Week 7 Insurance Notes

Introduction

Week 7: Insurance overview (Life, Health, and related types).
Purpose: prepare for unlikely, unlucky events and consider affordability and purpose of insurance.
Focus: intuition, concepts, and practical decision-making around insurance needs and policies.

Intuition and core concepts (foundational ideas)

Example setup to illustrate risk transfer and premium: have net wealth $5{,}000$, 7-day trip, accident probability $p = 1 ext{%}$, cost of accident $L = 5{,}000$, insurance premium $ ext{premium} = 60$ (full coverage).
No accident scenario (probability 0.99): wealth remains $5{,}000$ (before considering premium).
Accident scenario (probability 0.01): wealth would drop to $0$ without insurance (costs exhaust wealth).
With insurance, premium paid regardless of accident; insurer pays up to $L$ if accident occurs.

Intuition with numbers: terminal wealth outcomes (travel scenario)

Without insurance:
- No accident: wealth = $5{,}000$ (probability 0.99).
- Accident: wealth = $0$ (probability 0.01).
- Expected terminal wealth: E[W_{ ext{no insurance}}] = 0.99 imes 5{,}000 + 0.01 imes 0 = 4{,}950.
With insurance (full coverage, premium $60$):
- Wealth after travel if no accident: $5{,}000 - 60 = 4{,}940$.
- Wealth after travel if accident occurs: $L - 60 = 5{,}000 - 60 = 4{,}940$ (since insurer pays the $5{,}000).
- Expected terminal wealth: E[W_{ ext{with insurance}}] = 4{,}940 ext{ (in either case)} = 4{,}940.
Interpretation: Paying a small premium can fully insure against a big cost, making the terminal wealth more certain, here giving the same outcome across states when full coverage is used.

Market framing: who gains from insurance?

Me (the individual) sells my risk to the insurance company for $60$ per policy.
Insurance Company buys my risk for $60$ and takes on the probability-weighted loss of $L = 5{,}000$ when the accident happens with probability $p = 0.01$.
Me with insurance: always $4{,}940$; insurer’s per-policy expected profit is not guaranteed, but across many policies it can be positive.

Insurance in a nutshell (macro view)

1) An individual has a small probability of a big loss $L$.
- Loss probability: No fire vs big fire; other large losses also modeled similarly.
2) Insurance company pools many individuals like me to diversify risk.
- Reinsurer: an insurer for insurers; used for very large payouts.
3) Policy price is the expected payout plus a markup to cover costs (admin, profit).
- Expected payout per policy: $ ar{L} = p imes L$.
- Policy cost includes insurer’s costs and markup.
4) Indemnity principle: If a claim is made, the insured is indemnified; there is no gain from claiming beyond the insured amount.

How to think about the two-sided market (policy design and pricing)

The reason the insurance market exists: different degrees of risk aversion; risk pooling across many individuals keeps individual risk manageable.
For any given policy, the insurer’s objective is to set a premium that covers expected payouts plus costs, while remaining attractive to customers.

Insurance basics and policy structure

An insurance policy specifies: which losses are covered, the policy cost (premium), and who receives payment (beneficiary).
Price is not everything; importance of reading the policy, understanding exclusions, and checking claims experience.
Avoid over-insuring or under-insuring; beware of multiple overlapping policies; check for indemnity vs replacement-value coverage.
Useful sources: icnz.org.nz and consumer guidance on best/worst providers.

Buying insurance: practical considerations

List significant items to insure; ensure coverage is acknowledged in writing and that amounts are specified.
Don’t over-insure; don’t insure an item twice; use an excess to reduce administrative hassle and premium costs.
Consider excluding minor small-claim exposure via higher excess or fewer small claims.

Life insurance (overview and rationale)

Purpose: protect those who depend on your income.
- Life insurance protects dependents (e.g., spouse and children).
Income protection vs health insurance: income protection protects you and dependents from income loss; health insurance supplements the public system to access private care.
Life insurance is particularly relevant for the self-employed and for households with dependents.

Life insurance: key terms

Face amount / face value of policy: the amount paid out at death.
Policy owner / policyholder: person who pays premiums; their death triggers payout.
Beneficiary: person designated to receive proceeds.
Insurable interest: you may insure someone else’s life only if you have an insurable interest.

