Available Capital (Capital/Own Funds)
Definition
Any resources held by the company in excess of the value of its technical liabilities. It is the excess of financial resources over the value of liabilities. It may also be referred to as free reserves, free assets, the solvency margin, shareholders’ funds, or capital employed. In Solvency II terminology, it is also known as ‘Own funds’.
Required Capital
Definition
The amount of capital an insurer needs to hold, which depends on the purpose of the modelling exercise. It is determined by linking a measure of the required capital to a desired level of loss absorption ability.
Regulatory Capital (Solvency Capital)
Definition
The amount of capital the regulator deems appropriate in order to protect policyholders’ interests. This is often referred to as regulatory solvency capital. It is the minimum level that all companies must adhere to.
Economic Capital
Definition
The amount of capital an insurer believes it should hold to fulfil its own business objectives. It is typically determined based on the risk profile of individual assets and liabilities, the correlation of risks, and the desired level of overall credit deterioration the insurer wishes to withstand. It may be measured on a more realistic basis than regulatory capital.
Capital Allocation
Definition
Capital allocation involves allocating the overall capital required (which has been determined in a capital assessment exercise and which allows for diversification effects) between different classes of business or products. This is typically a ‘top-down’ exercise (starting with an overall position and breaking it down) and is done for performance measurement, pricing, and business planning purposes.
Excess Capital (Free Capital)
Definition
The balancing item derived from the relationship: Economic Capital + Excess Capital = Total Capital. This is also known as Free Reserves or Free Assets.
Calculation Process for Capital
Step by step method
- Define the Purpose and Risk Measure: Specify the purpose of the investigation and define the required risk measure (e.g., Value at Risk (VaR)). The risk measure links the outcome (e.g., balance sheet deficit) to the capital required, defined by a confidence level (risk tolerance) and a time horizon.
- Define the Risk Profile and Assumptions: Identify the significant risks facing the business (e.g., insurance, market, credit, operational risks) and determine the parameters and assumptions (premiums, claims, expenses, investment return, reinsurance, economic variables, etc.) required by the model.
- Construct the Model: Choose the form of the model (deterministic or stochastic). If calculating Economic Capital, produce an economic balance sheet by calculating the Market Value of Assets (MVA) and the Market Value of Liabilities (MVL). Available capital is MVA minus MVL.
- Run Simulation/Scenarios: Run the model using stress tests, scenario tests, or stochastic simulation (running the model many times) to project future cashflows and outcomes.
- Allow for Diversification: Adjust the required level of capital for the fact that risks may be negatively correlated (diversification effect).
- Quantify Required Capital: Use the output distribution to calculate the capital requirement corresponding to the chosen risk measure (e.g., the 99.5% VaR).
Proportions Method (Risk-Based Capital Allocation)
Step by step method
This method allocates the aggregate capital requirement according to the proportional standalone risk of each class.
Step-by-Step Methodology:
1. Calculate Standalone Requirements: Calculate the required capital separately for each line of business, assuming a standalone risk basis (i.e., before allowing for diversification benefits).
2. Determine Proportions: Calculate the proportion that each standalone requirement is of the total sum of all standalone requirements.
3. Calculate Aggregate Requirement: Calculate the aggregate capital requirement for the whole company, allowing for diversification benefits.
4. Allocate Capital: Allocate the aggregate capital requirement (from Step 3) to each class according to the proportions calculated in Step 2.
Marginal Capital Method
Step by step method
This method allocates capital based on the “last in” principle, measuring the reduction in total capital required if a segment were removed.
Step-by-Step Methodology (Focusing on a single portfolio permutation):
1. Select Class Order: Determine a sequence in which classes of business are hypothetically added to the portfolio (e.g., A then B then C).
2. Calculate Base Capital: Calculate the capital required for the first class (A).
3. Calculate Marginal Capital: Calculate the capital required for the combined portfolio (A+B), and the marginal capital for B is the increase in capital from A to (A+B).
4. Iterate: Repeat the marginal calculation for all subsequent classes (e.g., marginal capital for C is the increase from (A+B) to (A+B+C)).
5. Allocation: The marginal capital calculated for each class in this specific order is the allocated capital.
Shapley Method
Step by step method
The Shapley method extends the marginal capital method to ensure the allocation is independent of the order in which classes are considered.
Step-by-Step Methodology (for classes A, B, C):
1. Calculate All Permutations: Perform the Marginal Capital calculation (Step 1 to 4 above) for every possible permutation of the classes (e.g., ABC, ACB, BAC, BCA, CAB, CBA).
2. Average Marginals: Calculate the average of the marginal capital requirements determined for a specific class (e.g., A) across all permutations.
3. Final Allocation: The resulting average for each class is the allocated capital requirement.
Percentile Allocation Method
Step by step method
While the sources do not provide a rigid computational formula for the percentile method, its application is described within the context of allocating the total diversified capital requirement:
- Determine Aggregate Requirement: Calculate the company’s overall diversified capital requirement, typically using a high percentile (e.g., the 99.5th percentile) of the aggregate loss distribution, as determined by a stochastic capital model.
- Select Class Percentiles/Layers: For the purpose of allocation, select a specific percentile or a range of percentiles/layers to define the capital required for each individual class of business.
