Demand for insurance in a portfolio setting

This paper takes an additional step toward analyzing the demand for insurance in the context of a portfolio model. An investor is endowed with a portfolio containing a risky and riskless asset that can be augmented by purchasing insurance. Here, insurance is paid for by reducing the quantity of the risky insurable asset, holding the quantity of the riskless asset fixed. In the standard insurance demand model, insurance is paid for by reducing the amount of the riskless asset. This distinction leads to a different insurance demand function because the opportunity cost of purchasing insurance is now random.     

A portfolio view of consumer credit

To compute risk-adjusted returns and gauge the volatility of their portfolios, lenders need to know the covariances of their loans’ returns with aggregate returns. We use unique credit bureau data to measure individuals’ ‘covariance risk’, i.e., the covariance of their default risk with aggregate consumer default rates, and more generally to analyze the distribution of credit, including the effects of credit scores. We find significant heterogeneity in covariance risk across consumers. Also, the amount of credit they obtain significantly increases with their credit scores, and decreases with their covariance risk (especially revolving credit), though the effect of covariance risk is smaller.     

Risk factor contributions in portfolio credit risk models

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.     

Contagion effect on bond portfolio risk measures in a hybrid credit risk model

This paper illustrates how modelling the contagion effect among assets of a given bond portfolio changes the risk perception associated to it. This empirical work is developed in a hybrid credit risk framework that incorporates recovery rate risk. Dependence structures among firms and between external shocks affecting firms together are considered. The presence of correlations among firm leverage ratios and the interrelation between default probabilities and recovery rates produces clusters of defaults with low recovery rates. This has a major impact on standard risk measures such as Value-at-Risk and conditional tail expectation. Consequently, an appropriate measurement of the contagion has a tremendous effect on the capital requirement of many financial institutions.     

Interacting particle systems for the computation of rare credit portfolio losses

In this paper, we introduce the use of interacting particle systems in the computation of probabilities of simultaneous defaults in large credit portfolios. The method can be applied to compute small historical as well as risk-neutral probabilities. It only requires that the model be based on a background Markov chain for which a simulation algorithm is available. We use the strategy developed by Del Moral and Garnier in (Ann. Appl. Probab. 15:2496–2534, 2005) for the estimation of random walk rare events probabilities. For the purpose of illustration, we consider a discrete-time version of a first passage model for default. We use a structural model with stochastic volatility, and we demonstrate the efficiency of our method in situations where importance sampling is not possible or numerically unstable.      

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.     

A semiparametric model for the systematic factors of portfolio credit risk premia

The aim of this paper is to investigate the empirical relationship between daily fluctuations in the risk premium for holding a large diversified credit portfolio, which we approximate by a benchmark credit index, and some tradeable market factors which capture systematic risk. The analysis is based on an adaptive nonparametric modelling approach which allows for the data-driven estimation of the nonlinear dynamic relationship between portfolio credit risk premia and their hypothetical components. Our main finding is that the empirical weights of the systematic factors display sudden jumps during market crises and a less intense time-dependent behaviour during normal market conditions. In addition, we find that during market crises the directions of the empirical relationships are often inconsistent with ordinary economic intuition, as they are influenced by the specific circumstances of financial markets distress.     

A simulation study of Basel II expected loss distributions for a portfolio of credit cards

Credit scoring models have been used traditionally as the basis of decisions to reject or accept credit applications. They are also used to categorize applicants or existing accounts into risk groups. Based on estimates of probability of default (PD), the risk groups may seem well separated. However, by considering distributions on risk elements such as model estimation uncertainty, exposure at default and loss given default, a simulation approach is used to compute Basel II expected loss distributions for a portfolio of credit cards. These show that discrimination between risk groups is not as clear as is immediately suggested simply by PD estimates. Based on these distributions, we also show that measuring extreme credit risk with Value at Risk can lead to considerable underestimation if distributions on these risk elements are not entered into the computation.     

From insurance risk to credit portfolio management: a new approach to pricing CDOs

We present a new approach for pricing collateralized debt obligations (CDOs) which takes into account the issue of the market incompleteness. In particular, we develop a suitable extension of the actuarial framework proposed by Bayraktar et al. [Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities. J. Econ. Dyn. Control, 2009, 33, 676–691], Milevsky et al. [Financial valuation of mortality risk via the instantaneous Sharpe-ratio: Applications to pricing pure endowments. Working Paper, 2007. Available at: http://arxiv.org/abs/0705.1302], Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio: Theorems and proofs. Technical Report, 2007. Available at: http://arxiv.org/abs/0705.1297] and Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio. Insurance: Math. Econ., 2008, 42, 691–703], which is based on the so-called instantaneous Sharpe ratio. Such a procedure allows us to incorporate the attitude of investors towards risk in a direct and rational way and, in addition, is also suitable for dealing with the often illiquid CDO market. Numerical experiments are presented which reveal that the market incompleteness can have a strong effect on the pricing of CDOs, and allows us to explain the high bid-ask spreads that are frequently observed in the markets.     

