Mildenhall Chapter 8 Flashcards
(30 cards)
Demand For Insurance
- Risk Transfer: classical motivation
- Satisfying demand: statutory, regulatory, or contractual requirements to purchase insurance
- Risk financing: the insured is looking to finance future contingencies (reap tax savings sooner)
Components of an Insurance Company
Insurer managing a risk pool that has 2 critical functions
* Pool Co: controling access to the pool via underwriting and pricing
* Capital Co: keeping the pool solvent by maintaining assets and selling liabilities
Others:
* Claim Co: handles claims OR use 3rd party claim adjusters
* Customer Co: company’s own writer, or handled by independent agents and brokers
* Investment Co: asset management services
3rd Party Services:
* Reinsurance and sidecar arrangements can provide stand-alone Capital Co services
* Managing general underwriters can provide stand-alone Pool Co. services
* Independent investment co. provide asset management services for the pool’s assets, very common for smaller insurers
Why are insurer companies inefficient? Why do they exist?
Less efficient:
* Underwriting is costly
* Insurer capital is costly
Insurers offers strong advantages
* By aggregating private loss data, the insurer is able to better underwrite the risk
* Risk pools allow the capital to be used more efficiently
* If risk pools existed for a long time, investors will find the management competant, reducing the cost of capital
* Mandatory insurance laws are effective only if they require that insurance be purchased from well capitalized insurers
Requirements of Insurance Contract
- Clear and objective
- Easy to adjust
- Discourages fraud
- Pay no more than the subject loss. i.e. the insured should never profit from an insurance claim
Insurance Contract
Parametric Insurance
What is it? Pro/Cons
Pays based off an explicit event, defined by an objective physical description e.g. hurricane intensity and landfall or earthquake magnitude
Pros - easy to underwrite because it does not depend on the characteristic of the insured
Cons - hard to design to ensure that the insured has a loss when a claim is triggered - to prevent insured from profiting from a claim
Basis risk - mismatch between the subject loss and insurance recovery
Insurance Contract
Dual Trigger Basis / Indemnity Payment
An objective event occurs and it causes an economic loss to the insured
Indemnity Payment is a function of an underlying subject loss amount suffered by the insured:
* limits / sublimits
* occurrence
* aggregate deductible
Indemnity Function, f
Conditions, example where it fails
function of:
* limits / sublimits
* occurrence
* aggregate deductible
Indemnity function f, subject loss L
1. f(L) ≤ L - Pay no more than the subject loss. i.e. the insured should never profit from an insurance claim
2. f(L) ≥ 0
3. f(L) is a monotonic function of L
4. L - f(L) is a monotonic function of L
5. f is continuous
Monotonic - always increasing or staying constant OR always decreasing and staying constant
When it fails:
Franchise deductible (aka disappearing deductible) - when a loss exceeds deductible d then F(L) = L, otherwise f(L) = 0
Capital & Equity
Capital = Assets - Policyholder Liabilities
where policyholder liabilities predominantly consist of loss reserves and unearned premium reserves
Equity = Assets - Total liabilities
where total liabilities refers to liabilities owed to ALL parties
Types of Insurer Capital
Types of Insurer Capital
Common Equity - selling shares of stock to investors
* Includes (lowest priority) ownership interest by common stockholders
* Bear the ultimate risk and receive the benefit of success
Reinsurance Capital:
* Insurer selling a specified portion of business to a special class of investors called reinsurers
* Reinsurance functions as an “off-balance sheet” capital because regulatory capital formulas operate on a net basis
* Can also be issued as an insurance-linked security e.g. cat bond or industry loss warranty
Debt Capital - borrowing money (bank loan)
* Takes priority over equity if insurer was to default, but lower priority than insured’s claims (surplus notes)
* If insurer cannot replay, “defaults”, give debt holder authority to take over
Preferred Equity:
* Characteristics of both debt and equity
* Takes priority over equity, but lower priority than regular debt
Cost, Cost certainty, Tax deductible
Comparison of Types of Capital
Repay Obligation, Triggers “default”
Equity | Reinsurance | Debt
* Cost: High, Variable, Variable
* Cost Certainty: Residual, Contractual, Known
* Tax Deductible: No, Yes, Yes
* Replayment Obligation: No, No, Yes
* Triggers Default: No, No, Yes
Why Insurer Equity Capital Is Expensive?
