A bond's cash flows are written down in advance. What those cash flows finally compound to is not, and that gap is where the quoted yield quietly makes an assumption on your behalf.
11 min read · Level 2
Income is the most over-praised property in investing, and bonds are where the praise does the most quiet damage. A coupon arriving in your account is not obviously better than the same money staying at work; it is the same money, handed to you at a moment you did not choose, along with a decision you now have to make every six months for as long as you hold. Equity handles this differently and mostly better: a company that retains its earnings reinvests them on your behalf, at its own cost of capital, without asking you. The bondholder gets no such service. They get cash and an obligation to do something intelligent with it, repeatedly, in whatever rate environment happens to prevail on each payment date - and the evidence of the table above is that the default behaviour, letting it sit, costs about 29 basis points a year on an otherwise perfectly performing instrument. The uncomfortable implication is that the feature most often used to sell fixed income to individuals, that it pays you regularly, is also the feature most likely to erode what they finally receive. That is not an argument against bonds. It is an argument for deciding what happens to the coupon before the first one lands.
An equity's return has to be estimated. A bond's can be written out on one line per year before you buy it.
Take the anchor bond used through this subject: par 1,000, coupon 4%, five years to maturity, bought at par for 1,000.
Year 1 coupon 40 Year 2 coupon 40 Year 3 coupon 40 Year 4 coupon 40 Year 5 coupon 40 Year 5 par 1,000 -------------------------- Contracted total 1,200
That is the whole of what the issuer owes: 1,200 against 1,000 paid, if every payment is made as contracted. Two sources, and only two. The coupons, which arrive along the way, and the principal, which comes back at the end. Where a bond is bought at a discount to par, part of the return also comes from the price pulling up towards par as maturity approaches; where it is bought at a premium, the price pulls down and part of the coupon is really the return of what you overpaid. Both of those are the same two sources seen from a different purchase price.
There is a third component, and it is not printed anywhere on the instrument: what the coupons themselves earn between arriving and the end of the holding period. Forty arriving in your account in year one is not forty in year five unless you do something with it. This is not a technicality. It is the difference between the yield you were quoted and the return you finally get, and it is entirely outside the issuer's control.
Yield to maturity - the number quoted on every bond you will ever be shown - is the single rate that makes the present value of the scheduled cash flows equal the price paid. It is a genuinely useful figure and it embeds one assumption that is easy to miss: that every coupon is reinvested at the yield to maturity itself, from the day it arrives until maturity. Nobody guarantees that. Nobody can.
Because it is the one place where a contractual instrument stops being contractual, and most holders never notice the seam.
Run the anchor bond four ways. Same bond, same issuer, same 4% quoted yield, same 1,000 paid. The only thing that differs is the rate at which each coupon is put back to work as it arrives.
Coupons left as cash, earning nothing Coupon pot at year 5: 200.00 Total at year 5: 1,200.00 Annualised: (1,200/1,000)^(1/5) - 1 = 3.7137%
Coupons reinvested at 2% Coupon pot at year 5: 208.16 Total: 1,208.16 Annualised: 3.8544%
Coupons reinvested at 4% Coupon pot at year 5: 216.65 Total: 1,216.65 Annualised: 4.0000%
Coupons reinvested at 6% Coupon pot at year 5: 225.48 Total: 1,225.48 Annualised: 4.1505%
The 4% case is the quoted yield to maturity, and it is the only one of the four that produces it. That is not a coincidence; it is the definition. The coupon pot in that row is 40 x [(1.04^5 - 1) / 0.04] = 40 x 5.416323 = 216.65.
Look at the first row. A holder who takes the coupons and spends them - which is exactly what an income investor intends to do - earns 3.7137% on the money they committed, not 4%. Nothing has gone wrong, no payment was missed, and the bond performed precisely as contracted. The shortfall of roughly 29 basis points a year is the compounding they chose not to have.
Look at the last row. A holder in a rising-rate world reinvests at better and better rates and ends above the quoted yield - while the market price of the bond itself has been falling the whole time. Those two facts feel contradictory and are not. They are the two halves of what a rate rise does to a bondholder, and which one dominates depends entirely on how long you hold.
This is reinvestment risk, and it is the mirror image of the price risk covered in the next lesson. A fall in rates is good for the price of the bond you own and bad for every coupon you have yet to receive. A rise is the reverse. You cannot escape both.
