Cap, participation and spread on the same index path: a worksheet

Three accounts can look equally generous in a brochure and behave very differently in practice. One caps the credit, one gives you a share of the index gain, and one subtracts a fixed amount from it. Which pays more depends on what the index does, and the way to see that is to run all three on the same numbers. This worksheet does that with an invented five-year index path, shows each calculation, and then gives you blanks for the terms in your own contract.

Everything here is hypothetical. The index levels and the three sets of terms are made up for the arithmetic; real accounts come with their own terms, which the insurer declares and can change. The same mechanics apply to the index accounts in an indexed universal life policy and in an indexed annuity.

The three methods in one line each

• Cap. The credit equals the index change, up to a maximum, with a floor of 0%. Our example: a cap of 8%, participation of 100%.
• Participation rate. The credit equals a stated percentage of the index change, with no cap and a floor of 0%. Our example: 60%.
• Spread (also called a margin or asset fee). The credit equals the index change minus a fixed number of percentage points, never below the floor of 0%. Our example: a spread of 3 points, participation of 100%.

Terms for cap rate, participation rate and floor are in the glossary. Real products sometimes combine them, for example a participation rate with a cap, but separating them shows the effect of each.

Step 1: Write down the index path

Here is one invented path, path A, for a price index that starts at 1,000. Each year is one crediting term, annual point-to-point.

The index change is (end − start) ÷ start. Year 3: (1,008 − 1,120) ÷ 1,120 = −112 ÷ 1,120 = −10%.

Across five years the index rose from 1,000 to 1,153.15, a total gain of about 15.3%, or less than 3% a year. It is a bumpy path with one big up year, one flat year, one down year and two moderate gains.

Step 2: Compute each year's credit

For each year, apply the method to the index change. Show the work.

Cap 8% (participation 100%, floor 0%). Credit = the smaller of the index change and 8%, but not below 0%.

• Year 1: +12% is above the cap, so the credit is 8%.
• Year 2: 0%.
• Year 3: −10% is below the floor, so the credit is 0%.
• Year 4: +10% is above the cap, so 8%.
• Year 5: +4%, below the cap, so 4%.

Participation 60% (no cap, floor 0%). Credit = 60% of the index change, not below 0%.

• Year 1: 0.60 × 12% = 7.2%.
• Year 2: 0%.
• Year 3: 0% (the floor).
• Year 4: 0.60 × 10% = 6.0%.
• Year 5: 0.60 × 4% = 2.4%.

Spread 3 points (participation 100%, no cap, floor 0%). Credit = index change minus 3, not below 0%.

• Year 1: 12% − 3 = 9%.
• Year 2: 0% − 3 = −3%, so the floor gives 0%.
• Year 3: 0% (the floor).
• Year 4: 10% − 3 = 7%.
• Year 5: 4% − 3 = 1%.

Collected in one table:

Step 3: Compound the credits

Start with $10,000 in each account and multiply by (1 + credit) each year. Charges are ignored here; the policy's monthly deductions come on top of everything below.

• Cap: 10,000 × 1.08 × 1.00 × 1.00 × 1.08 × 1.04 = $12,130.56.
• Participation: 10,000 × 1.072 × 1.00 × 1.00 × 1.06 × 1.024 = $11,635.92.
• Spread: 10,000 × 1.09 × 1.00 × 1.00 × 1.07 × 1.01 = $11,779.63.
• The index itself, for comparison: 10,000 × 1.12 × 1.00 × 0.90 × 1.10 × 1.04 = $11,531.52.

On path A the cap account ends ahead, the spread account is second, the participation account is third and all three finish above the index, because the floor skipped the year-3 loss. That last point is worth sitting with: the index, which lost 10% in one year, ended below all three accounts. A floor is valuable when losses occur.

Step 4: Change the path and run it again

Method rankings are not fixed. Run two more invented paths through the same three sets of terms.

Path B: steady 5% a year for five years.

