FMP 2: Insurance Companies and Pension Plans
An insurance contract sells protection against a named adverse event. The buyer is the policyholder, and the price is paid in instalments called premiums. In most years nothing happens and the insurance company pays nothing. When the event occurs, the payment running the other way is large relative to the premium and covers all or part of the loss.
Almost every contract sits in one of two families. Life insurance in its simplest form takes a monthly or annual premium for as long as the policyholder lives, and death ends the premiums and triggers a lump sum to the named beneficiary. Property and casualty insurance runs for one year, pays for losses from accidents, fires, thefts and similar insured events, and is renewed annually. That cycle is the pricing difference: a life premium is generally fixed for the whole contract, while a property and casualty premium moves each year. Property and casualty cover is also called non-life insurance, with health insurance a third category.
Pension plans belong in the same conversation
Employer sponsored pension plans run on machinery a life insurance company would recognise. Employee and employer both pay in during working life, and the pot funds an income lasting from retirement until death. Because that cost turns on how long the retiree lives, a pension plan carries the demographic exposure of an annuity contract.
The risks an insurance company runs
On the liability side sit mortality risk and longevity risk, the two ways a population can fail to die on the schedule the pricing assumed, plus catastrophe risk, where one hurricane turns thousands of policies into a single correlated claim. On the asset side sit market risk and credit risk, since premiums received early are invested until needed. Across both run operational risk, moral hazard and adverse selection.
Actuaries price life contracts and value pension obligations off mortality tables. The extract used here is drawn from U.S. Social Security Administration data covering deaths among men and women at each age during 2016, with the sexes tabulated separately because their rates differ.
Three columns matter. The probability of death within one year is conditional: given somebody alive on their birthday, it is the chance they do not reach the next one. A man aged 70 faces 2.3122%, a woman of the same age a more favourable 1.5413%. The survival probability for year n is cumulative, the chance of living from birth to year n; it starts at 1 for year zero and falls thereafter. The third column is life expectancy, the average number of further years remaining.
| Age | Male | Female |
|---|---|---|
| 70 | 0.023122 | 0.015413 |
| 71 | 0.025265 | 0.017089 |
| 72 | 0.027585 | 0.018861 |
Source: U.S. Social Security Administration mortality data, 2016 death rates.
Survival probabilities run alongside: a man reaches 70 with probability 0.72843 and 71 with probability 0.71158, while a woman reaches 70 with probability 0.82573 and 90 with probability 0.29685.
Work with the male column above and the survival probability of 0.72843 for a man aged 70.
Life expectancy weights each possible year of death by its probability, on the convention that death arrives mid year, so for a man aged 70 it opens with 0.023122 multiplied by 0.5, then 0.024681 multiplied by 1.5, then 0.026266 multiplied by 2.5, and carries on in the same fashion.
Whole life insurance covers the policyholder for the whole of life. Premiums are paid monthly or annually until death, at which point the face value goes to the named beneficiary. A payout is therefore certain and the only open question is the date, which is why the product is sometimes called life assurance. Both premium and face value are normally held constant.
Why the early years fund the later ones
The expected payout in a given year is the face value multiplied by the probability of death during that year, and that probability climbs steadily with age. A flat premium set against a rising expected payout produces a predictable shape: early on the premium exceeds the expected cost of claims and the insurance company runs an expected surplus, while in later life the expected cost overtakes the premium and the position turns into an expected deficit. Neither figure means much on a single policy. Across a large book the pattern is reliable, and investment income earned on the early surpluses finances the later deficits.
Tax rules often reinforce the product, since funds inside a policy accumulate untaxed until it pays out, whereas funds a policyholder invests personally are taxed on their income each year. Selling the policy to a third party before death usually removes that shelter.
Three variations on the basic contract
Because a whole life policy has funds invested behind it, an obvious extension is to let the policyholder direct where they go. Variable life insurance does that, normally with a guaranteed minimum payout on death and anything above it depending on how the chosen investments perform.
