Introduction

• Insurance provides protection against specific adverse events. The company or individual obtaining protection is known as the policyholder. Typically, the policyholder must make regular payments known as premiums.
• Most insurance contracts can be categorized as either life insurance or property and casualty insurance. Another type of insurance is health insurance. While the premiums in a life insurance policy do not usually change from year to year, those in a property and casualty policy generally do.
• There are similarities between pension plans and the contracts offered by life insurance companies. In an employer-sponsored pension plan both the employee and the employer make regular contributions to the plan. The contributions are used to fund a lifetime pension for the employee following the employee's retirement.

Mortality Tables

• Mortality tables are used extensively by actuaries for setting life insurance contract premiums and assessing pension plan obligations. This table shows an extract from mortality tables produced by the US Social Security Administration. This table is based on the death rates observed for men only of different ages in 2014.

Age (Years)	Probability of Death within 1 Year	Survival Probability	Life Expectancy
30	0.001498	0.97520	47.86
31	0.001536	0.97373	46.93
32	0.001576	0.97224	46.00
33	0.001616	0.97071	45.07
70	0.023380	0.73427	14.32
71	0.025549	0.71710	13.66
72	0.027885	0.69878	13.00
73	0.030374	0.67930	12.36

• The ‘Probability of Death within 1 Year’ column is the probability that an individual will die during the following year (providing that he or she is alive at the beginning of the year).
• The survival probability for Year n is the cumulative probability that an individual will live to Year n. The survival probability for Year zero is 1. The survival probability for Year n+1 can be calculated from the survival probability for Year n and the probability of death within one year for Year n. For example, the probability that a man will survive until age 71 is the probability that he survives until age 70 and does not die within the next year. This is:

This is the same as the survival probability for age 71 in the table.

• The probability that a man aged 71 will die in the following year is 0.025549. Thus, the probability that a man aged 70 will die between the first and second year is:

Similarly, the probability that he will die between the second and third year is:

• Assuming that (on average) a person dies in the middle of a year, the life expectancy of a man aged 70 (shown in the third column) can be calculated as:

Life Insurance – Types

• There are many different types of life insurance policies –
• Term Life Insurance,
• Whole Life Insurance,
• Endowment Life Insurance,
• Group Life Insurance, and
• Annuity Contracts

Life Insurance – Whole Life Insurance

• Whole life insurance provides insurance for the whole life of the policyholder. The policyholder makes regular monthly or annual payments, until he or she dies. At that time, the face value of the policy is paid to the designated beneficiary. This means that there is certain to be a payment by the insurance company to the policyholder, and the only uncertainty for the insurance company is when the payment will occur.
• In many jurisdictions, there are tax benefits associated with whole life insurance. When funds are invested by the policyholder, tax is paid on the investment income each year. But when the funds are invested by the insurance company, no tax is payable until there is a payout from the insurance policy.
• Consider a USD 1 million whole life policy where the policyholder is a 30-year-old male. The insurance company can calculate its expected payout each year. From table 1, the probability of a male who is 30 years old dying within one year is 0.001498. The insurance company's expected payout (in USD) during the first year is therefore:

• The probability that the policyholder will die during the second year is the probability that death does not occur during the first year multiplied by the probability of dying during the second year. From Table 1 this is:

So, the expected payout during the second year is USD 1,534.

• The expected payout increases year by year throughout the life of the policy. From Table 1, the probability that a policyholder aged 30 will survive until 70 can be calculated as:

The probability that the policyholder (currently 30 years old) will die between age 70 and 71 is therefore:

The expected payout from the policy during its fortieth year (i.e., when the policyholder is 70) is therefore USD 17,604.

• Suppose that the premium charged is USD 15,000 per year. It is clear from these calculations that the insurance company has an expected surplus during the early years and an expected deficit in later years. On any one policy, the results are uncertain. This figure shows how a typical whole life insurance policy generates expected surpluses and expected deficits during its life.

