Scenario Analysis and Stress Testing Chapter 19 Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Stress Testing Key Questions How do we generate the scenarios? How do we evaluate the scenarios? What do we do with the results? Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Generating the scenarios Stress individual variables Choose particularly days when there were big market movements and stress all variables by the amount they moved on those days Form a stress testing committee of senior management and ask it to generate the scenarios Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Core vs Peripheral Variables If scenario generated involves only a few “core” variables, regress other “peripheral” variables on the core variables to determine their movements. (Kupiec, 1999) Ideally the relationship between peripheral and core variables should be estimated for stressed market conditions (Kim and Finger, 2000) Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Making Scenarios Complete Often an adverse scenario has an immediate effect on the value of a portfolio and a “knock on” effect Examples Credit crisis of 2007 LTCM Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Reverse Stress Testing Use an algorithm to search for scenarios where large losses occur Can be a useful input to the stress testing committee. Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

What are the Incentives of a Financial Institution? If the stress testing committee comes up with extreme scenarios more regulatory capital is likely to be required The stress testing committee may therefore has an incentive to “water down” the scenarios they consider Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Scenarios Proposed by Regulators? Will regulators provide their own scenarios to be used by all banks? Part of the Basel Committee’s consultative document suggests that it is thinking about this as a possibility There is a danger that, if the scenarios are announced in advance, financial institutions will hedge only against the scenarios (See Business Snapshot 19.2; traffic light options) Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

What to do with the Results? Should managers place more reliance on stress testing results or VaR results One idea is to ask the stress testing committee to assign probabilities to scenarios (e.g. 0.05% or 0.2% or 0.5%) The stress scenarios can then be integrated with the historical simulation scenarios to produce a composite VaR Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Example from Chapter 14 Scenario Loss ($000s) Probability Cumul. Probability s5 850.000 0.00050 s4 750.000 0.00100 v494 477.814 0.00198 0.00298 s3 450.000 0.00200 0.00498 v339 345.435 0.00696 s2 300.000 0.00896 v349 282,204 0.01094 v329 277.041 0.01292 v487 253.385 0.01490 s1 235.000 0.00500 0.01990 v227 217.974 0.02188 v131 205.256 0.02386 v238 201.389 0.02584 …. Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012

Subjective vs Objective Probabilities Objective probabilities are calculated from data Subjective probabilities is base don a individual’s judgment. Objective probabilities are inevitably backward looking The procedure just described is a way of combining subjective and objective probabilities. Risk Management and Financial Institutions 3e, Chapter 19, Copyright © John C. Hull 2012