CVaR minimization by the SRA algorithm

Using the risk measure CV aR in �nancial analysis has become more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR

Tail Risk for Australian Emerging Market Entities

Whilst the Australian economy is widely considered to have fared better than many of its global counterparts during the Global Financial Crisis, there was nonetheless extreme volatility experienced in Australian financial markets. To understand the extent to which emerging Australia entities were impacted by these extreme events as compared to established entities, this paper compares entities comprising the Emerging Markets Index (EMCOX) to established entities comprising the S&P/ASX 200 Index using four risk metrics. The first two are Value at Risk (VaR) and Distance to Default (DD), which are traditional measures of market and credit risk. The other two focuses on extreme risk in the tail of the distribution and include Conditional Value at Risk (CVaR) and Conditional Distance to Default (CDD), the latter metric being unique to the authors, and which applies CVaR techniques to default measurement. We apply these measures both prior to and during the GFC, and find that Emerging Market shares show higher risk for all metrics used, the spread between the emerging and established portfolios narrows during the GFC period and that the default risk spread between the two portfolios is greatest in the tail of the distribution. This information can be important to both investors and lenders in determining share or loan portfolio mix in extreme economic circumstances. Classification-JEL:Conditional value at risk; Conditional distance to default; Australian emerging markets

CVaR and Credit Risk Measurement

The link between credit risk and the current financial crisis accentuates the importance of measuring and predicting extreme credit risk. Conditional Value at Risk (CVaR) has become an increasingly popular method for measuring extreme market risk. We apply these CVaR techniques to the measurement of credit risk and compare the probability of default among Australian sectors prior to and during the financial crisis. An in depth understanding of sectoral risk is vital to Banks to ensure that there is not an overconcentration of credit risk in any sector. This paper demonstrates how CVaR methodology can be applied in different economic circumstances and provides Australian Banks with important insights into extreme sectoral credit risk leading up to and during the financial crisis.Conditional Value at Risk (CVaR), Banks, Structural modelling, Probability of default (PD)

Reducing Asset Weights' Volatility by Importance Sampling in Stochastic Credit Portfolio Optimization

The objective of this paper is to study the effect of importance sampling (IS) techniques on stochastic credit portfolio optimization methods. I introduce a framework that leads to a reduction of volatility of resulting optimal portfolio asset weights. Performance of the method is documented in terms of implementation simplicity and accuracy. It is shown that the incorporated methods make solutions more precise given a limited computer performance by means of a reduced size of the initially necessary optimization model. For a presented example variance reduction of risk measures and asset weights by a factor of at least 350 was achieved. I finally outline how results can be mapped into business practice by utilizing readily available software such as RiskMetrics� CreditManager as basis for constructing a portfolio optimization model that is enhanced by means of IS. Dieser Beitrag soll die Auswirkung der Anwendung von Importance Sampling (IS) Techniken in der stochastischen Kreditportfoliooptimierung aufzeigen. Es wird ein Modellaufbau vorgestellt, der zu einer deutlichen Reduktion der Volatilität der Wertpapieranteilsgewichte führt. Durch eine Darstellung der verhältnismäßig einfachen Berücksichtigung der Importance Sampling Technik im Optimierungsverfahren sowie durch ein empirisches Beispiel wird die Leistungsfähigkeit der Methode dargelegt. In diesem Anwendungsbeispiel kann die Varianz der Schätzer sowohl für die Risikomaße als auch für die optimalen Anteilsgewichte um einen Faktor von mindestens 350 reduziert werden. Es wird somit gezeigt, dass die hier vorgestellte Methode durch eine Reduktion der Größe des ursprünglich notwendigen Optimierungs-problems die Genauigkeit von optimalen Lösungen erhöht, wenn nur eine begrenzte Rechnerleistung zur Verfügung steht. Abschließend wird dargelegt, wie die Lösungsansätze in der Praxis durch eine Ankopplung an existierende Softwarelösungen im Bankbetrieb umgesetzt werden können. Hierzu wird ein Vorgehen skizziert, das auf den Ergebnissen des Programms CreditManager von RiskMetrics ein Portfoliooptimierungsmodell aufbaut. Dieses wird um eine Importance Sampling Technik erweitert.Kreditrisiko ; Stochastische Optimierung; Varianzreduktion ; CVaR; CVaR ; credit risk ; stochastic portfolio optimization ; importance sampling ; CreditMetrics ; CreditManager

Credit Risk and Real Capital: An Examination of Swiss Banking Sector Default Risk Using CVaR

