Chapter 22: Capital Modelling - Allowance for diversification Flashcards
State why diversification effects arise.
Diversification effects arise because the various risks from a company’s operations are not perfectly correlated.
Since risks are not perfectly correlated, the sum of the standalone capital requirements for each risk will usually be greater than the capital requirement for all risks combined. In other words, an adverse event (eg a catastrophic claim event) should not affect diversified policies simultaneously (by definition), and so some credit can be given for the level of diversification. This will result in a lower overall capital requirement.
State why correlation effects arise.
Correlations may arise because specific types of risks affect different segments of the company’s overall portfolio. Correlations may also arise between the different types of risks.
Correlation can occur between:
- risks in the same class – this is often called risk clash
- risks in different classes – this may be called class correlation.
Capital modelling investigations
Mnemonic: When to allow for diversification (SPAR SPA)
Capital modelling investigations include:
- assessing solvency capital requirements
- allocating the capital held between classes, products or individual policies for
- performance measurement,
- pricing,
- business planning and
- strategy setting
- reinsurance purchasing
- asset allocation studies
- studies of enterprise level risks such as credit risk and operational risk.
SPAR SPA:
- Solvency assessment
- Performance measurement
- Asset allocation
- RI purchasing
- Strategy setting
- Pricing
- Assessing Enterprise level risks
Allocating the total capital held between classes, products or individual policies may be necessary for (3)
- performance measurement (to accurately assess the profit as a percentage of capital required)
- business planning and strategy setting
- pricing (Premiums include a capital / profit loading reflecting the cost of capital)
Capital Modelling investigations - assessing solvency capital requirements.
- The assessment of solvency capital requirements is a ‘ground-up’ exercise and could be at:
- product level
- class of business level, or
- whole company portfolio level.
- The assessment would also be net of reinsurance, with reinsurance being modelled either explicitly or implicitly.
- We assess the sum of the capital requirements for the various risks from each portfolio segment separately
- This sum is typically more than the capital requirement from all risks analyzed together for the whole portfolio because of diversification.
- However, there can be negative diversification or accumulation of risk because of operations risks associated with group structures and policies. There risks are dealt with by the enterprise risk management processes and they can be a source of negative diversification benefit leading to an additional capital requirement.
- In quantifying diversification effects, we will need to make assumptions about the extent of applicable dependencies (including correlation coefficients).
- To do this, we need to understand the various assumptions underlying the modelling of the risks in each portfolio and how they could interact when combined. This is necessary before we can assess the capital requirements of the overall portfolio.
- Dependencies can occur between: - risks in the same class – this is often called risk clash and risks in different classes – this may be called class dependencies.
- The allowance for dependencies within the stochastic model can either be implicit within the modelling process or explicit through the use of dependency assumptions (including correlation coefficient matrices).
- An implicit allowance might involve reducing the variability assumption when fitting a distribution.
Explain how operational risks may affect the diversification adjustment in a capital model.
A company may be exposed to operational risks associated with its corporate group structures and policies. These risks, which are likely to be targeted by the group’s enterprise risk management process, may be a source of negative diversification effects, that is, require additional capital to be held.
How can dependencies in a capital model be addressed? State the two methods by which such dependencies / correlations might be allowed for in a capital model.
In quantifying diversification effects, we will need to make assumptions about the extent of applicable dependencies (including correlation coefficients). To do this, we need to understand the various assumptions underlying the modelling of the risks in each portfolio and how they could interact when combined. This is necessary before we can assess the capital requirements of the overall portfolio. Dependencies can occur between: risks in the same class – this is often called risk clash risks in different classes – this may be called class dependencies.
The allowance for correlation within the stochastic model can either be implicit within the modelling process or explicit through the use of correlation matrices.
An implicit allowance might involve reducing the variability assumption when fitting a distribution.
Capital allocation for performance measurement is a ‘top-down’ exercise. Explain what is meant by a ‘top-down’ exercise in a capital model and why it would be appropriate here
A ‘top-down’ exercise is the opposite of a ground-up exercise. It involves starting with an overall position and subsequently breaking it down into individual components. In this context, the overall capital required would be modelled and the results then broken down (ie allocated between) different classes of business or products. If a ground-up approach was used, then capital would be calculated for each policy (or group of policies), but since there would be no allowance for diversification benefits, capital would be overstated for each policy (or group of policies) and so profits understated
Methods of allocating capital
- a marginal capital method
- the Shapley method
Capital allocation:
Percentile method
This method is applied to the output of a stochastic model.
We would take the simulation which determines the capital requirement and assess how the loss in that simulation was made up.
E.g., if we ran 10 000 simulations, the simulation giving the 50th worst results (1 in 200 loss) would be analysed to assess what the underwriting result was in each class, what the investment return was, etc.
In practice the insurer may look at a number of simulations on either side of this (to reduce randomness).
Explain why a lower percentile risk measure may be used when capital is alocated to different classes/products?
When we allocate the capital, we may use a different risk measure from that used in assessing the capital requirement. For example, a group’s solvency capital requirement may be based on a target percentile in the tail of the underlying aggregate loss distribution. But we may allocate the diversified capital down to individual classes of business or products for a company in the group with reference to a lower percentile, to prevent over-allocation to catastrophe-type business.
Marginal capital method
We allocate capital with reference to the marginal capital requirements of each segments.
I.e. we consider the additional capital that would need to be held if the element was to be added to the business.
Shapley method
An extension to the marginal capital method, based on game theory.
We allocate the capital with reference to an average of the marginal capital requirements, assuming that the class under consideration is added to the overall portfolio first, second, third, …
I.e. for any one class of business, calculate each capital amount that would be required if we add the class to the overall portfolio first, second, third, etc. We then take the ACTUAL CAPITAL REQUIREMENT AS THE AVERAGE of these amounts
The advantage is that the allocated capital is NOT DEPENDENT ON THE ORDER in which it was allocated to each class.
Proportions Method
May also allocate economic capital to each class of business in proportion to its contribution to the risk metric on a standalone basis.
We would first calculate the required capital separately for each line of business, and work out what proportion of each of these is of the total of the individual capital requirements.
We then calculate the aggregate capital requirement, allowing for any diversification benefits, and allocate this to each class, according to the proportions calculated.
Outline the factors to consider when choosing the capital allocation method.
In general, when we select the method for the allocation of capital across lines of business, we should have regard to the use to which the results will be put and consider desirable properties of the results, such as stability over time. There is not necessarily one method that is best suited in all cases. Typically, we would compare the results from several methods of allocation. We would use our judgement when recommending or setting the final allocation.