Defined benefit and defined contribution pension plans

Welcome to the World of Retirement Planning!

Hello there! If you’re studying for Exam FAM, you’ve likely realized that actuarial science isn't just about life insurance—it's also about ensuring people can live comfortably after they stop working. In this chapter, we’re diving into Defined Contribution (DC) and Defined Benefit (DB) pension plans. These are the two "pillars" of employer-sponsored retirement security. Don't worry if the terminology feels a bit heavy at first; we’re going to break it down into simple, manageable pieces using real-world logic.

1. The Big Picture: What is a Pension?

At its simplest, a pension is a way for an employee to defer some of their income today so they have money to spend tomorrow (during retirement). The two types of plans differ mainly in who makes the decisions and who takes the risks.

2. Defined Contribution (DC) Plans

Think of a Defined Contribution Plan like a personal "Retirement Savings Jar."

In a DC plan, the amount going into the jar (the contribution) is defined. For example, your employer might put in 5% of your salary every month. However, the amount you get out when you retire isn't guaranteed—it depends on how well the investments in that jar grow.

Key Characteristics of DC Plans:

- Defined Input: The contribution rate is fixed (e.g., \(5\%\) of salary).
- Individual Accounts: Each employee usually has their own account.
- Investment Choice: The employee often gets to choose how to invest the money (stocks, bonds, etc.).
- Portability: If you leave your job, you can usually take your "jar" with you to your next employer.

Who Bears the Risk?

In a DC plan, the Employee bears almost all the risk.
- Investment Risk: If the stock market crashes right before you retire, your account balance drops, and your retirement income shrinks.
- Longevity Risk: If you live to be 105 but your money runs out at 90, that is your challenge to manage.

Quick Formula Insight:
The accumulated value (\(AV\)) at retirement for a DC plan is simply the sum of contributions plus investment earnings:
\(AV = \sum (\text{Contributions} \times (1 + i)^t)\)

Key Takeaway: DC = Defined Input, Uncertain Output. The Employee is in the driver's seat (and bears the risk!).

3. Defined Benefit (DB) Plans

Think of a Defined Benefit Plan like a "Retirement Promise."

In a DB plan, the amount you get out (the benefit) is defined by a specific formula. The employer promises to pay you a monthly check for the rest of your life starting at retirement. It doesn't matter how the stock market performs; the employer is on the hook to fulfill that promise.

Key Characteristics of DB Plans:

- Defined Output: The benefit is calculated using a formula based on years of service and salary.
- Pooled Funds: There are no individual accounts; the employer manages one big pool of money for everyone.
- No Investment Choice: The employer (or a professional manager) decides how to invest the money.
- Longevity Protection: The benefit is usually paid as an annuity (a monthly check for life), so you can't "outlive" your money.

Who Bears the Risk?

In a DB plan, the Employer bears the risk.
- Investment Risk: If the pension fund's investments perform poorly, the employer must dig into their own pockets to make up the difference.
- Longevity Risk: If retirees live much longer than expected, the employer has to keep paying those monthly checks longer than planned.

Did you know? Because DB plans are risky and expensive for companies to maintain, many private employers have shifted toward DC plans over the last few decades.

Key Takeaway: DB = Uncertain Input, Defined Output. The Employer is the "guarantor" of the promise.

4. Common DB Benefit Formulas

Since the "Benefit" is defined, we need a way to calculate it. Most formulas look like this:
Annual Benefit = \( \text{Accrual Rate} \times \text{Years of Service} \times \text{Salary Base} \)

There are two common ways to determine the Salary Base:

1. Final Average Salary (FAS): The average of your highest-earning years (usually the last 3 or 5 years before retirement). This protects against inflation right before retirement.
2. Career Average Salary (CAS): The average of your salary over your entire career with the company. This usually results in a lower benefit than FAS because it includes your lower starting salaries.

Example Calculation:
If an employee works for 30 years, their Final Average Salary is \(\$80,000\), and the accrual rate is \(1.5\%\):
\n\( \text{Annual Benefit} = 0.015 \times 30 \times 80,000 = \$36,000 \text{ per year} \)

Key Takeaway: The more you work and the more you earn, the bigger your "Promise" becomes.

5. Comparing the Risks: A Quick Review

This is a favorite topic for exam questions! Let's summarize who handles what:

1. Investment Risk:
- DC: Employee (Your account might go down).
- DB: Employer (The company must fund the shortfall).

2. Longevity Risk (Living too long):
- DC: Employee (You might run out of cash).
- DB: Employer (They must pay as long as you live).

3. Inflation Risk:
- DC: Employee (The purchasing power of your savings might drop).
- DB: Shared (Some DB plans offer Cost of Living Adjustments, or COLAs, but many do not).

Common Mistake to Avoid: Don't assume DB plans are "better" for everyone. While they offer more security, they are often less portable. If you switch jobs frequently, a DC plan (like a 401k) might actually build more wealth for you than a DB plan where you never stay long enough to "vest."

6. Summary and Final Tips

- Remember the "D": In Defined Contribution, you know what goes in. In Defined Benefit, you know what comes out.
- Follow the Risk: If the question asks about investment volatility, think about who owns the assets. In DC, it's the individual; in DB, it's the company.
- Formula Practice: Make sure you are comfortable calculating the Annual Benefit using the formula: \( \text{Benefit} = k \cdot n \cdot S \). It’s the bread and butter of DB math!

Don't worry if the distinction between these plans feels subtle at first. Just keep asking yourself: "Who is responsible if the stock market crashes?" and "Who is responsible if the retiree lives to 110?" Once you answer those, the rest of the logic falls into place!