In a calm, steadily rising market the cap account matches the index because 5% never reaches 8%. The participation account gives up 40% of every gain and the spread account gives up 3 points each year, which is a larger share of a small gain. A spread hurts most when index changes are modest.

Path C: big swings, +20%, −5%, +20%, −5%, +20%.

Here the ranking flips. The cap account, which was best on path A, is last, because it gives up 12 points in each big year. The spread account is first and even finishes above the index, because the floor skips both losing years and the spread is a small share of a 20% gain. The index ended near $15,595 while the spread account ended near $16,016. These terms are invented, and no claim is made that a real account offers them; the point is only that the answer depends on the path, not on the label.

When does each method win? The break-even points

Because each method is a simple formula, you can find the index change at which two methods pay the same.

Look at the pattern. Caps favor small and middling years and give up the largest gains. Spreads favor large years and take a bigger bite from small ones. Participation rates sit between: they scale every gain down by the same share. If the index typically moves a few percent a year, a cap is usually the better tool; if you expect rare, large moves, a spread or a high participation rate does better. Nobody can forecast which kind of path is coming. Insurers set these terms partly from the cost of the options they buy to fund the credits, so a lower cap paired with a higher participation rate, or the reverse, can be built to cost the insurer about the same. That is a reason to compare designs by running paths through them, not by picking the one with the biggest single number.

Step 5: Your turn

Use the blanks below with the terms in your own contract or proposal. Make a copy and fill it in.

A. Terms (from the current declaration letter or illustration).

• Index name: ______
• Crediting method (annual point-to-point, monthly sum, averaging, multi-year): ______
• Cap: ______ % Participation rate: ______ % Spread: ______ % Floor: ______ %
• Guaranteed minimum cap or maximum spread in the contract: ______

B. The formula. Credit = (index change × participation) − spread, then no more than the cap and no less than the floor. Check the order in your contract; some apply the spread before the participation rate.

C. Compute. For each of the last five years, write the index start and end levels from the statement, then:

1. Index change = (end − start) ÷ start: ______ %
2. Multiply by participation: ______ %
3. Subtract spread: ______ %
4. Apply the cap: ______ %
5. Apply the floor: ______ %
6. Compare with the credit on your statement: ______ %

D. Test three alternative paths. Rerun step C on a flat year, a +15% year and a −20% year. Record the credit in each. Then rerun it at a lower cap or a lower participation rate than today's, to see what a change by the insurer would do.

E. Where you start giving up gains. With a cap, you receive the full index change only up to the cap divided by the participation rate (a cap of 8% with 100% participation means gains above 8% are trimmed). With a participation rate below 100% and no cap, you receive less than the index on every positive change. With a spread, you give up the spread on every gain, and gains smaller than the spread credit nothing. Write down which of these applies to you.

Reading the results: three lessons

Averages hide the path

Add up path A's index changes and divide by five and you get a 3.2% average a year. The index actually grew about 2.89% a year when compounded (1.1532 raised to the power of one fifth, minus one). The cap account's credits average 4.0% a year, and its compounded rate is about 3.94%. The participation account averages 3.12% and compounds at about 3.08%, and the spread account averages 3.4% and compounds at about 3.33%.

These differences are small in a five-year example and become large over twenty or thirty years. A sales illustration that shows a single steady rate, say 6% every year, is describing none of these paths. Real credits come in lumps, with zeros in between, and a policy's account has to survive the zeros. Ask for the crediting history of the account for the past ten or more years, with the cap actually in force each year, as IUL caps, participation rates and floors advises.

The floor is a feature with a price

All three accounts in path A skipped the year-3 loss. That protection is not free. It is paid for through the cap, the partial participation or the spread, and the insurer sets those terms with the cost of the protection in mind. When someone says "you get the upside with no downside," the accurate version is "you get part of the upside with no index downside, and you pay for the arrangement through the part you do not get." For some buyers that is a fair trade, and for others it is not, but both groups are better off seeing the numbers.