Should you buy life insurance? when/how much

Not always necessary if you are single with no dependents or if your household can absorb the loss.
Potentially wise if you have dependents or a single income with dependents, own a business, or to cover debts/ buy-out in business.
Payouts are generally not taxable.

Needs assessment and calculation approaches

Two main approaches to determine how much life insurance you need:
- Earnings Multiple Approach
- Needs Approach
Earnings Multiples approach (illustrative):
- Example: want 20 years of income for a replacement scenario: 20 years × annual income $80{,}000, investment return after tax 6%.
- Present value calculation corresponds to the PV of a 20-year annuity due, which yields a figure like 972{,}750. (after-tax) for the example provided.
Needs Approach: determine cash needs after death across several buckets.
- Immediate needs: debt elimination, transitional funds.
- Dependency expenses and ongoing needs: spousal income, child education, retirement income.
- Adjust for inflation; compute in real terms.

Term vs Whole-of-life vs other life insurance features

Term insurance:
- Pure life coverage for a specified term (e.g., 10, 25 years, or to age 55).
- Pros: lower cost, may allow higher coverage; cons: cost may rise at renewal, no cash value, potential non-renewal.
Whole-of-life (permanent) insurance:
- Provides life coverage and a cash-value component; premiums typically higher; continues to age or illness; not always available in NZ.
- Advantages: coverage continues even with health changes; cash value accumulates; nonforfeiture rights.
Increasing/ decreasing term and group term:
- Decreasing-term: level premium, decreasing payout to reflect decreasing need (e.g., mortgage payoff over time).
- Renewable-term: right to renew without re-qualifying but at higher premium.
- Group-term: one policy for a group (e.g., employees); often tied to debt repayment in credit/mortgage insurance; payout decreases with debt.

Group term, mortgage, and business considerations

Group-term: single policy for a group; may be used for employees or partners; debt payoff alignment with mortgage or business needs.
For business owners: life insurance can help pay off business debts or enable buyouts.

Policy features and riders (optional enhancements)

Riders: add-ons that amend or extend coverage at extra cost.
- Waiver of Premium for Disability Rider
- Accidental Death Benefit Rider (or Multiple Indemnity)
- Guaranteed Insurability Rider
- Cost-of-Living Adjustment Rider
- Living Benefits Rider
Endorsements: tailor a policy to specific needs.
Settlement options: how death benefits are paid out.
- Lump-sum settlement
- Interest-only settlement
- Annuity settlement options: Straight Life Annuity; Period Certain Annuity; etc.
Non-forfeiture rights: option to take cash value instead of continuing death benefit if policy is surrendered.

Funds and payout mechanics

Cash value vs death benefit: Whole-of-life provides cash value; term provides only death benefit if term ends or dies during term.
Premium payment patterns: Continuous, single, or limited-premium payments.

Reading and comparing policies

Not all insurers are equal; check claims experiences and insurer stability.
Be mindful of brokers/agents: commissions may influence recommendations; seek independent quotes.
Beware of “best and worst providers” lists and use credible sources.

Health insurance (overview)

Health insurance can cover GP visits, specialists, surgery, and hospital stays.
Basic health cost components:
- Routine costs (GP visits, etc.)
- Surgery and hospital stays
Key idea: health insurance often aims to cover costly, high-value items; some costs are cash-consequential (covered by public system) and others are insured for private care.
Some people opt to self-insure (self-fund) rather than buy comprehensive health cover; coverage depends on policy and potential treatment exclusions.
Group health insurance (no medical exam) vs individual policy (age/health-based underwriting).

ACC and health issues

ACC (Accident Compensation Corporation) covers injuries from accidents and related time off work.
Moral hazard concerns: insurance can alter behavior; ACC also monitors claims criteria to avoid over-claiming.

Income replacement insurance (disability income protection)

Purpose: replace income if illness or disability interrupts earnings.
Source examples: ACC, sick leave; relatively affordable.
Key terms: definition of disability, residual/partial payments, benefit duration, waiting period, waiver of premium, noncancelable terms.

