Module 21: Use of Models in ERM

Sources of uncertainty

Model risk:

Risk arising from the use of an inappropriate or inaccurate model when assessing or managing risks

• True model of class of model is rarely known with certainty

Parameter risk:

Use of inappropriate or inaccurate parameters or assumptions within such models

• Use of simulated parameters to account for this

Stochastic uncertainty:

Arises from the randomness of a finite set of observations

• As # of observation $\uparrow$, certainty in the model, parameters, and its prediction $\uparrow$

• Stochastic models acknowledge this by producing a range of results

Use of simulated parameters

Due to limited observations, fitted parameters are never certain

• Projections that assume only stochastic volatility around unchanging parameters will lead to the range of projection being too narrow

• To allow for parameter uncertainty, use dynamic (simulated) parameters if the parameters can be modeled in some way

  e.g. if least square regression has been used and a covariance matrix for the parameters is available

  $\hookrightarrow$ Multivariate normal distⁿ can be used to simulate the parameters, which themselves are used in stochastic simulations

Approach to determining the CI for the parameters by estimating a joint distribution for the parameters

1. fit a model using $T$ data points

2. Simulate $T$ data points using the model

3. Re-fit the model to the simulate data points

4. Record the parameter values

5. Repeat the process a large number of times, starting with the original data set each time

Obtaining a joint distribution for the parameters this way means that rather than using a static set of parameters to carry out the simulations, dynamic parameters can be used instead

Three assumptions that can be made in relation to the choice of model

1. True model or class of model is known

2. Model used is a simplification of a known, more complex reality

3. Model used is an approximation to an unknown, more complex reality

   Most common in financial modeling

Caveat with the 3^rd assumption as it can lead to the wrong model

1. Inappropriate projection of past trends due to

   • Errors in historical data

   • Incomplete data

   • Heterogeneity in the data, where the underlying drivers and their dependencies are not known or not projected separately

2. Selection of an inappropriate underlying distribution due to

   • Insufficient data

   • Not investigating a range of alternative candidate distributions

3. The number of parameters being chosen without reference to:

   • Need to avoid over simplification and the risk of implicit assumptions

   • Principle of parsimony:

     Where there is a choice of fitted models, the optimal selection is the one with the fewest parameters as this should lead to more stable projections

Model Development

Application of statistical models in practical ERM context

Prime objective in building model:

1. Enable the actuary or risk manager to give an organization appropriate advice so that it can manage its risks in a sound financial way

2. Use in day-to-day running of the company

3. Provide checks and controls to the business

Use of model points

• A very large number of individual data points might need to be brought together into a manageable number of relatively homogeneous groups

• Groupings need to be made in a way that each policy in a group is expected to produce similar results when the model is run (i.e. homogeneous?)

• Then we can have a representative single policy in each group to be run through the model $\Rightarrow$ the result to be found $\Rightarrow$ Scale up this result in order to give the result of the total set policies in the group

• Model point: The representative single point in a group

  A number of such “model points” can then be used to represent the whole of the underlying business

Requirements for Models

For generic actuarial model

• Must be valid and sufficiently rigorous for the purpose to which it will be put and adequately documented

• Model points chosen must be such as to reflect adequately the distribution of the business being modeled

• Components of the model must allow for all those features of the business being modeled that could significantly affect the advice being given

• Input parameter should be appropriate to the business being modeled

  Take into account the special features of the company and the economic and business environment in which it is operating

• Workings of the model should be easy to appreciate and communicate

  Results should be displayed clearly

• Outputs should be capable of independent verification for reasonableness

  Should be readily communicable to those to whom advice will be given

• Model should be capable of subsequent development and refinement

• Model must NOT be:

  • Overly complex

    So that either the results become difficult to interpret and communicate

  • Too long or expensive to run (unless this is required by the purpose of the model)

    Avoid the impression that everything an be modeled

Additional items for ERM

• Model should be amenable to an analysis of the impact of parameter uncertainty or incorrectly specified parameter values

• Should exhibit behavior in simulations that is consistent with the past

  However should not exclude plausible future scenarios that might be quite different from historical patterns

