Pension Plans

Insurance Companies and Pension Plans

3.12 Pension Plans

Pension plans are set up by companies for their employees. Typically, contributions are made to a pension plan by both the employee and the employer while the

employee is working. When the employee retires, he or she receives a pension until death. A pension fund therefore involves the creation of a lifetime annuity from regular contributions and has similarities to some of the products offered by life insurance companies. There are two types of pension plans: defined benefit and defined contribution.

In a defined benefit plan, the pension that the employee will receive on retirement is defined by the plan. Typically it is calculated by a formula that is based on the number of years of employment and the employee's salary. For example, the pension per year might equal the employee's average earnings per year during the last three years of employment multiplied by the number of years of employment multiplied by 2%. The employee's spouse may continue to receive a (usually reduced) pension if the

employee dies before the spouse. In the event of the employee's death while still employed, a lump sum is often payable to dependents and a monthly income may be payable to a spouse or dependent children. Sometimes pensions are adjusted for inflation. This is known as indexation. For example, the indexation in a defined benefit plan might lead to pensions being increased each year by 75% of the increase in the consumer price index. Pension plans that are sponsored by governments (such as Social Security in the United States) are similar to defined benefit plans in that they require regular contributions up to a certain age and then provide lifetime pensions.

In a defined contribution plan the employer and employee contributions are invested on behalf of the employee. When employees retire, there are typically a number of options open to them. The amount to which the contributions have grown can be

converted to a lifetime annuity. In some cases, the employee can opt to receive a lump sum instead of an annuity.

The key difference between a defined contribution and a defined benefit plan is that, in the former, the funds are identified with individual employees. An account is set up for each employee and the pension is calculated only from the funds contributed to that account. By contrast, in a defined benefit plan, all contributions are pooled and payments to retirees are made out of the pool. In the United States, a 401(k) plan is a form of defined contribution plan where the employee elects to have some portion of his or her income directed to the plan (with possibly some employer matching) and can choose between a number of investment alternatives (e.g., stocks, bonds, and money market instruments).

An important aspect of both defined benefit and defined contribution plans is the deferral of taxes. No taxes are payable on money contributed to the plan by the employee and contributions by a company are deductible. Taxes are payable only when pension income is received (and at this time the employee may have a relatively low marginal tax rate).

Defined contribution plans involve very little risk for employers. If the performance of the plan's investments is less than anticipated, the employee bears the cost. By contrast, defined benefit plans impose significant risks on employers because they are ultimately responsible for paying the promised benefits. Let us suppose that the assets of a defined benefit plan total $100 million and that actuaries calculate the present value of the obligations to be $120 million. The plan is $20 million underfunded and the employer is required to make up the shortfall (usually over a number of years).

The risks posed by defined benefit plans have led some companies to convert defined benefit plans to defined contribution plans.

BUSINESS SNAPSHOT 3.2 A Perfect Storm

During the period from December 31, 1999, to December 31, 2002, the S&P 500 declined by about 40% from 1469.25 to 879.82, and 20‐year Treasury rate in the United States declined by 200 basis points from 6.83% to 4.83%. The impact of the first of these events was that the market value of the assets of defined benefit pension plans declined sharply. The impact of the second of the two events was that the discount rate used by defined benefit plans for their liabilities decreased so that the fair value of the liabilities calculated by actuaries increased. This created a “perfect storm” for the pension plans. Many funds that had been overfunded became underfunded. Funds that had been slightly underfunded became much more seriously underfunded.

When a company has a defined benefit plan, the value of its equity is adjusted to reflect the amount by which the plan is overfunded or underfunded. It is not surprising that many companies have tried to replace defined benefit pension plans with defined contribution plans to avoid the risk of equity being eroded by a perfect storm.

Estimating the present value of the liabilities in defined benefit plans is not easy. An important issue is the discount rate used. The higher the discount rate, the lower the present value of the pension plan liabilities. It used to be common to use the average rate of return on the assets of the pension plan as the discount rate. This encourages the pension plan to invest in equities because the average return on equities is higher than the average return on bonds, making the value of the liabilities look low.

Accounting standards now recognize that the liabilities of pension plans are

obligations similar to bonds and require the liabilities of the pension plans of private companies to be discounted at AA‐rated bond yields. The difference between the value of the assets of a defined benefit plan and that of its liabilities must be recorded as an asset or liability on the balance sheet of the company. Thus, if a company's defined benefit plan is underfunded, the company's shareholder equity is reduced. A perfect storm is created when the assets of a defined benefit pension plan decline sharply in value and the discount rate for its liabilities decreases sharply (see Business Snapshot 3.2).