• From the insurance company's perspective, the investment income from the expected surpluses must be sufficient to finance the expected deficits. The above figure illustrates the general pattern of expected surpluses and deficits in a whole life policy. It does not include investment income.
• Whole life insurance can be further sub-divided into 3 categories based on how the funds are to be invested:
  • Variable life insurance is the name used to describe policies where the policyholder can specify how the funds are to be invested. Typically, there is a minimum guaranteed payout on the policyholder's death. However, the payout can be greater than this if the investments do well.
  • Universal life insurance is another variation on the standard whole life policy where the policyholder can reduce the premium down to a specified minimum. While reducing the premium reduces the benefits, it does not result in the policy lapsing.
  • Variable-universal life insurance incorporates the features of both variable and universal life insurance.

Life Insurance – Term Life Insurance

• Term life insurance lasts a specified number of years. If the policyholder dies during the life of the policy, there is a payout equal to the face value of the policy. Otherwise, there is no payout. Mortgages are a common reason for purchasing term life insurance.
• This table shows a small extract from mortality tables produced by the US Social Security Administration. This table is based on the death rates observed for women only of different ages in 2014.

Age of Women (Years)	Probability of Death within 1 Year	Survival Probability	Life Expectancy
50	0.003189	0.95794	33.24
51	0.003488	0.95488	33.34
52	0.003795	0.95155	31.45
53	0.004105	0.94794	30.57

• As a simple example, a three-year term life insurance contract offered to a woman aged 50 can be considered. The probability that she will die in the first year is given by Table 1 as 0.003189. The probability that she will die during the second year is:

And the probability that she will die during the third year is:

• It is assumed that death always occurs halfway through a year and that the discount rate is 5% (with annual compounding). This leads to the present value of the expected payout per dollar of face value being calculated as indicated in this table.

Time (Years)	Expected Payout	Discount Factor	PV of Expected Payout
0.5	0.003189	0.9759	0.003112
1.5	0.003477	0.9294	0.003232
2.5	0.003770	0.8852	0.003337
Total			0.009681

• Now suppose the premium paid by the policyholder this is X and that it is paid in advance. (as is the case with most insurance contracts). The insurance company is certain to receive the first premium at time zero. It will receive the second premium after one year if the policyholder is still alive. The probability of this is 1-0.003189=0.996811. It will receive the third premium after two years if the policyholder is still alive at that time. The probability of this is:

• The present value of the expected premiums received by the insurance company can therefore be calculated as indicated in this table.

Time (Years)	Probability of Receiving Premium	Discount Factor	PV of Expected Payout
1	1.00000	1.00000	X
2	0.996811	0.952381	0.949344X
3	0.993334	0.907029	0.900983X
Total			2.850327X

• The breakeven premium is calculated by equating the present value of expected premiums with the present value of the expected payout:

2.850327X = 0.009681

This gives X = 0.003396.

• The breakeven cost of three-year term insurance for a 50-year-old female is therefore 0.003396 per dollar of face value. For a policy with a face value of USD 1 million, the breakeven premium is therefore USD 3,396 per year.

Life Insurance – Endowment Life Insurance

• Endowment life insurance is a type of term life insurance where there is always a payout at a pre-specified contract maturity. If the policyholder dies during the life of the policy, the payout occurs at the time of the policyholder's death. Otherwise, it occurs at the end of the life of the policy. Sometimes the payout is also made when the policyholder has a critical illness.
• In the case of a 'with profits endowment life insurance policy,' the insurance company declares bonuses that depend on the performance of its investments. These bonuses increase the final payout (assuming that the policyholder lives until the end of the life of the policy). In a 'unit-linked endowment policy,' the policyholder chooses a fund, and the payout depends on the performance of that fund.

Life Insurance – Group Life Insurance

• Group life insurance is typically purchased by companies for their employees. The premiums may be paid entirely by the company or shared between the company and its employees. Note that while individuals are normally required to undergo medical tests when applying for life insurance, these tests are usually waived in group life insurance. This is because the insurance company knows it will be taking some better-than-average and worse-than-average risks.