A second variation loosens the premium. Under a standard policy, stopping payments ends the cover, and the policy is then said to be lapsing. Universal life insurance instead lets the policyholder cut the premium to a stated minimum: benefits shrink accordingly, but the contract stays alive. Variable-universal life insurance combines the two features.
Endowment life insurance always pays out at a pre-specified maturity. Death inside the term brings the money then; otherwise it arrives at the end of the contract, and some versions also pay on diagnosis of a critical illness. A with profits endowment life insurance policy adds bonuses declared out of the performance of the insurance company investments, lifting the final payout. In a unit-linked endowment policy the policyholder picks a fund and the payout tracks that fund.
Group life insurance is bought by employers for their staff, with premiums met entirely by the company or split with employees. Medical tests, normally required of an individual buying cover alone, are usually waived here, because the insurance company is accepting a whole workforce and knows the pool contains better than average and worse than average risks together.
Annuity contracts run life insurance backwards
A life policy turns a stream of premiums into a lump sum; an annuity contract does the reverse, turning a lump sum into a stream of payments that normally lasts for the rest of the policyholder’s life. Payments can begin as soon as the deposit is made, or, under deferred annuities, only after some years. Tax again favours the arrangement, since tax generally falls due only when the annuity is received, so the investments compound free of tax meanwhile and many policyholders face a lower marginal tax rate by then.
The pot behind the contract is the accumulation value. Early withdrawal is usually allowed but often carries penalties. Some contracts embed options designed to stop the accumulation value falling, for example by tracking the S&P 500 with the annual return floored at zero and capped at 7%. That structure means the insurance company has written the policyholder a put option and has bought a call option from them.
Deferred annuity contracts in the United Kingdom have sometimes guaranteed a minimum on future payments, for instance an annuity beginning in ten years that pays at least 8% of the accumulation value at that date. Such a guarantee looks cheap when written and becomes costly if interest rates fall and life expectancies lengthen together. Equitable Life, founded in the United Kingdom in 1762 and holding 1.5 million policyholders at its peak, failed on guarantees of this kind.
Longevity risk is the risk that a population outlives what the mortality table predicted. The table used here rests on the proportion of people at each age who died during 2016, and it puts the life expectancy of a female aged 30 at 52.01 years, implying an average age at death of 82.01. Medical advances and better nutrition can make such an estimate too pessimistic: someone born today can expect about 20 years more life than a comparable person born 100 years ago. Mortality risk is the mirror image, the risk that wars, epidemics or other shocks pull deaths forward.
The two risks land on opposite sides of the business
A life insurance book should welcome people living longer than expected, because whole life policyholders keep paying premiums for more years and the payouts arrive later. Mortality risk is the genuine threat there, since early deaths mean paying out before enough premium has been collected. An annuity book faces the reverse: annuitants who live longer collect payments for longer, which makes the contract more expensive. Writing both lines gives a partial internal hedge, but the offset is never exact and the residual exposure must be managed.
Hedging with longevity derivatives
Longevity derivatives come in several shapes, but each has a payoff driven by the gap between a mortality rate agreed in advance for a defined age group and the rate that materialises.
Read the formula against an annuity book. If people die more slowly than the fixed rate assumed, the realized mortality rate comes in low, the bracket turns positive, and the derivative pays out exactly when the annuity liabilities are becoming more expensive. Other longevity derivatives are bonds whose principal or interest moves with the same difference. Defined benefit pension plans are natural buyers too, and the reference rate can be the mortality of plan members currently drawing pensions.
Life policies and annuity contracts generate large pools of money that will not be needed for years or decades, which makes the investment strategy central to results. Much of the portfolio goes into long-term corporate bonds, whose maturities can be lined up against the obligations they fund.