3.12.1 Are Defined Benefit Plans Viable?

A typical defined benefit plan provides the employee with about 70% of final salary as a pension and includes some indexation for inflation. What percentage of the

employee's income during his or her working life should be set aside for providing the

pension? The answer depends on assumptions about interest rates, how fast the employee's income rises during the employee's working life, and so on. But, if an insurance company were asked to provide a quote for the sort of defined benefit plan we are considering, the required contribution rate would be about 25% of income each year. (Problems 3.15 and 3.19 provide an indication of calculations that can be carried out.) The insurance company would invest the premiums in corporate bonds (in the same way that it does the premiums for life insurance and annuity contracts) because this provides the best way of matching the investment income with the payouts.

The contributions to defined benefit plans (employer plus employee) are much less than 25% of income. In a typical defined benefit plan, the employer and employee each contribute around 5%. The total contribution is therefore only 40% of what an insurance actuary would calculate the required premium to be. It is therefore not surprising that many pension plans are underfunded.

Unlike insurance companies, pension funds choose to invest a significant proportion of their assets in equities. (A typical portfolio mix for a pension plan is 60% equity and 40% debt.) By investing in equities, the pension fund is creating a situation where there is some chance that the pension plan will be fully funded. But there is also some chance of severe underfunding. If equity markets do well, as they have done from 1960 to 2000 in many parts of the world, defined benefit plans find they can afford their liabilities. But if equity markets perform badly, there are likely to be problems.

This raises an interesting question: Who is responsible for underfunding in defined benefit plans? In the first instance, it is the company's shareholders who bear the cost.

If the company declares bankruptcy, the cost may be borne by the government via insurance that is offered.⁴ In either case there is a transfer of wealth to retirees from the next generation.

Many people argue that wealth transfers from one generation to another are not acceptable. A 25% contribution rate to pension plans is probably not feasible. If defined benefit plans are to continue, there must be modifications to the terms of the plans so that there is some risk sharing between retirees and the next generation. If equity markets perform badly during their working life, retirees must be prepared to accept a lower pension and receive only modest help from the next generation. If equity markets perform well, retirees can receive a full pension and some of the benefits can be passed on to the next generation.

Longevity risk is a major concern for pension plans. We mentioned earlier that life expectancy increased by about 20 years between 1929 and 2013. If this trend continues and life expectancy increases by a further five years by 2029, the underfunding problems of defined benefit plans (both those administered by companies and those administered by national governments) will become more severe. It is not surprising that, in many jurisdictions, individuals have the right to

work past the normal retirement age. Depending on the rules governing pensions in a particular jurisdiction, this can help solve the problems faced by defined benefit pension plans. An individual who retires at 70 rather than 65 makes an extra five years of pension contributions and the period of time for which the pension is received is shorter by five years.

Summary

There are two main types of insurance companies: life and property‐casualty. Life insurance companies offer a number of products that provide a payoff when the policyholder dies. Term life insurance provides a payoff only if the policyholder dies during a certain period. Whole life insurance provides a payoff on the death of the insured, regardless of when this is. There is a savings element to whole life insurance.

Typically, the portion of the premium not required to meet expected payouts in the early years of the policy is invested, and this is used to finance expected payouts in later years. Whole life insurance policies usually give rise to tax benefits, because the present value of the tax paid is less than it would be if the investor had chosen to invest funds directly rather than through the insurance policy.

Life insurance companies also offer annuity contracts. These are contracts that, in return for a lump‐sum payment, provide the policyholder with an annual income from a certain date for the rest of his or her life. Mortality tables provide important

information for the valuation of the life insurance contracts and annuities. However, actuaries must consider (a) longevity risk (the possibility that people will live longer than expected) and (b) mortality risk (the possibility that epidemics such as AIDS or Spanish flu will reduce life expectancy for some segments of the population).

Property‐casualty insurance is concerned with providing protection against a loss of, or damage to, property. It also protects individuals and companies from legal

liabilities. The most difficult payouts to predict are those where the same event is liable to trigger claims by many policyholders at about the same time. Examples of such events are hurricanes or earthquakes.

Health insurance has some of the features of life insurance and some of the features of property‐casualty insurance. Health insurance premiums are like life insurance

premiums in that changes to the company's assessment of the risk of payouts do not lead to an increase in premiums. However, it is like property‐casualty insurance in that increases in the overall costs of providing health care can lead to increases in premiums.

Two key risks in insurance are moral hazard and adverse selection. Moral hazard is the risk that the behavior of an individual or corporation with an insurance contract will be different from the behavior without the insurance contract. Adverse selection is the risk that the individuals and companies who buy a certain type of policy are

those for which expected payouts are relatively high. Insurance companies take steps to reduce these two types of risk, but they cannot eliminate them altogether.

Insurance companies are different from banks in that their liabilities as well as their assets are subject to risk. A property‐casualty insurance company must typically keep more equity capital, as a percent of total assets, than a life insurance company. In the United States, insurance companies are different from banks in that they are regulated at the state level rather than at the federal level. In Europe, insurance companies are regulated by the European Union and by national governments. The European Union has developed a new set of capital requirements, known as Solvency II.

