Asset Correlation Research Articles

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

We review recent progress in modeling credit risk for correlated assets. We employ a new interpretation of the Wishart model for random correlation matrices to model non-stationary effects. We then use the Merton model in which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used, the correlations of which have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary, which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results, which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model.

DCC-GARCH Application in Formulating Dynamic Portfolio between Stocks in the Indonesia Stock Exchange with Gold

T his study tries to form a portfolio by using a method which may accommodate the dynamic of assets correlation and the abnormality of stock return distribution namely DCC-GARCH. Th e objective of th is study is to combine individual stocks with gold, so retail investor can also apply this method. This study us ing data from January 200 9 –December 201 7 period. Samples in this study were nine stocks. The results of this study showed that there were two stocks with higher Sharpe Ratio if combined with gold through dynamic portfolio formation (hedged portfolio) namely BBCA -Gold and SMCB -Gold than unhedged portfolio . And there are three stocks with higher Treynor Ratio if combined with gold through dynamic portfolio formation (hedged portfolio) namely BBCA -Gold , SMCB -Gold and UNTR-Gold than unhedged portfolio . This finding proves that the DCC-GARCH application can improve the risk-adjusted return of these stocks when combined with gold.

On the cyclicality of default rates of banks: A comparative study of the asset correlation and diversification effects

Abstract In credit portfolio modeling the asset correlation parameter is used to describe the degree of default rates fluctuations. In this article we estimate the asset correlation parameter for banks and other industry sectors from default data. We find that estimates of the asset correlation vary substantially among the different segments and that banks exhibit a much larger asset correlation parameter, larger also than the regulatory value of the Basel Accord. For pooled data the asset correlation parameter shrinks due to diversification effects.

Fractional Wishart processes and [formula omitted]-fractional Wishart processes with applications

In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and ε-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend ε-fractional Wishart processes to the case with non-integer indices. Both processes include classic Wishart processes (if the Hurst index H equals 12) and present serial correlation of stochastic processes. Applying ε-fractional Wishart processes to financial volatility theory, the financial models account for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets’ returns but also between their volatilities and for stochastic serial correlation of the relevant assets.

Capital Regulation, Bailout and Banking Asset Correlation

AbstractWe study the effect of capital regulation on banking asset correlation. Banks are more efficient users of banking assets. This implies that it may be ex post optimal to bail out a failed bank. We show, under Basel 1 capital regulation, that the financial regulator is committed to a mixed bailout strategy in the state of systemic failure, which reduces banks’ incentive to choose highly correlated assets. The mixed strategy is not creditable under mark‐to‐market capital regulation. In the subgame perfect equilibrium, banking asset correlation increases, resulting in a high probability of systemic failure. We then discuss social losses under different capital regulations.

An Analysis of Cryptocurrencies Conditional Cross Correlations

This letter explores the behavior of conditional correlations among main cryptocurrencies, stock and bond indices, and gold, using a generalized DCC class model. From a portfolio management point of view, asset correlation is a key metric in order to construct efficient portfolios. We find that: (i) correlations among cryptocurrencies are positive, albeit varying across time; (ii) correlations with Monero are more stable across time; (iii) correlations between cryptocurrencies and traditional financial assets are negligible.

Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations

We review recent progress in modeling credit risk for correlated assets. We start from the Merton model which default events and losses are derived from the asset values at maturity. To estimate the time development of the asset values, the stock prices are used whose correlations have a strong impact on the loss distribution, particularly on its tails. These correlations are non-stationary which also influences the tails. We account for the asset fluctuations by averaging over an ensemble of random matrices that models the truly existing set of measured correlation matrices. As a most welcome side effect, this approach drastically reduces the parameter dependence of the loss distribution, allowing us to obtain very explicit results which show quantitatively that the heavy tails prevail over diversification benefits even for small correlations. We calibrate our random matrix model with market data and show how it is capable of grasping different market situations. Furthermore, we present numerical simulations for concurrent portfolio risks, i.e., for the joint probability densities of losses for two portfolios. For the convenience of the reader, we give an introduction to the Wishart random matrix model.

