D.1 Economic Capital for Life Insurance

Question 1

Available vs required Capital

Answer 1

Available assets= total available capital (assets - liabilities)

Required capital = capital needed to support the business

Question 2

describe / define Economic Capital

Answer 2

Economic capital = most realistic assessment of future risks.
-amount of capital required to ensure that certain goals are met with a high degree of certainty under a realistic assessment of future risk

calc methods:

• long term projections
• shorter horizon approaches
• hybrid approaches

Measure EC consistently with the economics of the company
-account for insurer objectives, business plans, mgmt decisions, constraints, economic circumstances

Stakeholders:

• policyholders
• regulators
• rating agencies
• shareholders

Question 3

main considerations for developing EC models

Answer 3

9 considerations of EC models:

1. Setting objectives
   - based on real world behaviors of the company
2. Risk Drivers
   - complex risks must be simplified for the models
   - group and classify risk families
   - identify underlying processes
   - collapsing highly correlated risks
   - grouping exposures into indices
   - imposing a structural view of the risk dynamics
   - too many factors can add more complexity than necessary
3. risk evolution
   - stress/scenario testing can be used to assess risk on the company
   - stochastic scenarios or hand picked
4. Management and PH actions
   - Mgmt actions should assumed to be realistic as possible
5. Time Horizon for projection
   considerations:
   -is a full runoff required for the cf model?
   -shorter projections usually align better with business plans
6. Valuation Metrics used for intermediate valuations
   - valuation metric should be linked to the objectives of the economic capital model
   - if assets are actively hedged = MC valuation on both assets and liabilities
   - assets held at book value = discount liabilities on a consistent basis
7. Statistical risk measure
   - Value at risk (VaR) = doesnt account for tail loss distr, encourages low probability + high severity risks
   - CTE = harder to explain, requires more robust model
8. Confidence level
   - regulators seek to reduce the likelihood of failures
   - CI can improve probability of being solvent
9. Inclusion of NB
   - high surplus period = more NB
   - profitable NB will increase capital over longer horizons

Question 4

Liability Runoff vs Finite Horizon Approach

Answer 4

1. Liability Runoff approach
   EC = Current MV of required assets - Best estimate liabilities
   Methodology:
   a. create a set of realistic scenarios for IRs, default rates, and insurance risk drivers
   b. project asset/liability CFs for each scenario
   c. calc intermediate values for each time period
   d. for each scenario: determine the beginning required assets needed to satisfy all future obligations
   e. rank scenarios for a distribution
   f. EC = VAR/CTE of the required assets - best estimate liabilities
2. Finite Risk Horizon Approach
   EC = MV of assets that would be required to ensure that the MC value of liabilities can be covered at a finite point in the future
   methodology:
   a. determine EC on an economic basis
   b. for a number of RW scenarios, project assets and liabilities forward one year, and determine the balance sheet in one year
   -calc the PV of projected economic value of net assets
   c. required assets of scenario = MV of assets at the valuation date - PV step (2)
   d. can calculate the VaR/CTE of the distribution of required assets.

Runoff vs horizon approach:

• runoff approach investigates a runoff of the business
• finite risk horizon approach looks at transfers to a third party
• runoff: not complicated by market movements that dont impact insurers ability to pay claims
• finite horizon approach: more aligned with financial markets, more transparent/comparable from a market perspective
• runoff approach is a better choice when companies have a strong view about long term investments and returns
• runoff looks at tail of outcome over time
• finite horizon models look at avg outcome after a big stress

Question 5

Risk Aggregation methods

Answer 5

accounting for correlations when aggregating EC:

• Total EC required is usually less than the sum of the parts
• however corr can also increase under extreme conditions

1. flat correlation matrix approach:
   total EC = sqrt[ EC1 ^2 + EC2 ^2 + 2 * Corr(risk1, risk2)]
2. scenario aggregation approach
   -integrated scenarios containing multiple risk factors
   -implicitly reflects diversification
   diversification benefit = sum of individual un-diversified amounts - aggregated EC w/ diversifcation

Question 6

types of risks and general shock levels most companies look at

Answer 6

equity risk shock: -45%
IR shocks: up-shock = 190 BPs, down-shock limited by floors
Equity and IR volatility = 17%
Credit risk: default rate shock = +3%
mortality: +/- 10%
mortality improvement: ~0.5%
 Lapse risk: +/- 25%
expense shock: 10%

Question 7

applications of EC

Answer 7

1. Capital Adequacy
   - integrate EC into capital mgmt process
2. capital allocation
   - pro-rata
   - Euler method
3. risk appetite
   - EC can be used to set quantitative target ranges and limits for risk taking
4. Performance Measurement
   - higher risk BUs have more EC allocated
   - EC can be combined with other measures to create a performance metric
   - RORAC = Economic Return / EC
   - Embedded Value uses EC as the basis for required capital
5. Strategic planning
   - EC creates incentive to pursue diversification benefits
   - EC shouldnt be the only metric
6. Pricing
7. M + A
   - Buyers may be influenced to purchase based on added diversification
   - buyers beware of increase capital requirements
   - sellers may lose diversification benefits on sale

Question 8

MC approach for Terminal Valuation

Answer 8

• value liabilities consistently with market prices
• RFR
• embedded options are valued consistently with similar options

advantages
1. assumes the insurer can completely de-risk the balance sheet

disadvantages
1. no standard trade-able assets for insurance liabilities