- Allocate Capital: The capital allocated to a class is then calculated based on the loss outcome corresponding to the selected percentile (or percentile-defined layer) of that class’s risk distribution.
Insurance risk
Definition and Assessment Methodology/Process
Risk of loss from the inherent uncertainties about the occurrence, amount, and timing of insurance liabilities, expenses, and premiums. This is split into Underwriting (Premium) Risk (risks yet to be written/earned) and Reserving Risk (risk that technical reserves already held are inappropriate).
Underwriting Risk: The capital required is the difference between the underwriting result at the chosen risk tolerance level and the underwriting result on a realistic basis (best estimate).
Reserving Risk: The capital impact is the difference between the eventual settlement cost at the chosen risk tolerance level and the current reserves on a best estimate basis. Claims should be divided into granular classes and claim types (attritional, large, catastrophe). Catastrophe claims are modelled using stress tests or proprietary catastrophe modelling software.
Market Risk
Definition and Assessment Methodology/Process
Risk resulting from market movements causing fluctuations in the value of assets or the income from assets. It exists when asset movements are not matched by corresponding liability movements.
Requires consideration of changed market values, variation in interest rates (if discounting liabilities), and currency movements. Can be modelled by stress testing (simple) or using an Economic Scenario Generator (ESG) in an integrated stochastic capital model. The capital charge allows for events that cause asset values to fall relative to liabilities at the chosen confidence level.
Credit Risk
Definition and Assessment Methodology/Process
Risk of loss if another party fails to meet its financial obligations (e.g., failure of reinsurers) or fails to perform them in a timely fashion. Split into Investment Credit Risk (e.g., non-government bonds) and Counterparty Credit Risk (e.g., reinsurance recoverables).
In stochastic modelling, assess the probability of default and the degree of loss given default for each counterparty. Investment credit risk often uses financial strength ratings and migration matrices (transitional probability of moving between ratings). Stress tests are necessary to check model reasonableness and calibrate assumptions.
Operational Risk
Definition and Assessment Methodology/Process
Risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events (e.g., fraud, mismanagement).
Identification: Compile a ‘risk register’ and involve senior management/staff with detailed working knowledge (brainstorming).
Modelling: Stochastic modelling is possible (often using frequency/severity simulations), but a deterministic scenario-based approach is often used in practice. The charge covers the balance of operational risks not dealt with elsewhere, avoiding double counting.
Liquidity Risk
Definition and Assessment Methodology/Process
The potential that a firm is unable to meet its obligations as they fall due as a consequence of having a timing mismatch between assets and liabilities.
Integrated Assessment: Assessed in conjunction with insurance and market risks, as scenarios from those risks (e.g., large claims (insurance risk) or asset value falls (market risk)) can trigger liquidity risk. Requires testing the impact on the firm’s cash position via stress/scenario tests or stochastic simulations.
Group Risk
Definition and Assessment Methodology/Process
The risk a firm experiences from being part of a group as opposed to being a standalone entity.
Scenario-based Approach: A stochastic modelling approach is unlikely to be appropriate. A scenario-based approach is often used in practice to assess the impact of group-wide losses or funding arrangements.
Data Requirements (Types and Items)
- Premiums/Exposure: Gross and net unexpired premiums and planned premiums (by class). Potentially planned written exposures and gross premium per unit of exposure.
- Claims: Gross unpaid claims (by class), claims payment profiles (sizes, frequencies, and settlement patterns).
- Large Losses/Catastrophe: Details of large individual claims and associated limits, and aggregate exposure by location (for catastrophe modelling).
- Reinsurance/Credit: Reinsurance exhaustion and reinsurer downgrade assumptions. Historical reinsurer failures and credit ratings for current reinsurers.
- Expenses: Proportion of acquisition costs, administration costs, and historical expense inflation.
- Investment/Economic: Historical inflation, government bond yields, corporate bond yields, equity returns, and exchange rates. Investment returns split by asset class.
- Operational/Group: The firm’s risk register (for operational losses) and input from risk/operations management on the likelihood and magnitude of extreme operational losses.
- Financial/Corporate: The tax rate on profit and tax offset from carried forward losses, and the board policy on dividend payments.
Assumptions Requirements
- Premium/Business Growth: Future rate changes and planned exposures for new business.
- Claims: Expected timing and amount of future claims on current and future business.
- Reinsurance: Reinsurance recoveries, costs, and payment profiles.
- Expenses: Fixed and variable expenses, commission, and expense inflation.
- Investment/Economic Variables: Expected investment returns, volatilities, and dependencies between asset classes and economic variables (inflation, interest rates, economic growth).
- Operational Losses: Assumptions needed to model the frequency, likelihood, costs, and variability of operational losses.
- Tax and Dividends: Tax rate on profit retained and dividend payments.
- Correlation: Assumptions specifying correlations between variables must be set (e.g., between underwriting classes, risk types, or years of account).
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Insurance Types29
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Risk Characteristics and Policy Design6
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Reinsurance and alternative risk transfer6
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Data and Reserving15
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Risk and Volatility6
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Regulatory and financial management5
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Operations and delays5
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Investment strategy6
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Pricing12
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Reserving36
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Reinsurance37
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Capital Modelling19
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Investments11
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Actuarial investigations23
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Products21