Numerical comparison of multivariate models to forecasting risk measures

We evaluated the performance of multivariate models for forecasting Value at Risk (VaR), Expected Shortfall (ES), and Expectile Value at Risk (EvaR). We used Historical Simulation (HS), Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedastic (DCC-GARCH) and copula methods: Regular copulas, Vine copulas, and Nested Archimedean copulas (NAC). We assessed the performance of the models using Monte Carlo simulations, considering different scenarios, regarding the marginal distributions, correlation, and number of portfolio assets. Numerical results evidenced the accuracy forecasting risk measures are associated with marginal distributions. For a data-generating process where the marginal distribution is Gaussian, Regular and Vine copulas demonstrated better performance. For data generated with Student’s t distribution, we verified better performance by NAC. In addition, we identified the superiority of copula methods over HS and DCC-GARCH, which reduces the model risk.

The Adequate Verification on Implication of the Asset Correlation of Commercial Bank Retail Portfolio using BIS II and CreditMetrics Method of OFM

The Adequate Verification on Implication of the Asset Correlation of Commercial Bank Retail Portfolio using BIS II and CreditMetrics Method of OFM

A Theoretical and Empirical Analysis of Alternative Discount Rate Concepts for Computing LGDs Using Historical Bank Workout Data

The paper summarizes the discussions of the Global Credit Data (GCD) Discount Rate Work Group (WG). The WG does not provide a “correct” number for the discount rate but derives guiding principles for Loss rate Given Default (LGD) discount rate approaches. The WG has analyzed five main discount rate approaches: 1) Contract rate at origination (Contract): contractual interest rate of a loan, which is the combination of a base rate plus a risk premium at loan origination; 2) Loan weighted average cost of capital (WACC): bank funding costs, which is the combination of the capital ratio weighted cost of equity funding and the debt ratio weighted cost of debt funding. The capital ratio may be based on the loan‐specific regulatory capital requirement; 3) Return on equity (ROE): cost of equity funding; 4) Market return on defaulted debt: return on the bond price at resolution (i.e., the realized recovery at resolution) relative to the bond price at default (i.e., the expected recovery at default); 5) Market equilibrium return: based on the combination of a base rate plus a premium for systematic risk. The risk premium is based on the product of the systematic risk sensitivity and the equity risk premium. The key theoretical findings of the WG are: a) Appropriate discount rates are based on a combination of the risk free rate and risk premium for systematic risk at the time of default; b) Discount rates should not compensate for realized risk; c) Approaches may be separated into contract specific, comparable and equilibrium approaches; d) WACC and market equilibrium return have a slight preference in the Working Group; e) Contract rates are popular in practice as they have practical advantages: they adjust automatically for changing supply/demand and risk aversion in the economy and align with accounting requirements. However, contract rates have shortcomings: i) Rates are based on the origination time: this is a violation of the principle that discount rates should relate to the default time; ii) Rates include the expected loss in relation to default risk: this is a violation of the principle that discount rates should not compensate for realized risk. The key empirical findings of the WG are: Declining risk free rates are in part offset by increasing market risk premiums in the period 2000‐2013; Common empirical discount rates are found to be between the risk free rate and the return on equity; The variation of empirical LGDs is moderate for the various discount rate approaches; GCD may consider providing simple measures for systematic risk for homogenous risk segments to facilitate the appropriate reflection of systematic risk in the discount rates. Risk measures may include asset correlations and variation coefficients.