Corporate bonds bring two exposures. Market risk here is essentially interest rate risk, since rising rates push bond prices down, and credit risk is the possibility that the bond issuers default. An insurance company could sidestep credit risk by buying government bonds instead, but over long horizons the extra return on corporate bonds has more than covered the losses defaults inflict, so the exposure is taken deliberately. Equity investments also appear, and a variable life contract or a unit-linked policy requires them.
Exposures on both sides of the balance sheet
The asset side carries market risk and credit risk from the investment portfolio. The liability side carries longevity risk and mortality risk, because the value of the obligations depends on how long the insured population lives. Sitting across both is operational risk, which for an insurance company looks much like the operational risk a bank runs. Regulators build minimum capital requirements from all of these components rather than any one of them.
A pension plan resembles an annuity contract, producing income from retirement until death. Contributions come from the individual and the employer during working life and are deductible for tax purposes. Plans often index the pension, for example by tying the annuity growth rate to 75% of the inflation rate, and terms commonly extend a usually smaller pension to the employee’s spouse and sometimes other dependents.
Defined contribution plans
Under a defined contribution plan the employee invests the funds and can normally choose how, with withdrawals beginning at retirement and some plans allowing a lump sum instead. The 401(k) in the United States is the familiar example. The arrangement is almost free of risk for the sponsoring company, since the employee ends up with whatever the invested funds have grown to. The only real exposure is a small operational risk of managing the funds badly and being sued for it.
Defined benefit plans
A defined benefit plan pools the contributions instead, and a formula fixes what each retiree receives. A plan might set the pension equal to average annual income over the final three years of employment, multiplied by years of employment, multiplied by 2%.
That promise is what makes the plan risky for the employer. Actuaries value the obligations each year against the assets held, and any shortfall must be made good by the company. It can often be spread across several years, but the shortfall is a liability reducing shareholders’ equity. That exposure explains why defined benefit plans are essentially no longer started, and why many sponsors have moved to defined contribution plans for new hires.
The discount rate matters enormously, because outflows run decades ahead. The present value of USD 1,000 payable in 40 years is about USD 453 at a discount rate of 2%, and at 5% it falls below one third of that. Accounting standards now require private sector plan obligations to be discounted at the yield on AA-rated bonds.
It might seem that a defined benefit plan should match bonds to liabilities the way a life insurance company does. In practice bond returns have not been high enough to fund the promised pensions, so plans put much of the portfolio into equities, with 60% equity and 40% debt a common mix. Equity markets of the kind seen since 1960 let plans meet their obligations, while a prolonged fall in equity prices alongside lengthening life expectancy produces very large deficits. Shareholders bear those deficits first, and in bankruptcy the burden can shift to the Pension Benefit Guarantee Corporation. Either way wealth passes from the next generation to retirees, which is the basis of the argument for sharing risk between generations.
Take a simplified defined benefit plan. Employees work for 30 years on a salary rising exactly with inflation, the pension is 45% of final salary and also rises with inflation, employees live for 24 years after retiring, and the plan invests in bonds earning the inflation rate. In real terms the salary and the pension stay constant, and the interest earned is zero.
Property insurance covers damage to the policyholder’s own property from fire, theft, flooding and comparable events. Casualty insurance covers liabilities the policyholder incurs when their actions injure somebody else or damage somebody else’s property. The two are frequently sold in one contract: a homeowners’ insurance policy covers fire and theft losses and the liability arising if a visitor is injured on the property, while a motor policy covers theft as well as claims brought by others for damage the driver caused. Because these contracts renew annually, the insurance company can reprice whenever its view of the risk changes, as it does when a driver is convicted of speeding.
Two categories of risk
The risks underwritten divide into two groups. In the first, the annual payout can be forecast reasonably well from history, because the total is assembled from many claims that are independent or close to it. In the second, one event such as a hurricane or an earthquake generates a mass of claims at once.
