Mildenhall CH 8-11 Flashcards
3 types of demand for insurance
- Risk transfer (To shift their risk to insurers. Diversification allows them to do this by pooling their risk with other insureds)
- Satisfying demand (to satisfies certain statutory, regulatory or contractual requirements in order for the insured to carry out another desired activity (such as auto insurance, third-party liability)
- Risk financing (the insured seeks to finance uncertainty future contingencies in an efficient manner) It’s typically performed for a single entity over time. It’s used to fund reasonably certain losses in a cost efficient manner. Examples: large deductible and retrospectively rated policies, self-insured retentions, captives
2 critical functions involved in managing a risk pool
- Controlling access to the pool through underwriting and pricing
- Ensuring the pool is solvent by funding risk-bearing assets through the sale of liabilities
Describe parametric insurance contracts
- Policies pay based on an explicit event outcome.
- Easy to underwrite because it does not depend on the characteristics of the insured.
- Hard to design to ensure that the insured has a loss only when a claim is triggered (to prevent the insured from profiting from a claim)
- Insured is also exposed to basis risk (a mismatch between their subject loss and the insurance recovery)
Describe dual-trigger insurance contracts
- Policies pay based on an objective event occurs and it causes an economic loss to the insured.
- The indemnity payment is a unction of an underlying subject loss amount suffered by the insured.
Define capital
Capital equals assets net of all liabilities owed to policyholders.
The largest policyholder liabilities are loss reserves and unearned premium reserves.
Definition: Capital is the funds intended to assure payment of obligations from insurance contract, over and above those funds backing the liabilities.
AKA, policyholder surplus
Define Equity
Equity is the value of the owner’s residual interest in the firm.
It equals assets net of liabilities owed to all parties except owners.
AKA, owner’s residual value, shareholder equity.
4 types of insurer capital
- Common Equity
- Reinsurance Capital
- Debt Capital
- Preferred equity
3 categories of common equity
- Capital stock (equals the par value or stated value of shares issued)
- Additional paid-in capital (equals the excess of amounts paid-in over par value. It’s created when shares are sold at a price higher than par)
- Retained earnings (cumulative undistributed earnings)
Describe reinsurance capital
Reinsurance transaction can be thought of as the sale of the residual value for a specific portion of the business.
If the premium collected by the reinsurer is greater than the ceded losses and expenses to the reinsurer, then there is positive residual value transferred to the reinsurer
Describe debt capital
Debt capital stands above equity in priority in the event of default.
When it is subordinate to policyholder claims, it creates capital. (AKA, surplus note)
Mutual companies use surplus notes to raise capital since they cannot issue shares.
Describe preferred equity
it blends characteristics of debt and equity. It sits above common equity but below debt in priority
Reasons why insurer equity capital is expensive
- Principal-agent problem: (investors and management do not have perfectly aligned incentives)
- No independent validation of insurance pricing. (insurance is not expertizable)
- Equity requires a long-term commitment to a cyclical business.
- Returns are left-skewed. While investors prefer right-skewed returns with big upside.
- Regulatory minimum capital standards can force an insurer into supervision before it’s technically insolvent. in this case, the regulators can restrict dividend payments.
- Double taxation: insurer’s corporate profits and dividend distributions are both taxed
How CAT bonds address the reasons equity capital is expensive
- CAT bonds are not equity and do not have market risk
- CAT bonds are a diversifying, zero-beta asset class. (independent of the financial market)
- CAT pricing can be validated (expertizable)
- There is limited adverse selection
- There is no principal-agent problems since CAT bond cash flows are contractually defined.
- No taxes. Bonds are usually written in tax-free jurisdictions
- CAT bonds are lightly regulated.
- CAT bonds have defined 3-5 year terms. (no long-term commitment)
Two theories of optimal capital structure
- Trade-off theory (the debt and equity mix trades off the costs and benefits of each)
- Pecking order theory (informational asymmetries between management and owners makes equity more expensive)
Describe Solvency II
It uses market valuation of assets and books liabilities on a best estimate basis plus risk margin.
Used in EU
3 components of own funds for Solvency II (assets minus liabilities)
- Minimum capital requirement (MCR) - lowest acceptable capital level before the firm must exit the market
- Solvency capital requirement (SCR) (reflects required capital) If a firm drops below the SCR, regulators can step in to address the issue.