Life Insurance – Annuity Contracts

• Most life insurance companies offer annuity contracts in addition to life insurance contracts. While life insurance converts regular payments into a lump sum, annuity contracts convert a lump sum into regular payments. Typically, the payments in an annuity contract last for the rest of the policyholder's life. In some cases, the annuity starts as soon as a lump sum is deposited with the insurance company. In the case of deferred annuities, it starts several years later.
• As with life insurance, taxes can be a consideration when an annuity is purchased as tax is normally payable only when the annuity is received.
• The amount to which the policyholder's funds grow in an annuity contract is referred to as the accumulation value. Funds can usually be withdrawn early, but there may be penalties. Some annuity contracts have embedded options designed to ensure that the accumulation value never declines. For example, the contract may be structured so that the accumulation value tracks the S&P 500 with a lower limit on the return of zero and an upper limit of 7%.

Longevity And Mortality Risk

• Longevity risk is the risk that people will live for longer than mortality tables indicate. Over the last century, the life expectancy of people born have steadily increased. On the other hand, mortality risk is the opposite of longevity risk. It is the risk that wars, epidemics, and other factors will lead to people dying sooner than expected.
• The life insurance business of an insurance company should welcome the possibility that people will live longer than expected. This will lead to premiums on whole life policies being paid for longer periods of time and payouts being later than expected. Mortality risk is more of a concern, however, because it could lead to earlier payouts without sufficient collected premiums to cover them.
• The annuity business of an insurance company has the opposite exposure compared to that of the life insurance business. If people live longer than expected, they receive the annuity to which they are entitled for longer and thus make the contract more expensive for the insurance company. If they die sooner than expected, the contract will prove to be less expensive for the insurance company.
• The longevity/mortality exposures on an insurance company's whole life business should (to some extent) offset the exposure on its annuity business. However, there is unlikely to be a perfect offset and the residual exposure must be managed.
• One approach to manage the residual exposure is the use of longevity derivatives. These instruments have been structured in a number of different ways so that the payoff depends on the difference between a prespecified (expected) mortality rate for individuals in a certain age group and the actual mortality rate. A simple payoff could be defined as:

• The above is similar to a forward contract on the mortality rate. Other longevity derivatives involve bonds where either the principal or the interest rate depends on the difference between a pre-specified mortality rate and an actual mortality rate.

Investments

• Life insurance policies and annuity contracts generate funds for investment. The investment strategy of a life insurance company is therefore very important. Many of these investments consist of long-term corporate bonds as well as equity.
• Life insurance companies can try to match the maturities of the bonds with the maturities of their obligations. However, corporate bonds give rise to both market risk and credit risk. The market risk relates to interest rates (as rates increase, bond prices decline). The credit risk relates to the possibility that bond issuers will default. Life insurance companies could avoid credit risk by investing in government bonds. Over the long term, however, the extra return earned on corporate bonds (over risk-free government bonds) more than compensates for losses arising from defaults.
• Life insurance companies have risks on both sides of their balance sheets: market and credit risks on the asset side along with longevity and mortality risks on the liability side. In addition, they are subject to operational risks. Regulators take all these risks into account in determining minimum capital requirements.

Pension Plans

• Pension plans are like annuity contracts in that they are designed to produce income for an individual for the remainder of his or her life following retirement. Typically, contributions to the plan are made by the individual and the individual's employer while the person is employed. These contributions are deductible for tax purposes.
• There may be some indexation of the pension. For example, it might be agreed that the annuity growth rate will reflect 75% of the inflation rate. The terms of the pension plan state that the employee’s spouse (and possibly other dependents) will receive a (usually smaller) pension if they are still alive when the employee dies.
• Pension plans typically put much of their assets into equities. If equity markets do well, these plans should be able to meet their obligations. If there is a prolonged decline in equity prices (particularly if it is combined with an increase in life expectancy), however, these plans are likely to chalk up huge deficits.
• There are two main types of pension plans:
  1. Defined contribution plans
  2. Defined benefit plans.