The global financial crisis (GFC) has placed the creditworthiness of banks under intense scrutiny. In particular, capital adequacy has been called into question. Current capital requirements make no allowance for capital erosion caused by movements in the market value of assets. This paper examines default probabilities of Swiss banks under extreme conditions using structural modeling techniques. Conditional Value at Risk (CVaR) and conditional probability of default (CPD) techniques are used to measure capital erosion. Significant increase in probability of default (PD) is found during the GFC period. The market asset value based approach indicates a much higher PD than external ratings indicate. Capital adequacy recommendations are formulated which distinguish between real and nominal capital based on asset fluctuations.Real capital; Financial crisis; Conditional value at risk; Credit risk; Banks; Probability of default; Capital adequacy

Australian mining industry: Credit and market tail risk during a crisis period

Industry risk is important to equities investors in determining portfolio mix. It is also important to lenders in managing credit portfolio risk. This article focuses on the mining industry in Australia, that country’s largest industry by exports. The study concentrates on extreme credit and market risk, to determine the riskiness of the mining industry relative to the broader market, with a focus on the Global Financial Crisis (GFC) period and the use tail risk metrics. These include Conditional Value at Risk (CVaR) for measuring market risk and Conditional Distance to Default (CDD) for measuring credit risk. Based on these metrics, the study finds market risk for mining shares to be higher than the broader market, but that the gap narrows during the crisis. From a credit perspective, despite higher volatility experienced by the mining industry, the default risk is lower than the broader market, due to the greater distance between mining entities’ asset and debt values

CVaR and Credit Risk Measurement

The link between credit risk and the current financial crisis accentuates the importance of measuring and predicting extreme credit risk. Conditional Value at Risk (CVaR) is a method used widely in the insurance industry to measure extreme risk, and has also gained popularity as a measure of extreme market risk. We combine the CVaR market approach with the Merton / KMV credit model to generate a model measuring credit risk under extreme market conditions. The Merton / KMV model is a popular model used by Banks to predict probability of default (PD) of customers based on movements in the market value of assets. The model uses option pricing methodology to estimate distance to default (DD) based on movements in the market value of assets. This model has been popularized among Banks for measuring credit risk by KMV who use the DD approach of Merton but apply their extensive default data base to modify PD outcomes. Our extreme credit model is used to compare default risk among sectors in an Australian setting. An in depth understanding of sectoral risk is vital to Banks to ensure that there is not an overconcentration of credit risk in any sector. This paper demonstrates how CVaR methodology can be applied to credit risk in different economic circumstances and provides Australian Banks with important insights into extreme sectoral credit risk leading up to and during the financial crisis. It is precisely at times of extreme risk that companies are most likely to default. This paper provides an understanding of which industries are at most risk during these extreme circumstances. The paper shows a significant increase in default probabilities across all industries during the current financial crisis. Industries with low equity are most affected. The increase is most prominent in the Real Estate, Financial and Mining industries. Industries which have best weathered the storm include Food, Beverage & Tobacco, Pharmaceuticals & Biotechnology and Technology. Both prior to and during the financial crisis, significant correlation is found between those industries that are risky from a market (share price) perspective and those industries that are risky from a credit perspective. There is significant movement in sector risk rankings since the onset of the financial crisis, meaning that those industries that were most risky prior to the financial crisis are not the same industries that are most risky during the financial crisis

Modeling a Distribution of Mortgage Credit Losses

One of the biggest risks arising from financial operations is the risk of counterparty default, commonly known as a “credit risk”. Leaving unmanaged, the credit risk would, with a high probability, result in a crash of a bank. In our paper, we will focus on the credit risk quantification methodology. We will demonstrate that the current regulatory standards for credit risk management are at least not perfect, despite the fact that the regulatory framework for credit risk measurement is more developed than systems for measuring other risks, e.g. market risks or operational risk. Generalizing the well known KMV model, standing behind Basel II, we build a model of a loan portfolio involving a dynamics of the common factor, influencing the borrowers’ assets, which we allow to be non-normal. We show how the parameters of our model may be estimated by means of past mortgage deliquency rates. We give a statistical evidence that the non-normal model is much more suitable than the one assuming the normal distribution of the risk factors. We point out how the assumption that risk factors follow a normal distribution can be dangerous. Especially during volatile periods comparable to the current crisis, the normal distribution based methodology can underestimate the impact of change in tail losses caused by underlying risk factors.Credit Risk, Mortgage, Delinquency Rate, Generalized Hyperbolic Distribution, Normal Distribution