A systematic approach to multi-period stress testing of portfolio credit risk

We propose a new method for analysing multi-period stress scenarios for portfolio credit risk more systematically than in current macro stress tests. The plausibility of a scenario is quantified by its distance from an average scenario. For a given level of plausibility, we search systematically for the most adverse scenario. This ensures that no plausible scenario will be missed. We show how this method can be applied to some models already in use by practitioners. While worst case search requires numerical optimisation we show that we can work with reasonably good linear approximations to the portfolio loss function. This makes systematic multi-period stress testing computationally efficient and easy to implement. Applying our approach to data from the Spanish loan register we show that, compared to standard stress test procedures, our method identifies more harmful scenarios that are equally plausible.     

Bayesian inference for generalized linear mixed models of portfolio credit risk

The aims of this paper are threefold. First, we highlight the usefulness of generalized linear mixed models (GLMMs) in the modelling of portfolio credit default risk. The GLMM-setting allows for a flexible specification of the systematic portfolio risk in terms of observed fixed effects and unobserved random effects, in order to explain the phenomena of default dependence and time-inhomogeneity in historical default data. Second, we show that computational Bayesian techniques such as the Gibbs sampler can be successfully applied to fit models with serially correlated random effects, which are special instances of state space models. Third, we provide an empirical study using Standard and Poor's data on U.S. firms. A model incorporating rating category and sector effects, and a macroeconomic proxy variable for state-of-the-economy suggests the presence of a residual, cyclical, latent component in the systematic risk.     

The impact of credit rating announcements on credit default swap spreads

We document the ability of the credit default swap (CDS) market to anticipate favorable as well as unfavorable credit rating change (RC) announcements based on more extensive samples of credit rating events and CDS spreads than previous studies. We obtain four new results. In contrast to prior published studies, we find that corporate RC upgrades do have a significant impact on CDS spreads even though they are still not as well anticipated as downgrades. Second, CreditWatch (CW) and Outlook (OL) announcements, after controlling for prior credit rating events, lead to significant CARs at the time positive CW and OL credit rating events are announced. Third, we extend prior results by showing that changes in CDS spreads for non-investment-grade credits contain information useful for estimating the probability of negative credit rating events. Fourth, we find that the CDS spread impact of upgrades but not downgrades is magnified during recessions and that upgrades and downgrades also differ as to the impact of simultaneous CW/OL announcements, investment-grade/speculative-grade crossovers, current credit rating, market volatility, and industry effects.     

The implications of the new capital adequacy rules for portfolio management of credit assets

Over the past several years, there has been an extensive discussion among practitioners and academics about whether and how a portfolio management approach could help banks to better manage risk capital and create shareholder value. In this article, the authors argue that there are four key drivers which require banks to move from a transactional to a more portfolio management like approach when managing credit assets. These are: structural changes in the credit markets, inefficiencies of risk transfer in lending markets, ballooning debt levels in the US, and the proposed changes for capital adequacy. The authors see the latter not as a one-time change in capital adequacy rules, but more as a first step towards full convergence between risk capital and regulatory capital for credit risk. These changes require banks to accelerate their efforts to build first class portfolio management skills and capabilities. Achieving best practice credit portfolio management is rewarded with attractive opportunities for shareholder value creation and enables bank to successfully compete going forward.     

The effect of sovereign wealth funds on the credit risk of their portfolio companies

We study how sovereign wealth fund (SWF) investments affect the credit risk of target companies as measured by the change in their credit default swap (CDS) spreads around the investment announcement. We find that the CDS spread of target companies decreases, on average, following an SWF investment. The reduction in the CDS spread is higher when the SWF is established by a politically stable non-democratic country that has a neutral political relationship with the host country of the target company. Our results suggest that creditors expect SWFs to protect target companies from bankruptcy when it is in the interest of their home country to build political goodwill in the host country of the company.     