• Shortcomings of the model should be clearly stated

Summary: models should…

• Be appropriate for purpose (with limitations recognized)

• Be robust

  Having been selected from various possible candidate models with a variety of structures

• Be as simple as possible whilst meeting their purpose

  Complex models can be difficult to check, maintain, communicate and may imply spurious accuracy and unjustified confidence

• Be developed over time

  With regular reviews identifying when parameters and /or structures need to change

• Sometimes be avoided

  When more importance is attached to other activities

  (e.g. identification and management of hard to quantify operational risks)

Risk management models should:

• Reflect the dynamics of the organization…

• both now and as expected in the future

• Should allow for wider external factors

• Implies that modeling scope should be defined to be comprehensive across all important and well-defined risks

• Different models may exits for component risks, but these need to feed into an overall modeling scheme

Overall objective is to achieve a balanced (not unduly exaggerated or smooth) modeling outcome

Use of Models

Reasons to build models for ERM decision making:

1. Pricing of products or service

2. Assess economic value of the company

3. Estimate possible volatility of future profits and earnings

4. Determine capital adequacy requirements (regulatory and internal)

5. Project future capital or solvency

6. Assess the effect of risk management and mitigation techniques on both profits and capital requirements

7. Assess the effect of other strategic decisions (e.g. changes in investment or new business strategy)

8. Evaluate projects

Modeling Process

Steps of developing and applying a model:

1. Specify the purpose of the investigation

2. Collect data and group or modify if necessary

3. Choose the form of the model, identify parameters and variables

4. Estimate the required parameters and any correlations between them

5. Check the goodness of fit

   (fit different model if poor fit)

6. Ensure that the model is able to project all required outputs

   (e.g. cash flow, etc and incl. interactions between them)

7. Run the model with the selected estimated variables (or stochastic variables)

8. Output in appropriate format

   (e.g. summarized for stochastic models)

9. Assess the sensitivity of results to different deterministic variable values

10. Monitor the results of the model and its application and make refinements as required

If cash flow projection over a long time horizon is required

• More frequently the cash flows are calculated $\Rightarrow$ more reliable the output from the model

  On the other hand: Less frequent $\Rightarrow$ model can run faster

Corporate Decision Making

Using models in the corporate decision making process involves:

• Inputs: information, data, assumption, parameters

• Model calculations: cash flows, projections, simulations

• Outputs: deterministic, ranges/sensitivities, stochastic distribution of outcomes (as appropriate)

• Review and discussion

Additional Considerations

• The latter stage of the process needs to reflect the risk policy, appetite and the overall use of judgement (not just outputs)

Formalized judgement

• Can have quantitative statements of risk appetite and utility functions built into the modeling rules

• Should NOT be seen as substitute for the intuition of decision makers

Market consistent analysis approach

• Some argues that corporate decision makers should worry only about the risk preferences and other investment opportunities of the company’s owner

  (i.e. the market consistent analysis approach)

• Assumes that:

  Investors can diversified away company specific risk

  Risk premium will compensate for systemic risk

• However in practice both external and internal perspectives are important

Economic Value Added Model

• A possible model output upon which decisions are made

• Economic Value:

  PV of all future s/h profits on economic basis

• EVA expressed as % of cost of capital:

  Difference between the increase in economic value and the WACC

  • Positive incremental EVA means go ahead

  • But in practice, should consider more than one risk metric that are distinct and independent but not overly complex

Consideration of different options might lead to further clarification of an organization’s risk appetite

• e.g. Model might identify a number of alternative strategies each of which lies on the efficient frontier and are within the risk tolerances

• Selection of the preferred option may require explicit expression of a corporate risk preference

Qualitative aspects

• Just as if not more important than quantitative aspects for ERM based corporate decision making in practice

• Reliance on quantitative models alone (esp. on one model and one specific calibration of that model) can be dangerous

  Esp. where the limitations of the data, parameters or model used are not fully understood or appreciated

• Many companies that failed during the economic downturn has theoretically sound quantitative risk models

More on use of capital model in corporate decision making in Module 30