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.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Stress testing credit risk: The Great Depression scenario

By employing Moody’s corporate default and rating transition data spanning the last 90 years we explore how much capital banks should hold against their corporate loan portfolios to withstand historical stress scenarios. Specifically, we will focus on the worst case scenario over the observation period, the Great Depression. We find that migration risk and the length of the investment horizon are critical factors when determining bank capital needs in a crisis. We show that capital may need to rise more than three times when the horizon is increased from 1 year, as required by current and future regulation, to 3 years. Increases are still important but of a lower magnitude when migration risk is introduced in the analysis. Further, we find that the new bank capital requirements under the so-called Basel 3 agreement would enable banks to absorb Great Depression-style losses. But, such losses would dent regulatory capital considerably and far beyond the capital buffers that have been proposed to ensure that banks survive crisis periods without government support.     

Pricing options on scenario trees

We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.     

Robust animal spirits

In a real business cycle model, an agent's fear of model misspecification interacts with stochastic volatility to induce time varying worst case scenarios. These time varying worst case scenarios capture a notion of animal spirits where the probability distributions used to evaluate decision rules and price assets do not necessarily reflect the fundamental characteristics of the economy. Households entertain a pessimistic view of the world and their pessimism varies with the overall level of volatility in the economy, implying an amplification of the effects of volatility shocks. By using perturbation methods and Monte Carlo techniques we extend the class of models analyzed with robust control methods to include the sort of nonlinear production-based DSGE models that are popular in academic research and policymaking practice.     

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.     

Selecting copulas for risk management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.     

Credit conditions and recoveries from financial crises

Recoveries from recessions associated with a financial crisis tend to be sluggish. In this paper, we present evidence that stressed credit conditions are an important factor constraining the pace of recovery. In particular, using industry-level data, we find that industries relying more on external finance grow more slowly than other industries during recoveries from recessions associated with financial crises. Additional tests, based on establishment size, on alternative definitions of financial crises, and on corporate-government interest rate spreads, support the findings. Moreover, for subsets of industries where financial frictions are more severe, we find much stronger differential growth effects.     

Exchange-rate return predictability and the adaptive markets hypothesis: Evidence from major foreign exchange rates

This study examines return predictability of major foreign exchange rates by testing for martingale difference hypothesis (MDH) using daily and weekly nominal exchange rates from 1975 to 2009. We use three alternative tests for the MDH, which include the wild bootstrap automatic variance ratio test, generalized spectral test, and Dominguez–Lobato consistent tests. We evaluate time-varying return predictability by applying these tests with fixed-length moving sub-sample windows. While exchange rate returns are found to be unpredictable most of times, we do observe a number of episodes of statistically significant return predictability. They are mostly associated with the major events such as coordinated central bank interventions and financial crises. This finding suggests that return predictability of foreign exchange rates occurs from time to time depending on changing market conditions, consistent with the implications of the adaptive markets hypothesis.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

Tempered stable and tempered infinitely divisible GARCH models

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation. This model, which we refer to as the rapidly decreasing tempered stable (RDTS) GARCH model, takes into account empirical facts that have been observed for stock and index returns, such as volatility clustering, non-zero skewness, and excess kurtosis for the residual distribution. We review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, we can find the risk-neutral price process, thereby allowing application to option-pricing. We propose algorithms to generate scenarios based on GARCH models with CTS and RDTS innovations. To investigate the performance of these GARCH models, we report parameter estimates for the Dow Jones Industrial Average index and stocks included in this index. To demonstrate the advantages of the proposed model, we calculate option prices based on the index.     

Pitfalls and remedies in testing the calibration quality of rating systems

Testing calibration quality by means of backtesting is an integral part in the validation of credit rating systems. Against this background this paper provides a comprehensive overview of existing testing procedures. We study the procedures’ deficiencies theoretically and illustrate their impact empirically. Based on the insights gained therefrom, we develop enhanced hybrid testing procedures which turn out to be superior to the commonly applied methods. We also propose computationally efficient algorithms for our calibration tests. Finally, we are able to demonstrate empirically that our method outperforms existing tests in a scenario analysis using rating data of Moody’s.     

Pricing multiasset equity options: How relevant is the dependence function?

In this paper we test how different choices for the dependence function can affect the prices of a set of multiasset equity options. We conduct the analysis for various 5-dimensional baskets of UK shares, and a wide range of payoffs for the multiasset options, consistent with the instruments traded on the market. We also test the relevance of the dependence specification over both volatile and quiet market scenarios. Interestingly, we find that, in most circumstances, the choice of a dependence structure richer than the standard linear correlation does not seem to affect option prices substantially. However, the dependence function becomes more relevant in particularly volatile market conditions.     

