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: 1. What do you do with the total capital? 2. How do you evaluate the components? 3. What does it mean to be in a portfolio?

Allocation vs Consumption Consumption Leave the total capital intact Allocation Take the total capital and split it up OR Allocate the marginal change in the total capital

Allocation vs Consumption Consumption Each component has “access rights” to make claims against the total capital Allocation Give the allocation to each component

Allocation vs Consumption Consumption Evaluate each component’s potential claims (likelihood and magnitude) on the total capital Allocation Evaluate each component as if standalone with their share

Being in a Portfolio means… Consumption Being standalone with potential access to all the capital But everybody else has similar access rights Allocation Being standalone with less capital But still having access to all the capital if necessary

Allocation vs Consumption Consumption Each component must pay for the likelihood and magnitude of its potential claims against the pool Allocation Each component must clear its marginal cost of capital hurdle

Allocation vs Consumption Consumption Uses an expanded risk- return evaluation framework similar to utility theory Allocation Uses a single risk measure to determine required capital

Allocation vs Consumption Consumption Uses scenario- level detail to evaluate scenarios and split the risk cost among the driver components Allocation Uses some dependency measure to split the covariance among components

Allocation vs Consumption Consumption Flexible framework and scenario detail is limited only by the dependencies in the generating model Allocation Choice of risk measure and aggregation methodology determines dependency relationship

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 Insurance 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?