Property insurance (home and contents)

Property insurance pools financial risk of property losses (fire, burglary, earthquake) to mitigate large losses.
Value bases:
- Indemnity (market value)
- Replacement cost
- Agreed value
Defined risk and umbrella policies cover additional liabilities.
Dwelling, other structures, and loss of use are common components.
Underinsurance risk: insure replacement cost, not just market value; revise regularly due to rising building costs.
Example: value $1,000,000; insured for $800,000 (80%); in a $500,000 claim, you may receive only 80% of the loss (i.e., $400,000).
Factors affecting cost: age of property, size, construction materials, excess, location (fire service access), use (home, rental, holiday), alarms (smoke, burglar).
Discounts and cost-saving strategies: high excess, security systems, multi-policy discounts, annual payment, other discounts (age, claims history).
Inventory and documentation: detailed asset inventory with purchase dates, costs, models, serial numbers; keep receipts.

Contents insurance

Covers contents and liability; often included with homeowners policies but may be separate if renting.
Contents bias toward replacement cost coverage; consider riders for high-value items (jewelry, art).
For students/first-year housing, contents insurance is especially relevant.

Vehicle insurance

Types:
- Third party (damage to others’ property or people; sometimes includes fire/theft)
- Comprehensive (damage to your own vehicle or theft; usually market value, sometimes agreed value)
Determinants of cost:
- Excess, vehicle type, usage, driver characteristics (age), driving record, location, discounts (alarm, multi-car, secure parking).
Strategies to reduce cost: defensive driving, choose a common make/model with readily available parts, maintain good driving record, raise excess, shop around.

After an accident: practical steps

Get medical help for the injured.
Move vehicles to a safe place.
Obtain witnesses' identification.
Cooperate with police.
Take a blood alcohol test if you suspect the other driver is intoxicated.
Write down your recollection of the accident.
Do not admit guilt or sign statements.
Obtain a copy of the police report and verify accuracy.
Contact your insurance agent promptly.
Cooperate with your insurer.
Keep records of all expenditures related to the accident.
For serious accidents, consult a lawyer to understand rights.

How to keep insurance costs down (summary of discounts and tips)

High excess ( Higher deductible ) can lower premium.
Security systems and alarms can yield discounts.
Multi-policy discounts (bundling) can lower total cost.
Pay annually rather than monthly to avoid recurring fees.
Other discounts: age, claims history, etc.
Shop around and compare quotes from high-quality insurers.

Summary of insurance types and roles

Life insurance: protects dependents; terms include face amount, policy owner, beneficiary, insurable interest.
Income protection: covers loss of income due to disability/illness.
Health insurance: complements public system; can be hospital-focused or more comprehensive.
Property insurance: protects home and possessions; includes dwelling, other structures, loss of use; watch for under-insurance; insure replacement cost.
Contents insurance: protects personal belongings and liability; may require riders for valuables.
Vehicle insurance: third party vs comprehensive; coverage depends on risk factors and driving behavior.
Business insurance: protects business risks (property, liability, etc.).
The insurance decision involves balancing cost, risk, and the need for protection; actuarial methods and risk pooling underlie pricing and coverage.

Final notes on policy design and ethics

Insurance aims to minimize severe financial consequences and enable risk pooling across many individuals.
Actuaries use statistics to estimate average payouts and set premiums accordingly.
Privacy, consent, and transparent policy terms are essential; ensure clear understanding of coverage, exclusions, and claim rights.
Moral hazard and adverse selection are practical concerns in designing insurance schemes and public programs like ACC.

Quick reference formulas and concepts

Expected payout per policy: E[ ext{payout}] = p imes L
Expected profit per policy (insurer): E[ ext{Profit per policy}] = ext{premium} - pL
For N identical policies with probability p of a claim and loss L: E[ ext{Total Profit}] = N imes ( ext{premium} - pL)
Example (from intuition): with $N=100$, premium $60$, $p=0.01$, $L=5{,}000$:
- Total premium: 100 imes 60 = 6{,}000
- Expected payout: 100 imes 0.01 imes 5{,}000 = 5{,}000
- Expected profit: 6{,}000 - 5{,}000 = 1{,}000
PV of a 20-year annuity due (earnings-multiple example):
- PV = 80{,}000 imes rac{1 - (1+0.06)^{-20}}{0.06} imes (1+0.06) ";
- Result given: approximately 972{,}750 (after-tax in example).
Underinsurance example: if replacement cost is $1{,}000{,}000$ but insured for $800{,}000$ (80%), a $500{,}000$ claim could be paid at only 80% of loss: 0.80 imes 500{,}000 = 400{,}000.$$n