January 18, 2009
Reverse Stress Testing: What's the Great Reversal?
FSA's recent Consultative Paper 08/24 proposes to introduce Reverse Stress Test requirement. It also proposes to change existing requirements on Pillar II Stress Testing, as well Pillar I requirement for those banks adopting IRB approaches.
Reason is obvious: Reverse Sweep the spinning Credit Crisis.
The primary objectives behind this new-born Reverse Stress Test are
(a) Use high impact stress events which may lead the banks to fail, and
(b) Force the banks to work out an implementable road map to protect against such failures.
So it is a high level approach towards a Quasi Zero Failure Strategy.
From modeling perspective, Reverse Stress Test lays bare two points for provocative thoughts:
1. How to measure the mode and magnitude of risk transmission and contagion design under extreme stress, and
2. How to measure effects on risk correlation under extreme stress.
The Central Banks are not prescriptive; so the open question before the Risk Managers - "HOW?"
The ICAAP framework is now being foisted on the banks hurriedly by the Regulatory Authorities in many countries, as part of Basel Pillar II compliance (or Bank Failures?). It is required to capture the "cross-market and cross-risk type dependencies on the assets of the firm as a whole".
So, the complete suite for Strategic Risk Management may include the following:
1. Capital allocation
2. Risk aggregation
3. Risk concentrations and diversification
4. Sensitivities & stress testing
5. Risk & return optimization
"Principles for sound stress testing practices and supervision" Issued for comment on January 2009 by Basel Committee on Banking Supervision gives guidance for stress testing during the crisis and says:
"First, given a long period of stability, backward-looking historical information indicated benign conditions so that these models did not pick up the possibility of severe shocks nor the build up of vulnerabilities within the system. Historical statistical relationships, such as correlations,proved to be unreliable once actual events started to unfold."
Point noted : Inefficacy of histrorical statistical measures - Break down in correlation pattern.
"Second, the financial crisis has again shown that, especially in stressed conditions, risk characteristics can change rapidly as reactions by market participants within the system can induce feedback effects and lead to system-wide interactions. These effects can dramatically amplify initial shocks as recent events have illustrated."
Point noted : Risk tramission and co-dependence structure - Contagion effects.
In the backdrop of the present credit crisis, main challenge before a Stress Testing framework is to make it adequate and proportionate.
Simplistically speaking, the steps for an ideal stress testing framework may contain the following:
1. Identify risk factors i.e. macro-economic and micro-economic factors which may affect the assets
2. Reclassify the asset classes based on identified risks
3. Define dependency structure of those risk factors and decide on the single/joint simulation routines for those identified risk factors, for revaluation purpose, under stressed conditions. Those routines must factor in contagion effects.
4. Define risk correlation under stressed conditions and decide on its effects in risk aggregation
5. Derive the results and revalidate the assumptions
6. Decide on the requirement of stress capital and risk mitigation requirements
7. Integrate the output in the decision making process and update risk strategy accordingly
From Quant's point of view, there are two enticing words in the professed Reverse Stress Test:
1. Correlations
2. Co-dependencies
Generally correlation is used to describe dependence between random variables. But eventually copula has proved its superiority to model dependence, especially in financial risk management. Ideally the dependence model should capture the risk expressed by the joint tail behavior of returns, without compromising the diversification possibilities that may be represented by the center of the return distribution.
There are many types of copulas that are used in risk management. Longin (1996) and Jansen et al. (2000) applied extreme value copula. Longin and Solnik (2001), & Poon et al. (2004) opted for the gumbel copula. Glasserman et al. (2002), Campbell et al. (2003), Mashal et al. (2003), Valdez and Chernih (2003), & Meneguzzo and Vecchiato (2004) used t-copula.
The process to evaluate the fit of a copula may broadly contain following steps:
1. Estimation - Here we estimate the parameters.
2. Evaluation - Here we evaluate the fit of the copula with the estimated parameters.
3. Simulation - Here we test whether the distance measure provide evidence against the fit of copula.
4. Test - Here we judge the values of the distance measure by determining p-values.
Amongst Gaussian copula, Student's t copula and Gumbel copula, which is the best fit may be determined case by case basis empirically. However, it is generally found that under normal market conditions, t copula performs better than Gaussian copula and Gumbel copula as Gaussian copula focuses on dependence in the center and exhibits tail independence, whereas Gambel copula focuses mostly on dependence in the tails. But t copula captures both central and tail dependence. Notwithstanding the fact, I have found that Gumbel copula proves extremely efficient under stressed scenarios for its tail dependence, as under extreme stressed scenarios, there is huge movement in the tails in the returns. So to so, one may consider Gumbel copula while modeling Stress Tests under extremely stressed scenarios. I think, choosing Gumbel will not be a big gamble under stressed scenarios as it may not underestimate the risk.
Posted by ddutta7 at 10:32 PM
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