The terms can change

The worksheet uses the same terms for five years. In a real contract the insurer declares new terms for each term, within guaranteed limits. In a period of lower interest rates, caps tend to be lower. The guaranteed minimum cap can be far below today's. Rerun step 2 at a cap of, say, 5% to see how path A changes: the year-1 and year-4 credits fall to 5%, and the cap account compounds to 1.05 × 1.00 × 1.00 × 1.05 × 1.04 = 1.1466, or $11,466 on $10,000, below the index's $11,531.52. That is how a cap that looks fine today can become a headwind if it is reduced.

A short guide to reading a proposal

When you are handed a proposal for an indexed account, spend ten minutes with the worksheet before you read the glossy pages.

1. Find the account list. Most policies offer several index accounts and a fixed account. Each has its own method and terms.
2. Find the current and guaranteed terms. Current terms are what the insurer says it will use now. Guaranteed terms are the worst the contract allows.
3. Run your own path. Use path A or any path you find realistic. If the illustration shows a steady 6.5% each year, run a path with flat and down years and see how far the credits fall short.
4. Notice the method. Annual point-to-point, monthly caps and averaging respond differently. If the proposal does not say, ask.
5. Compare designs by the same path. If one account has a lower cap and another a higher spread, run both on the same index changes before choosing.

One more variation: the same year under a monthly cap

Say the index changed month by month as follows in one year: +3%, +1%, −4%, +2%, +2%, 0%, +1%, −5%, +4%, +3%, +1%, +2%. Compounded, those twelve months add up to a year-end change of about +10.0% (the product of the twelve monthly factors is 1.1002).

• Annual point-to-point with the 8% cap: the insurer looks only at the start and end levels, sees +10.0%, and the cap holds the credit to 8%.
• Monthly cap of 2%, with the floor applied to the annual total: each month's gain is limited to 2%, each month's loss counts in full, and the twelve results are added. The months become +2, +1, −4, +2, +2, 0, +1, −5, +2, +2, +1, +2, which sum to 6. The credit is 6%.

The same 10.0% year pays 8% under one method and 6% under the other, because the monthly method trimmed the +3% and +4% months while counting the −4% and −5% months in full. In a year of steady gains the monthly cap usually pays less than the annual cap. In a year that ends flat, the annual method pays 0% while a monthly method can still pay something if the capped gains outweigh the losses. A monthly cap and an annual cap are different numbers doing different jobs, so a headline cap alone cannot be compared across accounts that use different methods.

What the worksheet leaves out

• Charges. The policy deducts the cost of insurance and other charges every month. The returns above are credits, not what your policy earned after costs.
• Monthly and averaging methods. They produce different credits from the same index path. A monthly cap, for example, caps each month's gain and counts each month's loss, so a volatile year can credit less than an annual point-to-point method. Rerun the worksheet using the monthly changes if your account uses them.
• Changing terms. Caps and participation rates are declared for each term. A worksheet run on today's terms shows today's account, not next year's.
• Illustration rules. Regulators limit the rate an illustration may assume; see IUL illustrations and Actuarial Guideline 49 for the NAIC guideline. The limit shapes a sales illustration. It does not predict what an account will earn.

For the full picture of how a crediting year proceeds, read From index move to account value: one IUL crediting year in order, and for stress-testing an illustration at lower rates, Stress-testing an IUL illustration with lower assumed rates.

Key takeaways

• A cap, a participation rate and a spread are different ways to share an index gain. Which pays more depends on how large the typical year is, not on the label.
• On the invented bumpy path, the cap account ended highest ($12,130.56 per $10,000). On a steady 5% path the cap matched the index and the spread did worst. On a path with big swings the order reversed.
• A floor of 0% matters most in loss years; in the examples it lifted all three accounts above the index on path A.
• The break-even index changes (13.3%, 11% and 7.5% in this example) let you compare terms without guessing at the future.
• Recompute at least one credit from your own statement, and rerun the worksheet at a lower cap, because declared terms can change.