There are two types of pension plans: defined benefit plans and defined contribution plans. Defined contribution plans are straightforward. Contributions made by an employee and contributions made by the company on behalf of the employee are kept in a separate account, invested on behalf of the employee, and converted into a

lifetime annuity when the employee retires. In a defined benefit plan, contributions from all employees and the company are pooled and invested. Retirees receive a pension that is based on the salary they earned while working. The viability of defined benefit plans is questionable. Many are underfunded and need superior returns from equity markets to pay promised pensions to both current and future retirees.

Practice Questions and Problems (Answers at End of Book)

1. What is the difference between term life insurance and whole life insurance?

2. Explain the meaning of variable life insurance and universal life insurance.

3. A life insurance company offers whole life and annuity contracts. In which contracts does it have exposure to (a) longevity risk, (b) mortality risk?

4. “Equitable Life gave its policyholders a free option.” Explain the nature of the option.

5. Use Table 3.1 to calculate the minimum premium an insurance company should charge for a $1 million two‐year term life insurance policy issued to a woman age 50. Assume that the premium is paid at the beginning of each year and that the interest rate is zero.

6. From Table 3.1, what is the probability that a man age 30 will live to 90? What is the same probability for a woman age 30?

7. What features of the policies written by a property‐casualty insurance company give rise to the most risk?

8. Explain how CAT bonds work.

9. Consider two bonds that have the same coupon, time to maturity, and price. One is a B‐rated corporate bond. The other is a CAT bond. An analysis based on

historical data shows that the expected losses on the two bonds in each year of their life is the same. Which bond would you advise a portfolio manager to buy, and why?

10. How does health insurance in the United States differ from that in Canada and the United Kingdom?

11. An insurance company decides to offer individuals insurance against losing their jobs. What problems is it likely to encounter?

12. Why do property‐casualty insurance companies hold more capital than life insurance companies?

13. Explain what is meant by “loss ratio” and “expense ratio” for a property‐casualty insurance company. “If an insurance company is profitable, it must be the case that the loss ratio plus the expense ratio is less than 100%.” Discuss this

statement.

14. What is the difference between a defined benefit and a defined contribution pension plan?

15. Suppose that in a certain defined benefit pension plan

a. Employees work for 40 years earning wages that increase with inflation.

b. They retire with a pension equal to 75% of their final salary. This pension also increases with inflation.

c. The pension is received for 20 years.

d. The pension fund's income is invested in bonds that earn the inflation rate.

Estimate the percentage of an employee's salary that must be contributed to the pension plan if it is to remain solvent. (Hint: Do all calculations in real rather than nominal dollars.)

Further Questions

16. Use Table 3.1 to calculate the minimum premium an insurance company should charge for a $5 million three‐year term life insurance contract issued to a man age 60. Assume that the premium is paid at the beginning of each year and death always takes place halfway through a year. The risk‐free interest rate is 6% per annum (with semiannual compounding).

17. An insurance company's losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of $50 million. (Assume that the risks taken by the insurance company are entirely nonsystematic.) The one‐year risk‐free rate is 5% per annum with annual compounding. Estimate the cost of the following:

a. A contract that will pay in one‐year's time 60% of the insurance company's costs on a pro rata basis.

b. A contract that pays $100 million in one‐year's time if losses exceed $200 million.

18. During a certain year, interest rates fall by 200 basis points (2%) and equity prices are flat. Discuss the effect of this on a defined benefit pension plan that is 60%

invested in equities and 40% invested in bonds.

19. Suppose that in a certain defined benefit pension plan

a. Employees work for 45 years earning wages that increase at a real rate of 2%.

b. They retire with a pension equal to 70% of their final salary. This pension increases at the rate of inflation minus 1%.

c. The pension is received for 18 years.

d. The pension fund's income is invested in bonds that earn the inflation rate plus 1.5%.

Estimate the percentage of an employee's salary that must be contributed to the pension plan if it is to remain solvent. (Hint: Do all calculations in real rather than nominal dollars.)

Notes

2 See R. H. Litzenberger, D. R. Beaglehole, and C. E. Reynolds, “Assessing Catastrophe Reinsurance‐Linked Securities as a New Asset Class,” Journal of Portfolio Management (Winter 1996): 76–86.

3 See “How to Modernize and Improve the System of Insurance Regulation in the United States,” Federal Insurance Office, December 2013.

4 For example, in the United States, the Pension Benefit Guaranty Corporation

(PBGC) insures private defined benefit plans. If the premiums the PBGC receives from plans are not sufficient to meet claims, presumably the government would have to step in.

Dalam dokumen John C. Hull Risk Management and Financial Institutions Wiley 2018 (Halaman 125-134)