9.2 Insurance Companies and Pension Plans

Insurance Companies and Pension Plans

FMP–2 shifts from banks to institutions that pool idiosyncratic risks and provide long-dated promises: insurers and pension plans. Their balance sheets look different from banks—liabilities are policies and benefit promises rather than deposits—but the risk-manager’s questions rhyme: Who bears unexpected loss? How is capital sized? Where do incentives break?

Insurance Categories and Risks

Broad product families:

Life writers care deeply about mortality (deaths sooner than priced) and, for annuities, longevity (insureds living longer than priced). P&C writers care about frequency and severity of claims, catastrophes, and whether loss reserves are adequate. All insurers face investment risk on the assets backing reserves and surplus, plus operational and conduct risk.

Reinsurance transfers peaks (especially cat and large life risks) but introduces counterparty and basis risk if covers are incomplete.

Mortality Tables and Premiums

A mortality table gives probabilities of death by age (and often by sex, smoking status, or underwriting class). Life premiums are set so that the present value of expected benefits and expenses, loaded for profit and risk, is covered by premiums and investment income.

Conceptual one-year term premium for a benefit B at mid-year style simplification:

Net risk premium ≈ q_x × B / (1 + i)

where q_x is the probability a life aged x dies within the year and i is the valuation interest rate. Real pricing adds expense loads, profit margins, and capital costs; multi-year policies embed lapse and reserve dynamics.

Worked example

A one-year term policy pays $100,000 at year-end if death occurs. For a given underwriting class, q_x = 0.002 and the interest rate used in pricing is 3%. A simple net premium is:

Net premium ≈ 0.002 × 100,000 / 1.03 ≈ $194.17.

If expenses and profit require a 40% load on net, the gross premium is about $194.17 × 1.40 ≈ $272. If actual mortality runs at q = 0.003 instead of 0.002, expected claims jump 50% and the product can lose money unless capital and reinsurance absorb the miss.

Mortality Risk Versus Longevity Risk

These risks are not mirrors in a portfolio sense without careful hedging: a pure life book and a pure annuity book can natural-hedge each other to some degree (deaths hurt life writers but help annuity writers), but basis remains—different populations, selection, and improvement trends. Longevity improvement (medical advances) has been a major secular risk for annuity and DB books.

Defined Benefit Versus Defined Contribution

Defined-benefit (DB) plans promise a formula benefit (for example, 1.5% × final salary × years of service). The sponsor bears investment risk, longevity risk, and often inflation/salary risk. Underfunding creates contribution volatility and, in extreme cases, sponsor distress.

Defined-contribution (DC) plans (401(k)-style) specify contributions; the participant bears investment and longevity risk (how long savings must last). The sponsor’s main risks are operational, fiduciary process, and matching-cost commitments—not the open-ended longevity promise of a traditional DB plan.

Hybrid designs (cash balance, target-date defaults inside DC) blur edges but the risk-allocation question remains: who owns the unexpected?

Life Policy Types (Exam Map)

Common life products FRM candidates should recognize:

• Term life — pure death cover for a period; little cash value.
• Whole life — permanent cover with level premiums and cash value buildup.
• Universal / variable life — flexible premiums and/or investment-linked cash values; policyholder may bear more market risk in variable forms.
• Annuities — reverse of life insurance in risk terms: payments while alive; longevity is the core threat to the writer.

Investment-linked products transfer market risk to policyholders but leave the insurer with operational, guarantee (if any), and conduct risk.

P&C Ratios: Loss, Expense, Combined, Operating

Property-casualty performance is often summarized with ratio analysis on premiums earned.

Definitions (standard teaching forms):

• Loss ratio = losses and loss-adjustment expenses / premiums earned
• Expense ratio = underwriting expenses / premiums written (sometimes earned—know the convention stated in the question)
• Combined ratio = loss ratio + expense ratio
• Operating ratio = combined ratio − investment income ratio (investment income / premiums)

Interpretation:

• Combined ratio < 100% → underwriting profit (before considering investment income nuances).
• Combined ratio > 100% → underwriting loss; the insurer may still show overall profit if investment income is large enough that the operating ratio is under 100%.

Worked example

An insurer earns $500 million in premiums. Losses and LAE are $320 million. Underwriting expenses are $140 million. Investment income is $45 million.

• Loss ratio = 320 / 500 = 64%
• Expense ratio = 140 / 500 = 28% (using earned premium for this example)
• Combined ratio = 64% + 28% = 92% → underwriting profit
• Investment income ratio = 45 / 500 = 9%
• Operating ratio = 92% − 9% = 83% → comfortable overall margin on this simplified view

If losses instead run $400 million, loss ratio = 80%, combined = 108%, operating = 108% − 9% = 99%. Underwriting is underwater; investment income barely rescues the operating ratio.

Exam trap: treating a combined ratio over 100% as automatic insolvency. Soft markets often run combined ratios over 100% and rely on float investment income—until markets crash or cats hit reserves.

Moral Hazard and Adverse Selection

Moral hazard: once insured, the policyholder takes less care (or claims more aggressively) because losses are partly borne by the insurer. Deductibles, coinsurance, exclusions, experience rating, and claims investigation mitigate it.

Adverse selection: higher-risk individuals buy more insurance, or buy it more eagerly, than lower-risk individuals when pricing cannot fully observe risk. Underwriting, medical exams, waiting periods, and risk classification fight adverse selection; bans on classification can intensify it.

Both problems inflate claims relative to a naive pooled premium. Risk managers and actuaries treat them as first-order pricing and capital issues, not footnotes.

Capital and Guaranty Funds Versus Banks

Insurers hold capital/surplus to absorb unexpected underwriting and investment losses, analogous to bank capital absorbing UL. Regulation is typically insurance-specific (risk-based capital, reserving rules, asset admissibility) rather than Basel banking ratios.

Guaranty associations/funds protect policyholders if an insurer fails—parallel in spirit to deposit insurance, but usually with coverage caps, assessment mechanisms on surviving insurers, and insurance-law priority rules. They reduce policyholder runs on confidence yet can create moral hazard if poorly designed, just as deposit insurance does for banks.

Key contrast for the exam: banks transform liquid deposits into illiquid credit; life insurers transform long-term premiums into long-duration liability promises. Both need capital and safety nets, but the liability optionality (lapse, surrender, claims inflation, longevity) differs from deposit run optionality.

Synthesis

When you see an FRM vignette about an annuity writer cutting premiums to gain share while longevity improves faster than tables assume, name longevity risk, inadequate capital, and possible adverse selection into the cheap product. When you see a P&C combined ratio of 105% with strong investment income, distinguish underwriting loss from possible still-acceptable operating results—and ask what happens if investment yields fall.