Pension Plans – Defined Contribution Plan

• In defined contribution plan, the funds are invested by the employer. Mostly, the employee can choose how the funds are invested.
• When the employee retires, he or she can begin withdrawing the funds. Sometimes, he or she can opt for a lump sum payment at retirement.
• The company merely acts as an agent investing the pension plan contributions on behalf of its employees. The pension obtained by an employee depends on the extent to which the employee's funds have grown.
• So, in defined contribution plans, contributions are clearly defined and known in advance but benefits to employees are not known in advance.
• The risk of the plan's investments not perform well and hence, the risk of not having enough money for retirement is borne by the employee. The employer is obligated simply to make a defined contribution and nothing else.

Pension Plans – Defined Benefit Plan

• In defined benefit plan, funds are also usually contributed by the employer and employee. In this case, however, the contributions are pooled, and a formula is used to determine the pension received by the employee on retirement. For example, the pension plan might state that the pension is the employee's average annual income during the last three years of employment multiplied by the number of years of employment multiplied by 2%. The company guarantees to its employees that pensions will be calculated in a certain way.
• A defined benefit plan is much riskier for an employer than a defined contribution plan. Each year, actuaries assess the present value of a defined benefit pension plan's obligations and compare it with the plan's assets. The company is required to provide contributions to the plan to make up for any shortfall that reduces shareholders' equity on its balance sheet.
• The risk for the company and its shareholders in defined benefit plans is the reason why defined benefit plans are not initiated today. Most companies that have defined benefit plans initiated them many years ago. Many companies have switched from defined benefit plans to defined contribution plans (at least for new employees) to avoid these risks.
• An important issue in estimating defined benefit plan obligations is the discount rate used. Plan outflows often stretch for many years into the future. Accounting standards now require pension plan obligations to be discounted at the yield on AA-rated bonds.
• Shareholders bear the cost of deficits in defined benefit plans. In cases of bankruptcy, the cost may be borne by government-sponsored entities. In either case, there is a transfer of wealth to retirees from the next generation. It has been argued that the terms of defined benefit plans must be altered so that there is some risk sharing between generations. If equity markets do well, some of the benefits can be passed on to the next generation. If they do badly, some of the costs should be borne by retirees.

Property And Casualty Insurance

• Property and casualty insurance contracts are quite different from life insurance contracts.
  • Property insurance provides protection against damage to property from fire, theft, flooding, and other loss-generating events.
  • Casualty insurance provides coverage for liabilities arising from injuries and damages sustained by others due to the insured party's actions.
• Unlike life insurance, property and casualty insurance is typically renewed from year to year. If the insurer feels that the risks have increased, the premium may be raised. For example, car insurance premiums are likely to increase if a driver has been convicted of speeding.
• The risks to a property and casualty insurance company can be divided into:
  • Risks where the average payout can be predicted reasonably well from historical data because the yearly payout arises from many independent claims by policyholders, e.g., car insurance.
  • Risks where a single event (such as a hurricane) can lead to many claims at the same time, also referred to as catastrophe risks. When a company does not want to keep catastrophe risks, it can pay a reinsurance company to take them on. It can also use derivatives known as CAT (catastrophe) bonds.

Property And Casualty Insurance – Loss Ratios

• A key statistic for a property-casualty insurance company is its loss ratio. This is the ratio of payouts to premiums. A loss ratio of 70% would mean that for every USD 100 of premiums received, the insurance company pays out USD 70 in claims. The remaining 30% is to cover expenses and (hopefully) make a profit. Two major expenses are:
  • Selling expenses, and
  • Expenses related to determining the validity of a claim (referred to a loss adjustment expenses).
• The expense ratio is total expenses divided by premiums received.
• The combined ratio is the sum of the loss ratio and the expense ratio. Sometimes a small dividend is paid to policyholders. The combined ratio after dividends is the sum of the combined ratio and the dividends paid to the policyholders as a percentage of premiums.
• The insurance company's operating ratio is a gross profitability measure. For any given year operating ratio is the combined ratio after dividends less investment income as a percentage of premium.

