguments, the answer of what is the actual relationship between bank internationalization and risk is left to the empirical analysis. In this paper, we study such relationship in the period leading to the financial crisis of 2007–2008. For a sample of 384 listed banks from 56 countries, we calculate two measures of risk for the period from 2001 to 2007 – the expected default frequency (EDF), a market-based and forward-looking indicator, and the Z-score, a balance-sheet-based and backward-looking measure – and relate them to the degree of banks’ internationalization. We find robust evidence that international diversification increases bank risk.     

Equally weighted portfolios vs value weighted portfolios: Reasons for differing betas

We prove that constituent companies’ capital structure and tax shield cause the difference in systematic risk between an equally weighted portfolio and a value weighted portfolio in an efficient market where the CAPM holds. The difference in systematic risk has positive association with component companies’ default risk.     

Integrating market and credit risk: A simulation and optimisation perspective

We introduce a modelling paradigm which integrates credit risk and market risk in describing the random dynamical behaviour of the underlying fixed income assets. We then consider an asset and liability management (ALM) problem and develop a multistage stochastic programming model which focuses on optimum risk decisions. These models exploit the dynamical multiperiod structure of credit risk and provide insight into the corrective recourse decisions whereby issues such as the timing risk of default is appropriately taken into consideration. We also present an index tracking model in which risk is measured (and optimised) by the CVaR of the tracking portfolio in relation to the index. In-sample as well as out-of-sample (backtesting) experiments are undertaken to validate our approach. The main benefits of backtesting, that is, ex-post analysis are that (a) we gain insight into asset allocation decisions, and (b) we are able to demonstrate the feasibility and flexibility of the chosen framework.     

Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then – unlike the case of asset portfolios – take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.     

Modeling the evolution of implied CDO correlations

CDO tranche spreads (and prices of related portfolio-credit derivatives) depend on the market’s perception of the future loss distribution of the underlying credit portfolio. Applying Sklar’s seminal decomposition to the distribution of the vector of default times, the portfolio-loss distribution derived thereof is specified through individual default probabilities and the dependence among obligors’ default times. Moreover, the loss severity, specified via obligors’ recovery rates, is an additional determinant. Several (specifically univariate) credit derivatives are primarily driven by individual default probabilities, allowing investments in (or hedging against) default risk. However, there is no derivative that allows separately trading (or hedging) default correlations; all products exposed to correlation risk are contemporaneously also exposed to default risk. Moreover, the abstract notion of dependence among the names in a credit portfolio is not directly observable from traded assets. Inverting the classical Vasicek/Gauss copula model for the correlation parameter allows constructing time series of implied (compound and base) correlations. Based on such time series, it is possible to identify observable variables that describe implied correlations in terms of a regression model. This provides an economic model of the time evolution of the market’s view of the dependence structure. Different regression models are developed and investigated for the European CDO market. Applications and extensions to other markets are discussed.     

Empirical credit cycles and capital buffer formation

We model 1927–1997 US business failure rates using an unobserved components time series model. Clear evidence is found of cyclical behavior in default rates. We also detect significant longer term movements in default rates and default correlations. In a multi-year backtest experiment we show that accommodation of default rate dynamics has important consequences for credit risk capitalization requirements. Static or myopic variants of credit portfolio models miss significant periods of credit risk accumulation. Empirically congruent dynamic models by contrast provide more timely warning signals of credit risk build-up. In this way they may mitigate some of the pro-cyclicality concerns.     

Checking for asymmetric default dependence in a credit card portfolio: A copula approach

Traditional credit risk models adopt the linear correlation as a measure of dependence and assume that credit losses are normally-distributed. However some studies have shown that credit losses are seldom normal and the linear correlation does not give accurate assessment for asymmetric data. Therefore it is possible that many credit models tend to misestimate the probability of joint extreme defaults.This paper employs Copula Theory to model the dependence across default rates in a credit card portfolio of a large UK bank and to estimate the likelihood of joint high default rates. Ten copula families are used as candidates to represent the dependence structure. The empirical analysis shows that, when compared to traditional models, estimations based on asymmetric copulas usually yield results closer to the ratio of simultaneous extreme losses observed in the credit card portfolio.Copulas have been applied to evaluate the dependence among corporate debts but this research is the first paper to give evidence of the outperformance of copula estimations in portfolios of consumer loans. Moreover we test some families of copulas that are not typically considered in credit risk studies and find out that three of them are suitable for representing dependence across credit card defaults.     

Hierarchical contagions in the interdependent financial network

We derive the default cascade model and the fire-sale spillover model in a unified interdependent framework. The interactions among banks include not only direct cross-holding, but also indirect dependency by holding mutual assets outside the banking system. Using data extracted from the European Banking Authority, we present the interdependency network composed of 48 banks and 21 asset classes. For the robustness, we employ three methods, called Anan, Hała and Maxe, to reconstruct the asset/liability cross-holding network. Then we combine the external portfolio holdings of each bank to compute the interdependency matrix. The interdependency network is much denser than the direct cross-holding network, showing the complex latent interaction among banks. Finally, we perform macroprudential stress tests for the European banking system, using the adverse scenario in EBA stress test as the initial shock. For different reconstructed networks, we illustrate the hierarchical cascades and show that the failure hierarchies are roughly the same except for a few banks, reflecting the overlapping portfolio holding accounts for the majority of defaults. We also calculate systemic vulnerability and individual vulnerability, which provide important information for supervision and relevant management actions.     

Liquidity risk and stock returns around the world

The recent global financial crisis demonstrates that market liquidity is a prominent systematic risk globally. We find that local liquidity risk, in addition to the local market, value and size factors, demands a systematic premium across stocks in 11 developed markets. This local pricing premium is smaller in countries where the country-level corporate boards are more effective and where there are less insider trading activities. We also discover that global liquidity risk is a significant pricing factor across all developed country market portfolios after controlling for global market, value, and size factors. The contribution of this risk to the return on a country market portfolio is economically and statistically significant within and across regions.     

Stock market volatility spillovers and portfolio hedging: BRICS and the financial crisis

The paper investigates the dynamic risk–return properties of the BRICS (Brazil, Russia, India, China, South Africa) capital markets and models potential time-varying correlations and volatility spillover effects with the US stock market. A VAR(1)–GARCH(1,1) framework contributes useful insight into US–BRICS market interactions and expands on a thin past empirical literature. A disaggregated approach pays attention to critical US–BRICS business sectors, namely the industrial and financial sectors. Significant return and volatility transmission dynamics are identified between the US and BRICS stock markets and business sectors. This is a critical input that can affect efficient global portfolio diversification and risk management strategies. Based on this empirical evidence, the study proceeds to assess effective portfolio hedge ratios and to construct optimal portfolio weights for diversified asset allocation to US–BRICS markets and business sectors.