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Capital Consumption. Don Mango American Re-Insurance 2002 CAS Risk and Capital Management Seminar. Building Bridges. TVaR is the best single risk measure we have found yet Particularly good for catastrophe budget allocation – additive
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Capital Consumption Don Mango American Re-Insurance 2002 CAS Risk and Capital Management Seminar
Building Bridges • TVaR is the best single risk measure we have found yet • Particularly good for catastrophe budget allocation – additive • I agree with Coherence axiom 1 (translation) and 4 (monotonicity)
But… • I am not sure Coherence axioms 2 (sub-additivity) and 3 (positive homogeneity) generally apply for reinsurance • There may be super-additive combinations (Kreps) • for large reinsurance limits • That is why reinsurers take shares of programs
Allocation vs Consumption • Three questions: • What do you do with the total capital? • How do you evaluate the components? • What does it mean to be in a portfolio?
Consumption Leave the total capital intact Allocation vs Consumption • Allocation • Take the total capital and split it upOR • Allocate the marginal change in the total capital
Consumption Each component has “access rights” to make claims against the total capital Allocation vs Consumption • Allocation • Give the allocation to each component
Consumption Evaluate each component’s potential claims (likelihood and magnitude) on the total capital Allocation vs Consumption • Allocation • Evaluate each component as if standalone with their share
Consumption Being standalone with potential access to all the capital But everybody else has similar access rights Being in a Portfolio means… • Allocation • Being standalone with less capital • But still having access to all the capital if necessary
Consumption Each component must pay for the likelihood and magnitude of its potential claims against the pool Allocation vs Consumption • Allocation • Each component must clear its marginal cost of capital hurdle
Consumption Uses an expanded risk-return evaluation framework similar to utility theory Allocation vs Consumption • Allocation • Uses a single risk measure to determine required capital
Consumption Uses scenario-level detail to evaluate scenarios and split the risk cost among the driver components Allocation vs Consumption • Allocation • Uses some dependency measure to split the covariance among components
Consumption Flexible framework and scenario detail is limited only by the dependencies in the generating model Allocation vs Consumption • Allocation • Choice of risk measure and aggregation methodology determines dependency relationship
Insurance Capital • Insurance Capital is a Claims Paying Reservoir • Subject to unpredictable future inflows and outflows • Covering shortfalls from pool of expected costs collected from revenues • Insurance capital allocation is more like the “granting of future water rights”
Insurance Capital • Critical issue is exposure of capital to possible consumption by contracts • Likelihood and magnitude of drawdowns • Co-incidence with other drawdowns • Systemic shocks • Current capital is most exposed to reserve shocks for all but shortest tail property
Insurance Capital • Cost of maintaining capital is • A cost of business • An overhead expense • Overhead expense? Risk-based allocation • Huge mismatch: Current underwriting activities are exposing future capital
Esoteric Arguments • Once you go down to the scenario level, supporting capital loses a lot of its meaning and relevance • Insurance products consume capital in the future, so focus the attention there • Allocated supporting capital is completely theoretical—prescriptive
Esoteric Arguments • Capital is a holistic portfolio phenomenon • May not be meaningfully divisible • Can we allocate life to our organs? • Can we allocate the Lakers success to each player?