- Principal-agent problem - investors and management can have different incentives. Difficult for investors to monitor management (especially for nonstandard LOBs)
- Not expertizable - hard to validate if insurance pricing is appropriate (except for cat risk, where theres 3rd party models)
- Equity requires a long term committment from investors. Because insurance is a cyclical business, investors maybe taking out money at a bad time
- Returns are left-skewed - lower upside, unlike tech stocks that are right-skewed with big upside
- Regulatory min capital standards can force insurer into supervision even before insolvent. Then the dividends and other capital withdrawals can be restricted
- Returns to investors may be souject to double taxation - insurer pays corporate tax and dividend distributions are also tax
Why Cat Bonds are better than Equity Capital
Disadvantage
- Do not have market risk
- Provides diversification, independant of market
- Cat bonds are expertizable - investors can validate loss costs and quantify risk independantly from management
- No taxes - bonds are usually written in a tax-free jurisdiction
- No regulation - bonds ar eusually written in a lightly regulated jurisdiction
- Lower tenor - bonds have a defined 3-5 year term
Disadvantage - illiquid and traded in a thin market
Optimal Capital Structure Considerations
Trade-Off Theory :
* Equity is generally more expensive than debt
* But with debt, debt holders have the right to force bankruptcy
Pecking Order Theory:
* Informational assymmetrices between management and owners make equity more expensive
Financial Market Assumptions
Competitive - many small buyers and sellers and undifferentiated products
Perfect aka. frictionless market
* No information or transaction costs
* No bid-ask spread
* Able to borrow/lend at the same risk free rate
* No restrictions on short sales
* No taxes
Complete - possible to replicate any set of future period cash flows by trading securities
Security is a set of cash flows
Redundant vs Fundamental
Redundant - securities that can be generated from the value of other securities
Otherwise, they are fundamental securities (e.g. company’s common stock)
Arrow-Debreau Security
Pays $1 in state w and $0 in other states
Arrow-Debreau Security, X = sum[X(w) * 1_w] where 1w is indicator function
1_w is worth P(w) - it only pays $1 when w occurs
Market value of 1_w is worth Z(w) * P(w)
Market Value of general security
* sum[X(w)Z(w)P(w)] - X is the cashflow, P probability, Z discount rate
* If $1 is certain, then sum[Z(w)P(w)] = E[Z] = 1/(1+r)
Z(w) = stochastic discount rate
Risk-Adjusted Probability, Q(w)
Risk-Adjusted Present Value
Q(w) = Z(w)P(w)(1+r) = Z(w)P(w) / E[Z] = Z(w)P(w) / sum[Z(w)P(w)]
E[Z] = sum[Z(w)P(w)] = 1/(1+r) = risk free rate
Risk adjusted PV = 1 / (1+r) * sum[X(w)Q(w)]
Z(w) = stochastic discount rate
Arbitrage
Opportunity to make a gain with no chance of loss, without making an initial investment
Discounted Cash Flow Models
DCF models discount each cash flow (including initial investment and recurring revenues and expenses) at an appropriate risk-adjusted rate
If total DCF is positive then the project should be taken
DCF analysis takes the insured’s perspective - focuses on premium and loss payments
DCF is forward looking, focusing on the cash flows from new policies
Myers-Cohn Fair Premium Condition
Premium is fair if: when a policy is issued, the resulting equity value equals the equity invested in support of that policy
aka the premium should not increase or decrease equity
If premium increases equity, then it implies a transfer of wealth from policyholders to investors and vice versa
If rates are unfair, invetors have an incentive to write more or less insurance
Fair Premium
Accounting value of liabiltiies = objective expected present value
Market value of liabilities = risk-adjusted expected present value
Market Value & Accounting Balance Sheet
After writing a policy
When is premium fair?
Market value balance sheet - assets a, liabilities D, equity S
Accounting BS - assets a, liabilities L, equity Q
Writing a new policy
* D > L because D includes a risk load
* a increases by premium P for both
* Q > S if if premiums contain a positive margin (accounting gain at issue)
* Market value of equity increases by P - D
Premiums are fair when P = D
Using both accounting values and market values
ROE
Premium when fair premium
Accounting Values:
Rs = (V1 - Q) / Q
= Rf + L/Q * (Rf -RL)/(1+RL) * (1-t)
Market Values:
Rs = Ra + D/S * (Ra - RL)
Can set Rs equal under Myers-Cohn’s fair premium condition that P = D
Rs = return on equity| Ra = return on assets | RL = return on loss
D = liabilties | S = equity
Required ROE
Rs = Ra + D/S * (Ra - RL)
Rs = return on equity| Ra = return on assets | RL = return on loss