Motor insurance illustrates the first group. Suppose an insurance company covers 100,000 car owners in a particular risk category and knows from experience that 10% of them file a claim in a given year, with claims averaging USD 3,000. Expected annual claims cost is then 100,000 x 0.1 x 3,000, or about USD 30 million.
The realised total will wobble around USD 30 million from year to year, but a large deviation is statistically very unlikely. Independence delivers that stability: Driver A having an accident does not make an accident by Driver B any more probable. Insurance companies still track accident frequency, repair costs and the damages courts award to accident victims.
Health insurance and when its premiums can rise
Health insurance is the third category of cover, supplied almost entirely by the government in many countries and historically a necessary expenditure for many people in the United States. What distinguishes it is the rule governing increases. Whole life premiums cannot be raised even after an expensive medical condition comes to light, while property and casualty risks are reassessed annually. Health insurance sits between the two: premiums may rise when the general cost of providing health care rises, but not because the policyholder has developed health problems unknown when the policy was written.
The second category of property and casualty exposure is catastrophe risk, which behaves nothing like a motor book. Consider an insurance company covering 100,000 homes in South Florida against hurricane damage. Those claims are not independent: either a hurricane arrives and most policyholders claim at once, or it does not and almost none do. That all-or-nothing shape makes catastrophe risk a far greater threat to solvency. Specialist firms build models estimating the probability of the events being insured against, but modelling improves the estimate without changing the shape of the exposure. One common convention sets premiums so that coverage runs to three times the largest cost produced by the simulations.
Reinsurance
An insurance company that would rather not carry catastrophe exposure can pay a reinsurance company to assume it. Reinsurance is insurance bought by insurers: the primary insurer pays a premium and passes a defined layer of loss to a counterparty better diversified across regions and perils. It does not make the risk disappear. The primary insurer replaces catastrophe exposure with credit exposure to the reinsurer, which is at its most dangerous in precisely the scenario where the cover is needed.
CAT bonds
The other route sends the risk to the capital markets through derivatives known as CAT bonds. A CAT bond is issued by an insurance company and pays interest at an above-market rate. In exchange, if payouts on a specified risk fall inside a stated range, the bond interest, and in some structures the principal too, funds those payouts.
Suppose an insurance company carries USD 100 million of Florida hurricane exposure and wants to cut that to USD 40 million. It can issue three bonds, each with a principal balance of USD 20 million: Bond A covers claims in the range USD 40 to 60 million, Bond B the range USD 60 to 80 million, and Bond C the range USD 80 to 100 million. Bond A carries more risk than Bond B, and Bond B more than Bond C, since the lower layer is reached first, so Bond A pays the highest interest rate of the three and Bond C the lowest. The alternative design issues much higher principal balances, so the promised interest alone covers claims and the principal stays intact.
Why would an investor want such a security? Whether a hurricane strikes Florida has nothing to do with the returns on the rest of a portfolio, so a CAT bond adds uncorrelated risk. Capital market theory says a security whose return is uncorrelated with the market should earn the risk-free rate. CAT bonds pay more than that, and the diversification benefit is what investors are buying.
The performance of a property and casualty insurance company is summarised by a short ladder of ratios, each built on the one before it. The starting point is the loss ratio, which compares claims paid with premiums collected.
The remaining 30% covers running costs and, if things go well, leaves a profit. Two cost lines dominate: selling expenses, and loss adjustment expenses, the costs of establishing whether a claim is valid. Total expenses divided by premiums received gives the expense ratio, and the two ratios added together give the combined ratio.
Some insurance companies pay a small dividend to policyholders, and adding it produces the combined ratio after dividends. The final step recognises that premiums arrive at the start of a year while claims are settled later, leaving money to invest in short and medium term bonds. Subtracting that investment income gives the operating ratio, a gross profitability measure.
| Percentage of premiums | |
|---|---|
| Loss Ratio | 70% |
| Expense Ratio | 26% |
| Combined Ratio | 96% |
| Dividends | 1% |
| Combined Ratio After Dividends | 97% |
| Investment Income | (2%) |
| Operating Ratio | 95% |
Source: illustrative income statement for a property and casualty insurance company as set out in the chapter.
