Tuesday, March 31, 2009

New Risk Measures For Post Global Financial Crisis 2008 Era

by Prof. Rajendra Shah

The Real Reasons for the Global Financial Crisis 2008

A common explanation that has been put forth about the real cause of the ongoing Global Financial Crisis that started in 2008 is the subprime mortgage lending. When significant number of those borrowers failed to meet their commitments, the lenders tried a recovery through selling of these mortgaged properties leading to a slump in the property market and subsequently assuring future recoveries to log losses and so on. The problem would have had a limited impact but for bold and beautiful tool of securitization (1). Use of securitization had multiplied the money available to lend many-fold and that was the reason why liberal subprime lending had become possible. The extensive use of securitization allowed the lenders to make hay because of untested optimism and lack of appropriate disclosure requirements.

Some believe that unprecedented upward move of several months in oil price up to US $147.50 per barrel led to use of substitutes like ethanol as fuel and that fueled rise in food prices and inflation causing subprime borrowers to fail in their commitments. Whether introduction of uncontrolled securitization provisions and a calculated strategy to allow oil prices to soar had terror-studded political motives or not, three root causes of all that we witnessed are greed, Greed and GREED.

Credit Related Models

The failure of mortgage borrowers makes us examine various models around Credit for their robustness and accuracy.

Credit Scoring Models: Credit score is a measure that can objectively assess credit risk of consumers. The objective of a credit scoring model is to maximize profits from lending operations. Credit scoring models can be built based on the experience data provided by banks about their past consumers. Credit bureau data can be helpful in testing and improving the accuracy of the credit scoring model. Credit scoring primarily determines the likelihood of default by a consumer based on the parameter values supplied by consumers in their credit application. It thus helps a bank to make its credit granting decisions based on objective and consistent methods thereby limiting default incidents.

Bayesian method can be used to improve credit scoring models (2).

Credit Migration Models: The companies that have active bonds are evaluated continuously to determine their credit worthiness. If a company’s financial position strengthens, its credit rating goes up and if it weakens, its credit rating goes down. While the credit ratings indicate a company’s financial strength, they do not talk about the chances of shifting or migrating into another rating. Credit migration modeling helps in this regard. The utility of credit migration models(3) is evident from the fact that Basel-II agreement requires banks to use credit migration models that are subjected to less uncertainty to reduce unnecessary risk. Modern credit derivative pricing models rely on the probabilities estimated by credit migration models to generate fair pricing. Therefore, developing credit migration models that are as accurate as possible is an essential task of risk management in front of us.

Credit Exposure Models: If a borrower defaults, the risk to a lender is the borrower’s credit exposure. In case of sub-prime borrowers, profile of exposure keeps changing and the banks lending short-term loans should well understand their credit profiles in order to deploy capital efficiently and with optimum safety. This requires banks to identify the probabilities of first-payment defaults and in the event of a default, the severity of obligation of the customer. The banks would also like to minimize their obligation which can be done using a credit exposure model (4).

The subprime borrower market is a uniquely homogeneous segment of the total borrower market. The loan decision factors such as the risk of default, the absence of collateral, the purposes of loan, the charge-off rates and the current market conditions are highly correlated. This is not conducive for building a scoring model. Statistical methods have their limitations due to high correlation between factors. In such a situation, the credit exposure models in addition to the first-payment default model are useful to deal with subprime borrowers.

