A $125,000 investment-grade ladder bought at par: income, the reinvestment rule, six years of income when rates move, and the price risk against one long bond.
A bond ladder splits a sum equally across bonds that mature one year apart, and reinvests each maturing bond at the long end, so the portfolio always has money coming back and always buys at the current rate. A $125,000 ladder of five investment-grade bonds maturing in two to six years pays $6,412.50 a year, an average yield of 5.13 per cent, and returns $25,000 every year from year two. If rates move two points either way after purchase, six-year income ranges from $34,312.50 to $44,312.50: half the range of buying short and rolling, and with less price risk than one long bond.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A ladder is not a way to earn more. It is a way to decide in advance how much of the portfolio meets each future interest rate, and it does that with arithmetic anyone can check.
| Bond | Rating | Matures, year | Coupon | Income a year |
|---|---|---|---|---|
| Aldermoor Utilities | A | 2 | 4.80% | 1,200.00 |
| Carrow Rail | A | 3 | 4.95% | 1,237.50 |
| Hesketh Foods | BBB | 4 | 5.15% | 1,287.50 |
| Penrith Medical | BBB | 5 | 5.30% | 1,325.00 |
| Stanwick Networks | BBB | 6 | 5.45% | 1,362.50 |
| Ladder | 4.0 average | 5.13% | 6,412.50 |
Rung size = sum invested / number of rungs = 125,000 / 5 = 25,000
Income a year = Σ face × coupon = 6,412.50; average yield = 6,412.50 / 125,000 = 5.13%
Rule: when a rung matures, buy a new bond at the longest rung
In Excel: =SUMPRODUCT(Face,Coupon)/SUM(Face) for the yield of a ladder bought at par, and =SUMPRODUCT(Face,Maturity)/SUM(Face) for its average maturity.
Year 2. Aldermoor repays $25,000. The ladder now runs from one to four years, so the cash goes into a new five-year bond, maturing in year 7. Year 3. Carrow repays and the same happens. After four maturities the ladder holds five bonds all bought at the market rates of years two to six, and it keeps rolling. Over the first three years, the five original bonds pay $18,037.50 of coupons.
Suppose rates move just after purchase and stay there, so every new five-year bond is bought at 5.30 per cent, or two points either side. Compare three ways of placing the same $125,000 for six years: the ladder, one six-year bond at 5.45 per cent, and a short strategy of two-year bonds at 4.80 per cent rolled into four-year bonds.
| Year | Ladder, rates −2 | Ladder, unchanged | Ladder, rates +2 | Six-year bond |
|---|---|---|---|---|
| 1 | 6,412.50 | 6,412.50 | 6,412.50 | 6,812.50 |
| 2 | 6,412.50 | 6,412.50 | 6,412.50 | 6,812.50 |
| 3 | 6,037.50 | 6,537.50 | 7,037.50 | 6,812.50 |
| 4 | 5,625.00 | 6,625.00 | 7,625.00 | 6,812.50 |
| 5 | 5,162.50 | 6,662.50 | 8,162.50 | 6,812.50 |
| 6 | 4,662.50 | 6,662.50 | 8,662.50 | 6,812.50 |
| Six years | 34,312.50 | 39,312.50 | 44,312.50 | 40,875.00 |
| Strategy | Rates −2 | Unchanged | Rates +2 | Range |
|---|---|---|---|---|
| Short: two-year bonds, then four-year | 27,750.00 | 37,750.00 | 47,750.00 | 20,000.00 |
| Ladder, two to six years | 34,312.50 | 39,312.50 | 44,312.50 | 10,000.00 |
| One six-year bond | 40,875.00 | 40,875.00 | 40,875.00 | 0.00 |
The ladder exposes half of what the short strategy exposes to the reinvestment rate. The six-year bond exposes nothing over six years, and earns the most if rates are unchanged, because it sits at the top of an upward-sloping curve. Its cost appears elsewhere: in price, and in access to the money. The comparison counts income only: at the end of year six the bullet and the short strategy have repaid their principal, while the ladder still holds five bonds, worth more than face if rates fell and less if they rose.
| Holding | Value before | Value after | Change |
|---|---|---|---|
| Ladder: rungs at 96.32, 94.67, 93.15, 91.75 and 90.46 | 125,000 | 116,586 | −6.73% |
| One six-year bond, at 90.46 | 125,000 | 113,079 | −9.54% |
The ladder loses $8,414 on paper against $11,921 for the bullet, and it hands back 20 per cent of its principal every year to be reinvested at the new, higher rate. If the investor needs cash in year three, the ladder pays it from a maturing bond at 100; the six-year bond has to be sold at whatever the market offers. Hold every bond to maturity and neither paper loss is realised, which is the argument for ladders in one sentence.
The width of the ladder is the lever. A ladder of one to three years hands back a third of the money each year and behaves almost like rolling bills; one of one to ten years behaves more like a long bond, with more income on an upward-sloping curve and more price movement. Choose the longest rung for the income needed and the shortest for the cash that may be called on.
Equal amounts, maturities one year apart, each maturity reinvested at the long end: $6,412.50 a year at 5.13 per cent here, with half the reinvestment risk of going short and 6.73 per cent of price risk against 9.54 for one long bond. How each rung's price moves with yields is worked in how to calculate the modified duration of a bond, and this ladder is one sleeve of the seventeen-line portfolio carried from the screen yield to the return earned in the free workbooks for this book.
Enough that each maturity is a sum you would be content to reinvest at one rate. Five rungs a year apart put 20 per cent of the money back each year; on a $125,000 ladder that is $25,000 a year. More rungs smooth reinvestment further but need more bonds, and each bond needs a minimum size to trade at a fair price.
Its market value falls, but less than a long bond's, and each maturing rung is reinvested at the higher rate. In the illustration a two-point rise cuts the ladder's value by 6.73 per cent against 9.54 for a six-year bond, and income climbs from $6,412.50 to $8,662.50 by year six as rungs roll.
It is different. A ladder of individual bonds returns principal on known dates and its paper losses disappear at maturity if held. A fund keeps a constant maturity and never repays. The illustrative ladder returns $25,000 a year at 100, whatever the market does to prices in between.
This article is one calculation from The Credit Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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