Asset Correlation, Diversification and the Basel Accord: A Comparative Study

The 2008-2009 financial crises revealed that the Basel Accord of 2004 was inadequate to ensure a stable financial sector. In this paper we analyze whether the Basel Accord's assumption of a single risk factor contributed to the instability. The asset correlation parameter describes the degree of default rate fluctuations and is part of the Basel Accord's formula on capital requirements. We estimate the asset correlation parameter for homogenous segments such that of banks from default data. We find that the regulatory asset correlation parameter cannot be considered prudent for some homogenous segments. If such a segment is material, effects of diversification, expressed by the single risk factor and its associated asset correlation parameter, become then overestimated.

The currency composition of firms' balance sheets, asset value correlations, and capital requirements

We extend the Tasche (2007) model on the asset correlation bias caused by a currency mismatch between assets and liabilities to the more realistic situation where just some assets and liabilities are denominated in a foreign currency. To test the significance of the remaining bias we rely on a unique database constructed by the Inter-American Development Bank (IADB) containing time-series of the asset and liability currency composition of firms in some Latin American countries. We find that the asset correlation bias and associated underestimations of Basel II capital charges are economically significant even when we account for the actual (partial) currency mismatch.

Online learning of time-varying stochastic factor structure by variational sequential Bayesian factor analysis

Investment tasks include forecasting volatilities and correlations of assets and portfolios. One of the tools widely utilized is stochastic factor analysis on a set of correlated time-series (e.g. asset returns). Published time-series factor models require either sufficiently wide time windows of observed data or numeric solutions by simulations. We developed a ‘variational sequential Bayesian factor analysis’ (VSBFA) algorithm to make online learning of time-varying stochastic factor structure. The VSBFA is an analytic filter to estimate unknown factor scores, factor loadings and residual variances. The covariance matrix of the time-series predicted by the VSBFA can be decomposed into loadings-based covariance and specific variances, and the former can be expressed by ‘explanatory factors’ such as systematic components of various financial market indices. We compared the VSBFA with the most practiced factor model relying on wide data windows, the rolling PCA (principal components analysis), by applying them to 9-year daily returns of 200 simulated stocks with the ‘true’ daily data-generating model completely known, and by using them to forecast volatilities of long-only and long/short global stock portfolios with 25-year monthly returns of more than 800 stocks worldwide. Accuracy of the forecast covariance matrices is measured by a (symmetrized) Kullback–Leibler distance, and accuracy of the forecast portfolio volatilities is measured by bias statistic, log-likelihood, Q-statistic, and portfolio volatility minimization. The factor-based covariance and specific variances predicted by the best VSBFA are significantly more accurate than those by the best rolling PCA.

Information Spillovers in Asset Markets with Correlated Values

We study information spillovers in a dynamic setting with correlated assets owned by privately informed sellers. In the model, a trade of one asset can provide information about the value of other assets. Importantly, the information content of trading behavior is endogenously determined. We show that this endogeneity leads to multiple equilibria when assets are sufficiently correlated. The equilibria are ranked in terms of both trade volume and efficiency. The model has implications for policies targeting post-trade transparency. We show that introducing post-trade transparency can increase or decrease welfare and trading volume depending on the asset correlation, equilibrium being played, and the composition of market participants. (JEL D82, D83, G14, G18)

Stochastic loss given default and exposure at default in a structural model of portfolio credit risk

In this paper, we develop a factor-type latent variable model for portfolio credit risk that accounts for stochastically dependent probability of default (PD), loss given default (LGD) and exposure at default (EAD) at both the systematic and borrower specific levels. By employing a comprehensive simulation study, we set our results in contrast to those obtained using the asymptotic single risk factor (ASRF) model that underlies Basel II and III. Several sensitivity and robustness analyses for different parameter assumptions are conducted to break down our results. As required by the regulator, we show how to map our portfolio credit loss quantiles with correlated PD, LGD and EAD into values for downturn LGD and EAD. Our analyses reveal that stochastically dependent defaults, LGD and EAD increase a credit portfolio’s tail risk significantly. Estimating risk markups separately can therefore lead to substantially underestimating the inherent risk of a portfolio with nondeterministic exposures. Further, we show that relative downturn markups on LGD and EAD depend strongly on asset correlations and, in particular, that credit portfolios with low asset correlations might be prone to an underestimation of additional capital charges for stochastically dependent LGD and EAD. Thus, our results are of economic significance for banks and regulators when setting up minimum capital requirements.