Bayesian inference for issuer heterogeneity in credit ratings migration

Rating transition matrices for corporate bond issuers are often based on fitting a discrete time Markov chain model to homogeneous cohorts. Literature has documented that rating migration matrices can differ considerably depending on the characteristics of the issuers in the pool used for estimation. However, it is also well known in the literature that a continuous time Markov chain gives statistically superior estimates of the rating migration process. It remains to verify and quantify the issuer heterogeneity in rating migration behavior using a continuous time Markov chain. We fill this gap in the literature. We provide Bayesian estimates to mitigate the problem of data sparsity. Default data, especially when narrowing down to issuers with specific characteristics, can be highly sparse. Using classical estimation tools in such a situation can result in large estimation errors. Hence we adopt Bayesian estimation techniques. We apply them to the Moodys corporate bond default database. Our results indicate strong country and industry effects on the determination of rating migration behavior. Using the CreditRisk+ framework, and a sample credit portfolio, we show that ignoring issuer heterogeneity can give erroneous estimates of Value-at-Risk and a misleading picture of the risk capital. This insight is consistent with some recent findings in the literature. Therefore, given the upcoming Basel II implementation, understanding issuer heterogeneity has important policy implications.     

ESG in credit ratings and the impact on financial markets

This study examines environment, social, governance (ESG) consideration in rating reports published by credit rating agencies. 3,719 Moody's credit rating reports between 2004 and 2015 are examined and the ESG consideration is analyzed using a latent dirichlet allocation (LDA) approach. We further analyze the stock returns and credit default swap (CDS) spread changes to check whether ESG consideration has an effect on the capital market reactions. We find a small but present consideration of ESG in rating decisions. Within ESG, corporate governance plays the most important role. Moreover, the results reveal that ESG consideration is a significant determinant in the stock return and CDS spread around the rating announcement. We find that all ESG criteria are important for equity and debt investors.     

Evaluating the impact of macroprudential policies on credit growth in Colombia

The purpose of this paper is to evaluate the effectiveness of two macroprudential policies in Colombia: marginal reserve requirements and dynamic provisions. The first measure was implemented to control excessive credit growth, while the latter was designed to increase systemic resilience by establishing a countercyclical buffer through loan loss provision requirements. To perform this analysis, a rich dataset based on loan-by-loan information for Colombian banks during the 2006–2009 period is used. Our identification strategy closely follows Khwaja & Mian (2008), so that only those observations with multiple banking relations are considered. Estimations are performed applying firm and firm-time fixed effects to control for demand factors, thus appropriately isolating loan demand from credit supply. Results from the econometric model suggest that dynamic provisions, the countercyclical reserve requirement and an aggregate measure of the macroprudential policy stance had a negative effect on credit growth, which varies according to bank and debtor-specific characteristics. Particularly, effects are intensified for riskier debtors, suggesting that the aggregate macroprudential policy stance in Colombia has worked effectively to stabilize credit cycles and reduce risk-taking.     

Measurement,estimation and comparison of credit migration matrices

Credit migration matrices are cardinal inputs to many risk management applications; their accurate estimation is therefore critical. We explore two approaches: cohort and two variants of duration – one imposing, the other relaxing time homogeneity – and the resulting differences, both statistically through matrix norms and economically using a credit portfolio model. We propose a new metric for comparing these matrices based on singular values and apply it to credit rating histories of S&P rated US firms from 1981–2002. We show that the migration matrices have been increasing in “size” since the mid-1990s, with 2002 being the “largest” in the sense of being the most dynamic. We develop a testing procedure using bootstrap techniques to assess statistically the differences between migration matrices as represented by our metric. We demonstrate that it can matter substantially which estimation method is chosen: economic credit risk capital differences implied by different estimation techniques can be as large as differences between economic regimes, recession vs. expansion. Ignoring the efficiency gain inherent in the duration methods by using the cohort method instead is more damaging than imposing a (possibly false) assumption of time homogeneity.     

The impact of securitization on the expansion of subprime credit

This paper investigates the relationship between securitization activity and the extension of subprime credit. The analysis is motivated by two sets of compelling empirical facts. First, the origination of subprime mortgages exploded between the years 2003 and 2005. Second, the securitization of subprime loans increased substantially over the same time period, driven primarily by the five largest independent broker/dealer investment banks. We argue that the relative shift in the securitization activity of investment banks was driven by forces exogenous to factors impacting lending decisions in the primary mortgage market and resulted in lower ZIP code denial rates, higher subprime origination rates, and higher subsequent default rates. Consistent with recent findings in the literature, we provide evidence that the increased securitization activity of investment banks reduced lenders' incentives to carefully screen borrowers.