Ladder, Barbell, Bullet or One Long CD

Which of these are you?

• You need all the money on one known date. Use a bullet: CDs that all mature on that date. One long CD is the simplest version.
• You need cash in pieces over several years. Use a ladder, with rungs that mature when the pieces are due.
• You want a few dollars of safety plus a long-term rate. Use a barbell, with short CDs for access and a long CD for yield, and nothing in between.
• You have no idea when you will need it. Favor shorter and staggered maturities, and read the failure mode near the end of this chapter before you lock any of it.

The four structures

All four structures answer the same question: given a lump sum and a menu of terms, how should the maturities be arranged?

• Ladder: equal amounts in terms that step up, such as 1, 2, 3, 4 and 5 years. One rung matures each year, and the maturing rung is renewed at the longest term. The ladder mechanics are in Chapter 6.
• Barbell: money at the two ends only, for example half in a 1-year CD and half in a 5-year CD.
• Bullet: several CDs bought to mature on one target date. A single long CD is a bullet with one position.
• One long CD: the whole amount at one long term, held to maturity.

The structure changes when money comes back, and that changes how much depends on the reinvestment rate: the rate you will earn later when a CD matures and you have to buy another. The Fed staff note on forward rates describes a forward rate as the market's expected short rate plus a term premium. A long CD contains that expectation already, locked in. A shorter CD leaves the expectation unresolved and asks you to renew at whatever the rate turns out to be.

Average maturity is not the whole picture

The average maturity of N equal rungs spaced s months apart is s x (N + 1) / 2 months. A five-rung annual ladder therefore averages 12 x (5 + 1) / 2 = 36 months. A barbell with half its money at 12 months and half at 60 months averages (12 + 60) / 2 = 36 months as well. A bullet at 60 months averages 60 months.

The ladder and the barbell share an average and have different shapes. The ladder has a rung coming due every 12 months, so it renews one-fifth of the money each year. The barbell renews half of the money every year, at the 1-year end, and locks the other half for five years. So the barbell has more money exposed to each renewal and less money in the middle terms. Average maturity is the first number to compute, not the last: it hides which dollars mature when.

The worked comparison: $50,000 over five years

This example holds the rate sheet fixed and moves only the reinvestment rate. It uses the tested comparison function behind the calculator below. All rates are hypothetical. Annual compounding, no taxes, no penalties, no call features.

Setup (hypothetical). Capital C = $50,000. Ladder: five equal $10,000 rungs at 4.00%, 4.10%, 4.20%, 4.30% and 4.40% APY for 1 through 5 years. One long CD: $50,000 at 4.50% APY for 5 years. Reinvestment APY before any shift: 4.00%. A shift moves the reinvestment rate by a parallel amount from the first day.

Formulas.

• Long CD value: L = C x (1 + y5)^5
• Ladder value: sum over rungs k = 1 to 5 of (C / 5) x (1 + yk)^k x (1 + r)^(5 - k), where r is the reinvestment APY after the shift and yk is the APY on rung k.

Steps at zero shift.

1. Long CD: 50,000 x 1.045^5 = $62,309.10.
2. Rung 1: 10,000 x 1.04 = $10,400.00 at year 1, then 4 years at 4.00%: $12,166.53.
3. Rung 2: 10,000 x 1.041^2 = $10,836.81, then 3 years at 4.00%: $12,189.94.
4. Rung 3: 10,000 x 1.042^3 = $11,313.66, then 2 years at 4.00%: $12,236.86.
5. Rung 4: 10,000 x 1.043^4 = $11,834.15, then 1 year at 4.00%: $12,307.52.
6. Rung 5: 10,000 x 1.044^5 = $12,402.31, matures at year 5 with nothing to reinvest.
7. Ladder total: 12,166.53 + 12,189.94 + 12,236.86 + 12,307.52 + 12,402.31 = $61,303.15.
8. Ladder minus long CD: 61,303.15 - 62,309.10 = -$1,005.95.

At unchanged reinvestment rates the ladder trails by $1,005.95, because its early rungs sit at lower APYs than the long CD and their reinvestment earns 4.00%. That is the price of access. Now move the reinvestment rate.

The break-even shift, the point where the ladder ties the long CD, is 0.85 points. Below that, the long CD leads. Above it, the ladder leads.