Read without the last two lines, the figures suggest an operating ratio of 97%. Including investment income, assumed here at 2% of premiums received, brings it down to 95%.
A property and casualty insurance company earns premiums of USD 400 million in a year. It pays USD 280 million in claims and incurs USD 104 million of selling and loss adjustment expenses. Policyholder dividends come to USD 4 million and investment income on the premiums held comes to USD 8 million.
Moral hazard
Moral hazard is the danger that having cover changes what the policyholder does. Deposit insurance supplies the classic case from the banking chapter: banks whose depositors are protected by a government guarantee can follow riskier strategies without seeing their funding leave. The same logic reaches retail cover. Somebody fully insured against burglary has less reason to install an alarm system or cameras, and somebody who has just bought health insurance visits the doctor more readily. Life insurance is largely free of the problem, since few take up sky diving on the strength of having bought a life policy.
Where moral hazard does bite, insurance companies design it out of the contract. A deductible leaves the policyholder carrying the first slice of any loss. Co-insurance goes further and pays only a stated percentage of the loss, so the policyholder retains a share of every claim rather than only the small ones. On top of both, the amount claimable is nearly always capped.
Adverse selection
Adverse selection is a pricing problem rather than a behavioural one: the danger that those who buy the cover are disproportionately those most likely to claim on it. Quote one motor premium to every applicant regardless of record and the price looks like a bargain to drivers with a history of accidents and poor value to careful ones. The bad risks accept, the good risks decline, and the pool is worse than the average it was priced for.
The defence is information. An insurance company needs to learn as much as it can about an applicant before quoting a premium, and to revise that assessment as new information arrives. Medical tests before an individual life policy serve exactly this purpose, and group life insurance can waive them because the insurance company takes a whole workforce rather than a self-selected subset.
Banks are governed by capital rules the Basel Committee sets at a global level. Insurance companies have no equivalent, so what applies depends on where the insurance company is incorporated and where it writes business.
Solvency II in the European Union
The European Union closed that gap for its own market with Solvency II, implemented in 2016 and covering every insurance company operating there. It sets two thresholds. The solvency capital requirement, or SCR, is the level at which supervisors expect capital to sit. The minimum capital requirement, or MCR, is the floor beneath it, usually set somewhere between 25% and 45% of the SCR. Falling below the SCR obliges the insurance company to formulate a plan for restoring capital above that level. Falling below the MCR is far more serious: the insurer may be barred from writing new business, and its policies may be moved to another insurance company.
Solvency II borrows the architecture of the Basel rules, offering both standardized approaches and internal model-based approaches. Capital charges are levied for investment risk, which sits on the asset side and subdivides into credit risk and market risk, for underwriting risk on the liabilities side, and for operational risk. Property-casualty underwriting attracts a higher charge than life insurance underwriting, because its catastrophe risks are greater than the longevity and mortality risks of the latter.
Regulation in the United States
American insurance regulation belongs to the states rather than the federal government. The National Association of Insurance Commissioners provides a forum in which state regulators exchange ideas and publishes statistics, including loss ratios for insurance companies across the country, but it does not impose the rules. Practice varies from state to state, and a large insurance company writing business nationwide may answer to 50 different regulators.
The guaranty system compared with deposit insurance
Protection for policyholders is built differently from protection for bank depositors. Premiums paid by banks accumulate in a fund administered by the Federal Deposit Insurance Corporation, which compensates depositors when a bank fails, and the federal government has added to it when necessary. Policyholders have no permanent fund behind them: insolvencies are dealt with state by state, and when one insurance company fails the survivors must contribute to a fund. Limits apply to what can be claimed, and settlement takes time.