Bond Ladders

Why this matters

Bond Funds vs. Individual Bonds ended with the one thing an individual bond does that a fund can't: pay a known amount on a known date. A single bond does that once. Most people who want that certainty want it more than once, as income every year or as a run of bills to be paid. A ladder is the arrangement that provides it. It's also the simplest answer to a question nobody can settle, whether to buy short bonds or long ones: it buys both and keeps buying.

How a ladder is built

A ladder divides a sum equally among bonds that mature at regular intervals. Each maturity is called a rung.

Rung	Amount	Matures in	Yield	Yearly income
1	$10,000	1 year	4.4%	$440
2	$10,000	2 years	4.7%	$470
3	$10,000	3 years	4.8%	$480
4	$10,000	4 years	4.9%	$490
5	$10,000	5 years	5.0%	$500
The ladder	$50,000	3 years on average	4.76%	$2,380

Each bond is bought at face value and pays its coupon yearly.

In a year, rung 1 matures and returns $10,000. Every other bond is now a year shorter: the 2-year has become a 1-year, the 5-year a 4-year. The owner has two choices.

• Roll it. Buy a new 5-year bond with the $10,000. The ladder again runs from one to five years, and the process repeats every year for as long as the owner likes.
• Spend it. Take the $10,000. The ladder is then one rung shorter, and in five years it has paid out everything.

A rolled ladder is a permanent holding, close in character to a bond fund with an average maturity of about three years. A spent ladder is a schedule of payments. The two uses are worth keeping apart, and this lesson takes them in turn.

A rolled ladder when rates change

Suppose every yield rises by two points the day after the ladder is built, and stays there. A new 5-year bond now pays 7.0%.

Year	Rungs at old yields	Income if yields rose	Income if yields fell
1	5 of 5	$2,380	$2,380
2	4 of 5	$2,640	$2,240
3	3 of 5	$2,870	$2,070
4	2 of 5	$3,090	$1,890
5	1 of 5	$3,300	$1,700
6	None	$3,500	$1,500

Each year the maturing rung is replaced with a new 5-year bond, at 7.0% in one case and 3.0% in the other. The ladder's income moves a fifth of the way toward the new level each year and arrives there in the sixth.

That gradual adjustment is the ladder's defining behaviour. It never gets the full benefit of a rate rise at once, and it never takes the full damage of a fall at once. Compare it with the two simpler ways of investing the same $50,000.

Hypothetical, using the yields in the first table.

The short strategy has the most uncertain income. This is reinvestment risk, the risk that money coming back can only be reinvested at lower rates.¹ The single 5-year bond has perfectly certain income, for five years. Then all $50,000 has to be reinvested on one day at whatever rates exist, which is the same risk postponed and concentrated. The ladder's income is half as variable as the short strategy's, and it never bets everything on one day's rates. It's a way of buying at the average of many years' yields.

The price side

Income is half the picture. The value of the bonds moves too.

Hypothetical, calculated as in Duration and Convexity.

A ladder isn't immune to rates. Its bonds are worth about 5% less after a two-point rise, and the last lesson showed that the loss is real whether or not anything is sold. What the ladder adds is that nothing ever has to be sold. Cash arrives every year from a bond maturing at full face value, so a holder who needs money takes it from the maturing rung and leaves the bonds that are below their purchase price to recover as they approach maturity. That's a real advantage over a fund for someone drawing on the money, and it's a matter of cash flow. The wealth is the same.

A ladder for known expenses

The second use doesn't roll anything. Each rung is sized to pay a particular bill.

A family expects to need $25,000 a year for four years, starting three years from now. It buys zero-coupon Treasuries maturing on each date.

Needed in	Amount	Yield on a zero of that maturity	Cost today
3 years	$25,000	4.8%	$21,720
4 years	$25,000	4.9%	$20,646
5 years	$25,000	5.0%	$19,588
6 years	$25,000	5.1%	$18,549
Total	$100,000		$80,503

Yields are compounded yearly. For $80,503 today, the $100,000 is secured, in dollars, whatever happens to interest rates between now and then.

