Chapter 9: Stress testing and scenario analysis

Question 1

Why do we stress test?

Answer 1

• To account for extreme events: traditional risk measures like VaR/Es have important limitations: they are often unable to pick up true nature of risk events:
  
  • There are some (huge) events located in far left end of tail of the P&L distribution (see graph), which will not be properly captured in many of the risk measures.
  • The future ultimately differs from the past, and thus we are regularly surprised by risks that we have never seen before

Question 2

How can we overcome these limitations of traditional risk measures?

Answer 2

• To overcome some of these limiations, modification have been developed:
• By updating volatility and using a tailored weighting scheme, we aim at improving our forecasts of P&L returns
• By using EVT to parametrize the tails of the distribution, or a CF quantile estimation, we aim at estimating more accurately the tail of the P&L distribution
• Such modifications are a first step to improve our risk measurement. This is in general however not sufficient.

Question 3

What is the stress testing program?

Answer 3

• An important supplement to traditional risk measures consists of the analysis of the portfolio under more extreme, but plausible scenarios:
  
  • Shocks that have never occured
  • Shocks that occur more than predicted by your sample
  • Shocks reflecting a temporary change in pattern:
    
    • Eg. temporary widening of currency band
  • Shock reflecting a permanent structural break
    
    • Eg. exchange rate regime breakdown.
• The impact of such shocks can be studied by a stress test: it allows us to analyze the losses that follow from a stress event.
• Events nto in a recent historical sample are mayby unlikely but now impossible.

Question 4

Is stress testing required?

Answer 4

• Yes, nowadays, such stress testing program is required by regulator and consists of a number of actions:
  
  1. Scenario analysis and stressing models and parameters
  2. Incorporation of stress results in a VaR/ES analysis
  3. Defining policy responses to extreme scenarios

Question 5

What is the basic principle of scenario analysis?

Answer 5

• The basic principle of a stress test is to analyze the impact of a simulated ’new reality’ on the portfolio.
• Formally: Assume a simple case where we impose a shock event to asset V:
  
  • Define the impact of the stress event on the value of the instrument as ∆V
  • Analyze the impact of this shock on our portfolio as V ′ = V + ∆V

Question 6

How can we implement scenario analysis?

Answer 6

• One of the most challenging aspects is to translate such stress scenarios into associated impacts. Depending upon how we proceed, we introduce a different degree of complexity
  
  1. In a simple unidimensional scenario we only stress a single variable
  2. In a more complex multi-dimensional scenario, we stress multiple variables at once: such multi-dimensional scenario can then analyze the direct impact of a shock, or the indirect impact (through correlations)

Question 7

What is a unidimensional analysis?

Answer 7

• When implementing a unidimensional analysis, we induce a large move in a single variable.
• The advantage of this approach is that it is simple, computationally fast and highly intuitive (measure of sensitivity, ceteris paribus)
• The drawback is that it ignores any cross-effects of risk factor movements

Question 8

What is multidimensional analysis?

Answer 8

• To allow for such cross-effects, we could analyze a more realistic case where multiple changes and correlations in risk factors movements are accounted for. To build such multidimensional scenarios, we can rely on:
  
  • An hypothetical/prospective reality with the main challenge of how to build realistic scenario
  • An historical reality with the main drawback that history, typically, does not repeat itself exactly

Question 9

What are hypothetical scenarios?

Answer 9

• Developing hypothetical scenarios is most flexible, but also most challenging.
• Scenarios that ’might’ occur should incorporate a wide range of developments such a financial market dynamics, world politics, the economic environment and global uncertainties
• The main advantage of hypothetical scenario building is that it obliges you to think out-of-the-box (brainstorm).
• In addition to stress testing, we could also implement reverse stress testing: in that case, we start from a failure, and then identify the events that could trigger such failure.
• The drawback is clearly that it is difficult to implement as defining the associated impacts is not easy.

Question 10

How do we solve the problem of building your own scenarios?

Answer 10

• One could focus on scenarios that we have witnessed in the past.
• Advantage: easily implemented as we are guided by actual risk factor impacts.
• The disadvantage is that we only have a limited choice of historical scenarios and that history does not repeat itself.

Question 11

What are testing models and parameters?

Answer 11

• Finally, a stress testing program also requires us to stress test the models that are used and the parameters that are estimated/set.
• This allows us to get a better understanding of how sensitive VaR is to the model choices we have made.
  
  • e.g. numerous valuation models exist, and our choice could heavily impact the VaR results
• Also in terms if parameter choice, it is important to know how sensitive VaR to this choice.
  
  • e.g. numerous models exist to estimate correlations

Question 12

What to do with stress test results?

Answer 12

• Unfortunately, the results of stress tests are too often ignored:
  
  • The reason is that potential losses are extremely large, while its probability of occurrence is extremely low
  • The consequence then is that it is/seems uneconomical to set aside capital
• We need regulatory requirements.

Question 13

What are the advantages of stress testing?

Answer 13

• The major advantage of a stress test is that it identifies the vulnerability of a portfolio to a range of extreme events
• Traditional banking activity is vulnerable to flattening or inversion of the term structure of interest rates. A short ’gamma’ derivatives portfolio suffers from a volatility increase

Question 14

What are the drawbacks of stress testing?

Answer 14

• A drawback is that the generation of reasonable scenarios is a process that requires quantitative skills + good understanding of financial markets.
• In addition, one should be aware of arbitrary combinations of stress shocks: the scenarios need to make economic sense
• Moreover, stress testing is time-consuming and computationally intensive: which scenarios to run is again an arbitrary choice
• Also, stress tests are static: no consideration for the dynamic process of the crisis and the possible actions of the financial institution
• Finally, stress testing results give worst case losses without associated probabilities: this makes them difficult to interpret.

Question 15

How do we integrate stress tests in VaR?

Answer 15

• To ease interpretation, we can assign subjective probabilities to scenarios
• Once probabilities are associated with outcomes, we can incorporate them into a probability distribution, and thus into a VaR calculation

Question 16

How can we build stress scenarios?

Answer 16

• We can distinguish between two approaches to build stress scenarios:
  
  1. Event-driven scenarios: we start by defining a stress scenario (an ’event’), and then list the associated event-impacts (e.g. a trade war between US and China)
  2. Portfolio-driven scenarios: we start from a worst case impact and then construct an associated scenario (e.g. Interest rate increase; volatility increase)

Question 17

What are regulatory requirements?

Answer 17

• Regulatory requirements are needed:
  
  • Rigorous and comprehensive stress tests are required
  • Stress test results to determine capital buffers
  • Undertake careful planning
  • Prepare sources of funding
  • Contingency planning
  • Restructure business model