Two cautions on reading the table. First, the barbell column is a side calculation on the same sheet, with $25,000 in a 1-year CD at 4.00% rolled annually at the reinvestment rate, and $25,000 in the 4.50% five-year CD. It beats the ladder here because half its money sits at 4.50% for five years while the ladder's rungs earn 4.00% to 4.40%. That is a fact about this hypothetical rate sheet, not a general property of barbells. Second, the shift is applied to every reinvestment from day one. Real rate paths wobble, rise and fall, and no table like this forecasts one.

What the table teaches

The long CD is a decision to pay for certainty: it delivers $62,309.10 whatever happens to reinvestment rates, because there is nothing to reinvest. The ladder is a decision to pay for access and adaptability: it delivers less than the long CD at unchanged rates and more if reinvestment rates rise enough. The gap between them at zero shift, $1,005.95, is the premium you pay for a maturing rung every year.

Whether that premium is worth paying depends on facts the table does not contain: whether you might need a rung of cash, whether you would be forced to break a long CD, and whether the sheet you see today is steep or inverted. On an inverted sheet the long CD may pay less than the shorter ones, and the ladder's cost falls or disappears. Chapter 11 shows how to test that.

Reinvestment risk versus lock-in

Reinvestment risk is the risk that maturing money can only be renewed at a lower rate. Lock-in is the opposite exposure: you are stuck at a rate that later looks low, and cannot take a higher one without a penalty. A long CD removes reinvestment risk and takes on lock-in. A short-term or laddered structure reduces lock-in and takes on reinvestment risk. Neither structure escapes both, and you cannot know in advance which one will hurt.

What you can control is whether either risk can force a bad outcome. Reinvestment risk hurts if you depend on the interest for spending. Lock-in hurts if you might need the money early and would pay a penalty. The penalty mechanics and the break-even replacement rate are in Chapter 3. A bullet CD for a dated goal, such as tuition due on a known date, removes reinvestment risk exactly where you care about it.

The price-risk point for brokered CDs

A bank-direct CD has no market price: if you break it, you pay a penalty set in the account agreement. A brokered CD trades in a secondary market, and if you sell before maturity the price moves with rates. FINRA's notice on brokered CDs says that when interest rates rise, the market value of a long-term CD declines, that sellers generally incur a transaction cost such as a commission, and that there is no insurance coverage for principal losses on a secondary-market sale. Chapter 9 covers the full comparison.

Worked example, price risk (hypothetical). A $1,000 par brokered CD pays a 4.50% annual coupon, 3 years remain, and it was bought at par. Assume an annual coupon of $45 for simplicity. Price = sum of coupon / (1 + y)^t plus par / (1 + y)^3.

1. At a market yield of 4.50%: price = $1,000.00.
2. Yield rises 1 point to 5.50%: 45 / 1.055 + 45 / 1.055^2 + 1,045 / 1.055^3 = $973.02, a loss of $26.98 (2.70%).
3. Yield falls 1 point to 3.50%: 45 / 1.035 + 45 / 1.035^2 + 1,045 / 1.035^3 = $1,028.02, a gain of $28.02.
4. Approximation: change in price is about minus modified duration x change in yield x price. Modified duration here is 2.749, so the estimate for a 1 point rise is 2.749 x 0.01 x $1,000 = $27.49 loss, against $26.98 exact. The approximation slightly overstates the loss because price and yield are convex.

For structure, a long brokered CD you may sell early adds price risk that a bank-direct CD held to maturity does not have. If you will hold to maturity the price moves do not matter. If a sale is possible, count it.

Choosing a structure

Use the tiers from Chapter 2 to decide which money belongs in which structure. Tier 3 money, the dated goals inside 181 to 720 days, is a natural bullet or short ladder. Reserve money belongs in savings or Treasury bills, not in a long CD. Anything needed after 720 days is outside the cash tiers.

Cadence matters as well: a ladder with monthly rungs behaves differently from one with annual rungs, and the extra accounts have costs. Chapter 7 covers the choice.

Run your own numbers with the CD ladder calculator. Set the rung APYs from a real rate sheet, then move the reinvestment shift to see where your break-even sits. If the break-even shift is small, the ladder costs little for its flexibility. If it is large, the long CD is paying you a lot to lock the money, and you should be sure of your date before you take it.