The index fund rationality paradox

Mutual funds that track the S&P 500 are popular because they have significantly lower costs than the average, actively managed equity fund. However, a measurable number of investors select index funds with excessive fees and uncompetitive returns. We call this observation the Index Fund Rationality Paradox because it conflicts with the belief that index fund investors are making a rational, low-cost choice in their ‘type of fund’ decision. In our analysis of this paradox, we find that both retail and institutional index investors tended to make better choices in recent years, but the cost of poor choices among both groups continues to be significant. In fact, we are able to identify an arguably naïve group of retail investors that seem to be unduly influenced by brokers and financial advisors. These investors are largely responsible for the remaining paradox.     

International diversification: A copula approach

The viability of international diversification involves balancing benefits and costs. This balance hinges on the degree of asset dependence. In light of theoretical research linking diversification and dependence, we examine international diversification using two measures of dependence: correlations and copulas. We document several findings. First, dependence has increased over time. Second, we find evidence of asymmetric dependence or downside risk in Latin America, but less in the G5. The results indicate very little downside risk in East Asia. Third, East Asian and Latin American returns exhibit some correlation complexity. Interestingly, the regions with maximal dependence or worst diversification do not command large returns. Our results suggest international limits to diversification. They are also consistent with a possible tradeoff between international diversification and systemic risk.     

Forecasting the performance of hedge fund styles

This article predicts the relative performance of hedge fund investment styles using time-varying conditional stochastic dominance tests. These tests allow for the construction of dynamic trading strategies based on nonparametric density forecasts of hedge fund returns. During the recent financial turmoil, our tests predict a superior performance for the Global Macro investment style compared with the other strategies of ‘Directional Traders’. The Dedicated Short Bias investment style is stochastically dominated by the other directional styles. These results are confirmed by simple nonparametric tests constructed from realized excess returns. Further, by utilizing a cross-validation method for optimal bandwidth parameter selection, we discover the factors that have predictive power regarding the density of hedge fund returns. We observe that different factors have forecasting power for different regions of the returns distribution and, more importantly, that the Fung and Hsieh factors have power not only for describing the risk premium but also, if appropriately exploited, for density forecasting.     

Long-term bank balance sheet management: Estimation and simulation of risk-factors

We propose a dynamic framework which encompasses the main risks in balance sheets of banks in an integrated fashion. Our contributions are fourfold: (1) solving a simple one-period model that describes the optimal bank policy under credit risk; (2) estimating the long-term stochastic processes underlying the risk factors in the balance sheet, taking into account the credit and interest rate cycles; (3) simulating several scenarios for interest rates and charge-offs; and (4) describing the equations that govern the evolution of the balance sheet in the long run. The models that we use address momentum and the interaction between different rates. Our results enable simulation of bank balance sheets over time given a bank’s lending strategy and provides a basis for an optimization model to determine bank asset–liability management strategy endogenously.     

Optimal portfolios under worst-case scenarios

In standard portfolio theories such as Mean–Variance optimization, expected utility theory, rank dependent utility heory, Yaari’s dual theory and cumulative prospect theory, the worst outcomes for optimal strategies occur when the market declines (e.g. during crises), which is at odds with the needs of many investors. Hence, we depart from the traditional settings and study optimal strategies for investors who impose additional constraints on their final wealth in the states corresponding to a stressed financial market. We provide a framework that maintains the stylized features of the SP/A theory while dealing with the goal of security in a more flexible way. Preferences become state-dependent, and we assess the impact of these preferences on trading decisions. We construct optimal strategies explicitly and show how they outperform traditional diversified strategies under worst-case scenarios.     

Managing liquidity: Optimal degree of centralization

Large banking groups face the question of how to optimally allocate and generate liquidity: in a central liquidity hub or in many decentralized branches. We translate this question into a facility location problem under uncertainty. We show that volatility is the key driver behind (de-)centralization. We provide an analytical solution for the 2-branch model and show that a liquidity center can be interpreted as an option on immediate liquidity. Therefore, its value can be interpreted as the price of information, i.e., the price of knowing the exact demand. Furthermore, we derive the threshold above which it is advantageous to open a liquidity center and show that it is a function of the volatility and the characteristic of the bank network. Finally, we discuss the n-branch model for real-world banking groups (10-60 branches) and show that it can be solved with high granularity (100 scenarios) within less than 30 s.     

The credit crisis around the globe: Why did some banks perform better?

Though overall bank performance from July 2007 to December 2008 was the worst since the Great Depression, there is significant variation in the cross-section of stock returns of large banks across the world during that period. We use this variation to evaluate the importance of factors that have been put forth as having contributed to the poor performance of banks during the credit crisis. The evidence is supportive of theories that emphasize the fragility of banks financed with short-term capital market funding. The better-performing banks had less leverage and lower returns immediately before the crisis. Differences in banking regulations across countries are generally uncorrelated with the performance of banks during the crisis, except that large banks from countries with more restrictions on bank activities performed better and decreased loans less. Our evidence poses a substantial challenge to those who argue that poor bank governance was a major cause of the crisis because we find that banks with more shareholder-friendly boards performed significantly worse during the crisis than other banks, were not less risky before the crisis, and reduced loans more during the crisis.