Scenario Analysis and Stress Testing Chapter 17 Risk Management and Financial Institutions 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

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 17.1; traffic light options) Risk Management and Financial Institutions 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009

Example from Chapter 12 Scenario Loss ($000s) Probability Cumul. Probability s5 850.000 0.00050 s4 750.000 0.00100 h494 499.395 0.00198 0.00298 s3 450.000 0.00200 0.00498 h339 359.440 0.00696 h329 341.366 0.00894 s2 300.000 0.01094 h349 251.943 0.01292 h487 247.571 0.01490 h131 241.712 0.01688 s1 235.000 0.00500 0.02188 h227 230.265 0.02386 h495 227.332 0.02584 h441 225.051 0.02782 …. Risk Management and Financial Institutions 2e, Chapter 17, Copyright © John C. Hull 2009

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 2e, Chapter 17, Copyright © John C. Hull 2009