This is the matching idea from Interest Rate Scenarios at its cleanest. Each payment is met by a bond that matures exactly then, so there's no price risk and no reinvestment risk on the amounts needed. Zero-Coupon Bonds and STRIPS covers the bonds used here, including the tax on their accrued interest in a taxable account. Ordinary coupon bonds work too, with the coupons contributing to earlier years' needs.

Two limits apply. The amounts are fixed in dollars, so if the costs rise with inflation the ladder will fall short, and inflation-protected bonds are the tool for that. And a plan that changes, with money needed sooner, means selling bonds at whatever the market offers.

Choices in building one

• What kind of bond. Treasuries need no diversification, and bills and notes can be bought for as little as $100²³ at auction, where every buyer pays the same price.⁴ A ladder of corporate or municipal bonds adds yield, or a tax advantage, and needs several issuers on each rung to be safe from one default, which takes more money. Bank certificates of deposit can be laddered the same way, as Savings Accounts, CDs, and Money Market Funds describes.
• How long. A longer ladder holds longer bonds, so it has a higher duration, an income that changes more slowly, and a higher yield when the curve slopes upward. A ladder to ten years responds to rates half as fast as one to five.
• How many rungs. More rungs mean smaller, more frequent maturities and smoother income. Rungs can be a year apart, or six months, or a quarter.
• Callable bonds. A bond that can be called may be redeemed when rates are falling,¹ which removes a rung just when its yield is most valuable. Bonds that can't be called keep a ladder intact.

Ladder, barbell, bullet

The Yield Curve in Depth compared a bullet, concentrated at one maturity, with a barbell, split between short and long. A ladder is the third pattern, spread evenly across all of them. It takes no view on the shape of the curve, which is its attraction for an investor who doesn't have one.

What a ladder doesn't do

• It doesn't beat a fund on return. A rolled ladder and a fund of the same average maturity and quality hold much the same bonds and earn much the same, before costs. The ladder saves a fund's fee and costs the owner markups and effort.
• It doesn't remove interest rate risk. It spreads it over time. The table above showed a 5% fall in value and an income that still drifts with rates.
• It doesn't protect against inflation, unless it's built from inflation-protected bonds.
• It doesn't diversify credit risk by itself. Five rungs of five corporate bonds is five issuers.
• It isn't liquid in the middle. A bond sold between rungs goes at the dealer's bid, and corporate and municipal bonds can be hard to sell at a fair price in a stressed market.⁵

Key takeaways

• A ladder holds equal amounts in bonds maturing at regular intervals. Each maturing rung is spent or replaced at the long end.
• A rolled ladder's income follows rates gradually: a five-rung ladder moves a fifth of the way each year.
• It sits between short bonds, with steady value and unsteady income, and a long bond, with the reverse.
• A ladder's value still falls when rates rise, but cash comes from maturing bonds, so nothing has to be sold at a loss.
• Sized to known expenses, a ladder secures fixed dollar amounts on fixed dates.
• Treasuries suit ladders best. Other bonds need more issuers per rung, and callable bonds break the pattern.

Check your understanding

An investor holds a ten-rung ladder, one bond maturing each year, and rolls each maturity into a new 10-year bond. Interest rates fall sharply and stay low. What happens to the ladder's income?

1. It falls to the new level immediately, as all yields have dropped.
2. It falls gradually, about a tenth of the way each year for ten years.
3. It never changes, because every bond's coupon was fixed at purchase.

Someone needs $30,000 on a fixed date in each of the next three years and wants the amounts to be certain. Which arrangement fits?

1. Three Treasuries, each maturing just before one of the three dates.
2. One intermediate-term bond fund, selling $30,000 of it each year.
3. One 10-year Treasury, selling a third of it in each of the years.

What's next

That's the last lesson of Fixed Income in Depth. Practice: Credit and Markets works through credit, spreads, municipal yields, mortgage securities, and ladders with numbers of your own to calculate.