Credit Portfolio Models: Following heavy losses in late eighties and early nineties, the banks started to develop more sophisticated credit risk management techniques that stressed on the credit risk of individual exposures and the intensities to which these risks were diversified. Credit portfolio models were developed to differentiate credit-risk along multiple dimensions and for large corporate exposures on an individual basis. The credit portfolio models (5) have empowered banks to take advantage of the increasing liquidity of the credit markets and to adopt a far more active approach to credit portfolio management than was previously possible. Active credit portfolio optimization has enormous potential to enhance profitability. There are a number of credit portfolio models that are characterized by their correlation structures and choice of risk measures. The risk measures used by the models are loss- based and/or NPV- based. The advantages maybe in terms of simplicity, data availability, speed of calculation, versatility, etc. The disadvantages are also in terms of limitations imposed by the same features. Credit portfolio models are useful in:

  • Solvency analysis

  • Credit risk concentrations and portfolio optimization

  • Sensitivity analysis and stress testing
What Precautionary Indicators Could Have Helped in Avoiding the Crisis

It appears that the sub-prime crisis could have been avoided had the lending institutions acted more cautiously in choosing their customers by paying adequate attention to their credit exposures. The indicators of rising average exposure within the limit on a credit card, increasing frequency of delayed payment instances, increasing average delay times could have given early indications of the problems in the offing.

Limitations of Standard Risk Measures

Most standard models are based on normal distribution. Building such models was an initial step towards more realistic models. In real life situations, we often come across investment returns where the distributions are leptokurtic and/or have heavy tails. The normal models are misfit in such cases. Therefore models such as CAPM, APT which are developed under the assumption of normal distribution lead to misleading results. The bank’s cumulative distribution of sold (not marketed) loans is asymmetric, leptokurtic and contains extreme values. Normal models cannot be applied to them. In mean-variance model, the risk of a portfolio was defined in terms of variance of return which required variances and covariances between the returns of all securities. The concept of introduction of the β based portfolio method was motivated by insufficient data to compute the variance covariance matrix. Now Boot-strapping techniques allow resolving this issue. As a result, βs are almost abandoned in portfolio management techniques.

To measure risk under very generic conditions the concept of VaR was introduced. Basically VaRα is α-percentile of the loss distribution. VaR (6) is not a suitable risk measure for the following reasons:

  • It does not measure losses exceeding VaR

  • It may provide inconsistent results at different confidence levels

  • Non-convexity makes it impossible for the use of VaR in optimization problems

  • A reduction of VaR may result in extending the tail beyond VaR

  • Non-sub-additivity of the measure means that portfolio diversification may lead to an increase in the risk and does not allow to add up the VaR of different risk sources

  • Many local extremes of VaR leads to unstable VaR ranking

  • VaR can destabilize an economy and induce crashes that would not otherwise occur
Some desirable properties of a good risk measure are:

  • Positive homogeneity: f(λx) = λ.f(x) for λ > 0 and all random variables x

  • Sub-additivity: f(x+y) ≤ f(x) + f(y) for all random variables x and y
For risk measure f( ) satisfying the above properties, convexity is implied. Additionally, if the following properties hold, then f( ) is called coherent risk measure.

  • Monotonicity : x ≤ y implies f(x) ≤ f(y) for all random variables x and y

  • Transitional invariance f(x+λr0) = f(x) – λ for all random variables x and real numbers λ and all risk free rates r0.
Need to Design New Risk Measures

The measures like Variance and VaR in case of non-elliptical joint distributions have two major drawbacks, viz.

  1. They are not coherent and lead to non-convex risk measures and consequently to absurd results.

  2. They fail to measure non-linear correlation between the random variables.
To overcome the first drawback, the following coherent risk measures are developed

  • Expected Regret (ER)

  • Conditional Value at Risk (CVaR)

  • Expected Shortfall (ES)
Expected Regret is defined as the expected value of the loss distribution beyond a threshold α.
CVaR is the expected value of the loss exceeding VaR.
In case of continuous random variables, the definition of expected shortfall coincides with that of CVaR.
To overcome the second drawback listed above, measures of dependence based on copulas were developed. Dependent extreme events have been the major sources of losses for banks. Therefore copulas-based measures need to be emphasized and strengthened. Parametric models based on copulas such as Marshall-Olkin method and maximum likelihood method are useful but complex. Non parametric dependence measures based on copulas still require some efforts to provide user-friendly algorithms.
Newer Risk Measures and their Increasing Significance
A variation of the VaR methodology known as economic capital (7) is used to determine the expected funding and borrowing levels for credit and default funding and provisioning levels for credit and default expectations. Economic capital in its simplest form, may be defined as sufficient surplus to cover potential losses at a given risk tolerance level over a specified time horizon. Economic capital is useful in