Extreme Portfolio Loss Correlations in Credit Risk

The stability of the financial system is associated with systemic risk factors such as the concurrent default of numerous small obligors. Hence it is of utmost importance to study the mutual dependence of losses for different creditors in the case of large, overlapping credit portfolios. We analytically calculate the multivariate joint loss distribution of several credit portfolios on a non-stationary market. To take fluctuating asset correlations into account we use an random matrix approach which preserves, as a much appreciated side effect, analytical tractability and drastically reduces the number of parameters. We show that for two disjoint credit portfolios diversification does not work in a correlated market. Additionally we find large concurrent portfolio losses to be rather likely. We show that significant correlations of the losses emerge not only for large portfolios with thousands of credit contracts but also for small portfolios consisting of a few credit contracts only. Furthermore we include subordination levels, which were established in collateralized debt obligations to protect the more senior tranches from high losses. We analytically corroborate the observation that an extreme loss of the subordinated creditor is likely to also yield a large loss of the senior creditor.

A test for the global minimum variance portfolio for small sample and singular covariance

Recently, a test dealing with the linear hypothesis for the global minimum variance portfolio weights was obtained under the assumption of non-singular covariance matrix. However, the problem of potential multicollinearity and correlations of assets constitutes a limitation of the classical portfolio theory. Therefore, there is an interest in developing theory in the presence of singularities in the covariance matrix. In this paper, we extend the test by analyzing the portfolio weights in the small sample case with a singular population covariance matrix. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented.

Examining the flight-to-safety with the implied volatilities

This paper investigates the flight-to-safety phenomenon by examining the interactions between the stock market volatility (VIX) and volatilities of the Treasury note, gold, and silver markets. We find that increases in VIX lead to contemporaneous and delayed increases in the volatilities of T-note, gold, and silver prices. The VIX Granger causes the volatilities of T-note, gold, and silver markets, but the latter volatilities do not predict the stock market volatility. Changes in VIX explain more of volatility increases in T-note and gold prices during the financial crisis than in other periods. The leading positive effect of VIX on other expected volatilities, along with the possible negative asset correlations, complements the cross-market hedging and is consistent with the flight-to-safety phenomenon.

Market risk management in a post-Basel II regulatory environment

We propose a novel method of Mean-Capital Requirement portfolio optimization. The optimization is performed using a parallel framework for optimization based on the Nondominated Sorting Genetic Algorithm II. Capital requirements for market risk include an additional stress component introduced by the recent Basel 2.5 regulation. Our optimization with the Basel 2.5 formula in the objective function produces superior results to those of the old (Basel II) formula in stress scenarios in which the correlations of asset returns change considerably. These improvements are achieved at the expense of reduced cardinality of Pareto-optimal portfolios. This reduced cardinality (and thus portfolio diversification) in periods of relatively low market volatility may have unintended consequences for banks’ risk exposure.

AN IMPROVED APPROACH TO EVALUATE DEFAULT PROBABILITIES AND DEFAULT CORRELATIONS WITH CONSISTENCY

We provide (i) a simplified analytic closed form formula for evaluating joint default probability, (ii) an improved method to resolve the inconsistency between the univariate process underlying firm-specific default probability and the correlated bivariate process of the first-passage-time default correlation model, (iii) illustration of risk management implications from misspecification of the default state space. Our closed form formula provides a natural extension of previous structural first-passage-time models and shows the sensitivities of default correlation numerically with respect to the underlying asset correlation, obligor credit quality and time horizon. We emphasize the disparate credit risk management implications of our result in contrast to commonly used risk measurement methods.