16.9 Setting Capital Requirements

ERM help insurer find the optimum level of capital that balances efficiency and prudence

  • Policyholders (acting through regulators and rating agencies) demand adequate capital

  • Shareholders require that capital be used efficiently

Set capital to maximize insurer’s value creates a conceptual framework that unifies the competing requirements of prudence and efficiency

Approaches to setting capital requirements:

1. Default Avoidance:
Focused on the tail and protecting policyholders

Caveat:

  • S/h will be hurt at much lower loss amount

  • We have the least confidence in the tail of the model

\(\hookrightarrow\) More feasible and relevant to focus on thresholds less extreme than default

2. Other Thresholds (Lower than probability of ruin):

  1. Probability of downgrade

    • Significant loss \(\leadsto\) \(\downarrow\) financial rating \(\leadsto\) \(\downarrow\) franchise value > loss itself

    • Franchise value: customer base, agency relationships, reputation, infrastructure and expertise

  2. Sufficient capital to service renewals

  3. Survive and thrive after major cat

3. Other practical method

16.9.1 Convert Probability to Loss

Associate the selected probability level with amount of financial loss

  • Smallest amount of loss, \(\alpha \%\) of the time \(\Rightarrow\) \(VaR_{100 - \alpha \%}\)

  • Average loss, \(\alpha \%\) of the time \(\Rightarrow\) \(TVaR_{100 - \alpha \%}\)

  • 1-in-\(x\) years event loss no more than \(y \%\) of capital \(\Rightarrow\) \(\dfrac{100}{y} \times TVaR_{1 - \frac{1}{x}}\)

Important: Risk measures do not tell us how much capital to hold; They tell us for a given level of capital, what is the risk to the company

  • Determination of optimal capital level is not purely a risk measurement exercise

    • Need to balance sufficient financial strength to attract business and the need of shareholders to achieve attractive return

  • Risk measurement quantifies the risk the company is exposed to in relationship to the capital so established

  • Strategic risk decisions can then be made in the framework created

  • Capital is not set by risk measures, but analyzed by them to understand the sources of risk and for further strategic decision making

16.9.2 Risk Adjusted Performance

Allocate capital to business units \(\Rightarrow\) Calculate the rate of return \(\dfrac{\text{Profit}}{\text{Capital}}\) for that unit \(\Rightarrow\) Compare RoR across BUs

Can also allocate risk capital to investments \(\Rightarrow\) Compare riskiness of investments and u/w

  • Validity of such a comparison will depend on the consistency of the risk measures that are developed

  • See ERA 2.2 for more detail