- Free assets - own funds in excess of the SCR
Describe NAIC Statutory Accounting (SAP)
- used in US
- it’s a liquidation basis accounting framework and focuses on the balance sheet.
- Assets that cannot be readily converted to cash to pay policyholder claims are illiquid and considered non-admitted assets
Describe Generally Accepted Accounting Principles (GAAP)
- Used in multiple jurisdictions
- US GAAP follows the SAP treatment for loss reserves
- Unlike SAP, GAAP allows deferral of acquisition expenses
Describe International Financial Reporting Standards (IFRS)
- It focuses more on market values than GAAP
- Loss reserves are valued on a discounted basis and include a risk adjustment
assumptions about financial markets
- Competitive (many small sellers and buyers and undifferentiated products)
- Perfect (there are no information or transaction costs, no bid-ask spread. everyone can borrow or lend at the same risk-free rate.) AKA frictionless
- Complete (enough securities to replicate any set of future period cash flows by securities trading) AKA replicating portfolio
- Arbitrage-free (no potential for a risk-free gain on an initial investment of zero) No arbitrage implies the risk measure is linear. Linear implies additive and homogeneous.
- General Equilibrium (supply equals demand)
Two classes of general equilibrium models
- Classical general equilibrium (prices fundamental securties like stocks and insurance contracts. Classical model price based on supply and demand and rely on diversification and pool to manager risk)
- Derivative general equilibrium (price redundant securities like stock options. Rely on the fact that a redundant security can be replicated by securities trading)
Argument for using the risk-free rate
Premium profit margins should not depend on actual investment portfolios, but only on the risk-free rate and systematic underwriting risk.
Since policyholders do not share in the investment risks of the insurer, they should pay the same premium regardless of the firm’s investment strategy
Argument for using anticipated market return
Adding investment risk increases the probability of default for policyholders and changes their expected loss recoveries. Hence policyholder premiums should reflect the anticipated market return
Advantage and disadvantage of the IRR (Internal Rate of Return Model)
IRR model takes the investor’s perspective.
Advantage: It does not require us to determine discount rates for each cash flow
Disadvantage: it requires a hurdle rate to make the final decision
3 important kinds of frictional costs
- Agency and informational costs (Agency costs: the principal-agent problem where managers incentives do not align with the owners, Informational cost: insurer’s failure to control adverse selection and moral hazards of insureds)
- Double taxation
- Regulation (Regulator can restrict investment opportunities. minimal capital standards)
what is the total pricing problem
To decide the split of asset funding between policyholder premium and investor capital
What is debt tranching (or layering)
Setting the debt priority schedule to define the capital structure.
What does positive risk load mean
Since the distorted survival function increases the expected value of any excess layer, the layer premium is always greater than expected loss. creating positive risk load
Properties of concave distortion function
- g is continuous, except possibly at s = 0, where there can be a jump up to g(0+) >=0.
- g is differentiable, except for at most countably infinitely many points
- g is increasing
- The left-hand and right-hand derivatives of g exist everywhere on (0,1), both decreasing and the right derivative is less than or equal to the left
- g is second-order differentiable almost everywhere, except for a set of probability zero
- g is increasing at decreasing rate
- if g is differentiable then its concave iff g’ is decreasing
Properties of SRM (Spectral Risk Measure)
- it’s law invariant since it’s a function of the survival function of X
- It’s positive homogeneous
- It’s comonotonic additive
- It’s translation invariant if and only if g(0) = 0 and g(1) = 1. In other word, if g is distortion function then SRM is translation invariant
- It’s monotone
- It can be expressed as a weighted average of TVaRs if and only if g is increasing and concave. Since each TVaR is sub-additive, then SRM would also be subadditive.
- Since it’s monotone, translation invariant, positive homogeneous and subadditive, SRM is coherent
The following four statements are equivalent: - risk measure is coherent, comonotonic additive and law invariant
- risk measure equals an SRM for a concave distortion function g
- risk measure equals a weighted average of VaR, where the weights are positive and increasing
- risk measure equals a weighted average of TVaR, where weights are positive.
properties of proportional hazard transform
- It increases the hazard rate proportionately by a factor of alpha
- smaller alpha values correspond to greater risk aversion (greater g(s) values)
consideration when selecting a distortion function
- Simplicity
- Transparency
- Fairness
- Objectivity
- Data-Based
- Best Practice
