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Contrast defined benefit plans with defined contribution plans, setting out how they differ.

FRM® Part I · Financial Markets and Products · Insurance Companies and Pension Plans · FRM1.FM.2.d

The idea

In a defined benefit plan the employer promises a pension fixed by a formula. The typical formula is shown here. Pension = years of service × accrual rate × final salary. Some plans use average salary instead of final salary. The employer bears the investment risk, the longevity risk and any funding shortfall. Liabilities are valued by discounting the promised payments, so a lower discount rate raises liabilities and can turn a funded plan into an underfunded one. In a defined contribution plan the employer pays only an agreed contribution into an individual account and the employee receives whatever the account grows to. So the employee bears the investment risk and the risk of outliving the savings. Defined contribution accounts are also easily portable. Hybrid designs such as cash balance plans sit between the two. The exam point is who carries which risk: sponsor in defined benefit, member in defined contribution.

Formulas

Defined benefit annual pension

Pension = accrual × years × salary

accrual
the accrual rate per year of service
years
years of service
salary
the final or average salary the plan specifies

Use the salary the formula names; if it says the average of the final three years, average them rather than taking the last one.

Pension plan funded ratio

Funded ratio = Assets ÷ PV(L)

Assets
the market value of plan assets
PV(L)
the present value of the promised payments L, at the current discount rate

Compare assets with discounted, not undiscounted, liabilities. A lower discount rate raises the present value and lowers the ratio.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a defined contribution pension plan, who bears the investment risk on the plan assets?

  1. The insurer that administers the plan, which guarantees a minimum returnWhy not: Administrators of a defined contribution plan do not guarantee investment returns.
  2. The pension regulator, which compensates members for any shortfallWhy not: Regulators do not cover investment losses in a defined contribution plan.
  3. The employer, who must top up the account to a promised pensionWhy not: This describes a defined benefit plan; the employer promises only a contribution in a defined contribution plan.
  4. The employee, because the pension depends on the account balance - correct

In a defined contribution plan the employer's obligation ends once contributions are paid. The member keeps the investment risk and the risk of outliving the savings.

A harder one

A defined benefit plan pays an annual pension of 1.75% x years of service x average salary over the final three years. A member retires after 25 years of service with final three salaries of USD 90,000, USD 95,000 and USD 100,000. The annual pension is closest to:

  1. USD 43,750Why not: Uses only the final-year salary; the formula states the average of the final three years.
  2. USD 41,563 - correct
  3. USD 39,375Why not: Uses the lowest of the three salaries instead of the average.
  4. USD 124,688Why not: Sums the three salaries instead of averaging them, overstating the pension threefold.

Average salary = (90,000 + 95,000 + 100,000) / 3 = 95,000. Pension = 0.0175 x 25 x 95,000 = 41,562.50.

The hardest tier

A defined benefit plan has assets of USD 260 million and a single liability of USD 500 million due in 15 years, discounted at 5%. The discount rate then falls to 4% while assets are unchanged. The funded ratio (assets divided by present value of liabilities) after the fall is closest to:

  1. 52%Why not: Compares assets with the undiscounted liability of USD 500 million instead of its present value.
  2. 108%Why not: This is the funded ratio before the rate change; the liability must be re-discounted at 4%.
  3. 125%Why not: Applies the move in the wrong direction (6% instead of 4%), which lowers the liability value.
  4. 94% - correct

PV of liability at 4% = 500 / 1.04^15 = 277.6 million, versus 240.5 million at 5%. Funded ratio = 260 / 277.6 = 93.6%. Lower discount rates raise defined benefit liabilities.

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