  • Determining company/product risk profile

  • Capital budgeting

  • Evaluating required capital in merger/acquisition situations

  • Insurance product pricing

  • Assessing risk tolerance and constraints

  • Asset Liability Management

  • Calculating risk adjusted return on capital

  • Performance measurement

  • Incentive compensation

  • Regulatory and rating agency discussions
“Playing a key role in both the second pillar of the new Basel framework and the Solvency II project, economic capital models are becoming increasingly important.” – Iman Van Lelyveld (8).
The concept of economic capital is expected to gather momentum and according to James Lam (9), economic capital may replace VaR in risk management in the time to come.
Another new measure: “ShockVaR” developed by Riskdata (10), may provide a better understanding of risk across markets, asset categories and hedge funds. Riskdata developed "ShockVaR" in around 2007 to overcome the possibility of overestimating risk during calm periods and underestimating it in highly volatile markets. ShockVaR is designed to be highly sensitive to market changes than typical VaR measures, which focus on the maximum estimated amount of loss at a given time horizon for a specific confidence level. ShockVaR is expected to increase sharply within days of a shock or anticipated shock and drop down to its initial value if the market volatility is back to previous levels. Riskdata’s ShockVaR calculations, for example, accurately pointed to the increased possibility of a dramatic drop in the Japanese equity markets in the week of October 2008 anticipating the big drop experienced on October 24.
The goal of ShockVaR is to help investors better analyze their portfolios in the current market crisis.
Some New Measure Suggestions
Credit Scoring models need to consider the following aspects to differentiate between customers:

  • More open accounts that are reported as “Paid as agreed”

  • More types of credit accounts

  • More open accounts than closed accounts

  • Low balance compared to credit limits

  • More active accounts but with lower balances

  • Fewer credit scoring assessment requests
However, care needs to be taken to ensure that customers’ credit rating does not go down if the credit card provider (increasingly possible under the current status of the global economy)

  • slashes credit limit based on new norms

  • closes unused or unprofitable accounts
The credit scoring models need to overcome vicious cycle effect, cascading effect of the use of credit scores and inaccuracy problems. Use of option pricing model and neural networks for credit scoring can be useful.
An improvisation of Economic capital using Bayesian approach may give a long handle. I see rigorous researches and authentication through sensitivity analysis and scenario testing for various kinds of coherent risk measures and tools to be the order of 2009 and thereafter.

  1. The Global Credit Crisis and Securitization in East Asia by Douglas W. Arner, Paul Lejot and LottSchou-Zibell, Publisher: Capital Markets Law Journal.2008; 3: 291-319

  2. Bayesian Methods for Improving Credit Scoring Models by Gunter Lofler, Peter N. Posch and Christiane Schone

  3. An Introduction to Credit Migration Modeling by Neil McBride

  4. Potential Exposure – How To Get A Handle On Your Credit Risk – By Jim Rich and Curtis Tange

  5. Active Credit Portfolio management by Andrew Kuritzes

  6. Exploring the Limitations of Value at Risk: How Good Is It in Practice? By Andreas Krause Journal of Risk Finance, Winter 2003, pp 19-28

  7. What Is “Economic Capital?” - A Quick Guide to the Differences between Economic Capital and Regulatory Capital, By Eric Banfield

  8. Economic Capital Modelling : Concepts, Measurement and Implementation, Edited By Iman van Lelyveld

  9. Enterprise Risk Management From Incentives to Controls, By James Lam, Published by John Wiley and Sons

  10. Riskdata is now providing free access to daily shockVaR and long term VaR indicators for major equity indices.

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