Health Insurance

• Another category of insurance is health insurance. In many countries, health care is provided almost entirely by the government. In other countries, public and private health care systems run side by side. In the United States, private health insurance is a necessary expenditure for many people.
• One difference between health insurance and other types of insurance concerns the circumstances when premiums increase. In whole life insurance, premiums typically remain constant. Even if it becomes known that a policyholder has a short life expectancy because of a terminal disease, premiums cannot be increased. In property-casualty insurance, risks are reassessed every year, and premiums may increase or decrease. In health insurance, premiums may increase because the overall costs of health care have increased. However, they cannot do so because the policyholder develops unexpected health problems that were unknown at the time the policy was initiated.

Moral Hazard

• Moral hazard is the risk that the behavior of the policyholder will change as a result of the insurance. Banks might be tempted to follow riskier strategies when depositors have government insurance because the insurance makes it less likely that depositors will transfer their funds elsewhere. Other examples of moral hazard include the following:
  • If an individual's house insurance fully insures you against burglaries, he may be less likely to install alarm systems and cameras.
  • As a result of buying health insurance, a person may visit the doctor more frequently.
• Moral hazard is not a big problem in life insurance. It is difficult to imagine that an individual would take up a risky pursuit (such as sky diving) because he or she has bought life insurance.
• Insurance companies attempt to reduce moral hazard in a number of ways, such as:
  • Most insurance policies have a deductible so that the policyholder bears the first part of any loss.
  • Sometimes there is co-insurance where the insurance company pays only a certain percentage of any loss.
  • There is nearly always a limit on the amount that can be claimed.

Adverse Selection

• Adverse selection is the risk that insurance will be purchased only by high-risk policyholders. If an insurance company offers the same car insurance rates to everyone, for example, the rates will seem more attractive to those who have bad driving records. It is therefore important that insurance companies know as much as possible about the risks they are taking on before quoting a premium. The risk assessments should be updated as more information is obtained.

Regulation

• The Basel committee determines global regulatory requirements for banks. In contrast, there are no similar global regulatory requirements for insurance companies. In the European Union, however, a regulatory framework known as Solvency II was implemented in 2016 and applies to all insurance companies.
• Solvency II specifies a minimum capital requirement (MCR) and a solvency capital requirement (SCR). If capital falls below the SCR, an insurance company is required to formulate a plan to bring it back up above the SCR level. If it falls below the MCR level, the insurance company may be prevented from taking new business, and existing policies might be transferred to another insurance company. The MCR is typically between 25% and 45% of the SCR.
• Just like Basel committee rules, there are both standardized approaches and internal model-based approaches to determining capital requirements. There are capital charges for:
  • Investment risk (this relates to the asset side of the balance sheet),
  • Underwriting risk (this relates to the liabilities side of the balance sheet), and
  • Operational risk.

  Investment risk is divided into credit risk and market risk.

• The capital requirements for property-casualty underwriting tend to be higher than those for life insurance underwriting. This is because the catastrophe risks associated with the former are greater than the longevity/mortality risks associated with the latter.
• In the United States, insurance is regulated at the state level rather than at the federal level. The National Association of Insurance Commissioners is a national forum for insurance regulators to exchange ideas.
• The guaranty system for policyholders in the United States is different from the deposit insurance system for bank depositors. Premiums paid by banks create a fund administered by the Federal Deposit Insurance Corporation (FDIC) that is used to compensate depositors for losses. The federal government has added to the fund when necessary.
• There is no permanent fund to provide protection for policyholders. And insolvencies are handled on a state-by-state basis. When one insurance company fails, others are required to make contributions to a fund, and there are limits on what can be claimed as well as delays in settlement.