Educational, not personalised financial advice. Nothing in the Investor Academy is a recommendation to buy, sell or hold anything — what is right for you depends on your own circumstances and the rules where you live.
Now the instrument that removes the assumption entirely.
A zero-coupon bond pays no interest at all. It is sold below par and redeemed at par, and the whole return is the pull to par. There are no coupons, so there is nothing to reinvest, so there is no reinvestment risk. A five-year zero yielding 4% costs 1,000 / 1.04^5 = 821.93 today and pays 1,000 at maturity. The annualised return, if the issuer pays, is (1,000 / 821.93)^(1/5) - 1 = 4.0000% exactly, with no assumption attached.
Compare the two side by side, both bought today, both yielding 4%, both held five years:
4% coupon bond at 1,000, coupons left as cash: 3.7137% 4% coupon bond at 1,000, coupons at 4%: 4.0000% (the quoted yield) 4% coupon bond at 1,000, coupons at 6%: 4.1505% Zero-coupon bond at 821.93: 4.0000% (certain, given payment)
The zero is the only row in that list whose figure does not depend on something happening after the purchase. That is what you are buying when you buy a zero: not a higher return, but the removal of a variable.
One more arithmetic point, small and frequently mishandled. Most bonds pay twice a year rather than annually, and a bond described as paying 4% semiannually pays 2% every six months. Reinvested for the remaining half-year, that is 1.02^2 - 1 = 4.0400% a year, not 4.00%. Four basis points is small and it is not nothing when comparing an annual-pay instrument with a semiannual-pay one, and the convention differs between markets. Check which one you are reading before you compare two yields.
The first mistake is reading yield to maturity as a promise. It is a promise about the schedule and an assumption about everything after each payment lands. The issuer can honour the schedule perfectly and you can still finish below the quoted figure, as the first row of the table above shows.
The second is spending the coupons and describing the result as compounding. Compounding is what happens to money that stays at work. Income that is drawn is income that has stopped compounding, and there is nothing wrong with drawing it - that is often the entire point of holding the bond - but the return should then be measured against what was actually done with the cash, not against the yield on the ticket.
The third is comparing a bond's yield to maturity with an equity's expected return as though the two numbers meant the same thing. One is derived from a contract; the other is somebody's estimate of an unknowable residual. They can be compared as decisions, and they should never be compared as measurements.
The fourth is ignoring the payment convention. A 5.00% semiannual coupon and a 5.00% annual coupon are not the same instrument, and the difference compounds over the life of the bond.
One line per payment, with the actual calendar date and the actual amount, ending with the par value. It takes two minutes and it turns an abstract yield into a set of arrivals you can plan around. It also makes obvious how much of the total is the final principal rather than the income - in the anchor bond, 1,000 of the 1,200 is the return of your own money.
Reinvested into the same issue, swept into a money-market fund, or spent. All three are legitimate and they produce materially different outcomes, as the four rows above show. What produces the worst outcome is not deciding, so that coupons accumulate as idle cash by default - the 3.7137% row, chosen by nobody.
If you would not put a coupon to work at anything above the prevailing deposit rate, then recompute the total at that rate rather than at the yield to maturity. The gap between the two figures is the part of the quoted yield that depends on you rather than on the issuer, and knowing its size is what stops a later shortfall reading as a defect in the bond.
If the point of the holding is to have a known amount available on a known date, an instrument with no coupons to reinvest matches that requirement more exactly than a coupon bond of the same maturity. You give up the interim income, which was never the objective, and you remove the one variable a coupon bond leaves open.
Whenever you are comparing two bonds on yield, whenever the income from a holding is intended to be spent rather than reinvested, and whenever you need a specific sum on a specific date and are choosing between a coupon bond and a zero.
Do not use yield to maturity as the sole basis for choosing between two bonds of different coupon structures, and do not use it at all as a forecast of what you will finish with - it is a discount rate that reconciles a price to a schedule, and it becomes a realised return only under one specific assumption about your own behaviour.
In a long period of falling interest rates, holders of coupon bonds experience two things at once and usually notice only one. The market value of what they already hold rises, which shows up on every statement and feels like skill. Meanwhile every coupon that arrives, and every bond that matures and has to be replaced, goes back to work at a lower rate than the one it came from. The statement records the first effect immediately and the second only slowly, as the portfolio's income declines year after year for reasons that are never attributable to any single decision. Holders who set their spending against the income of the early years find the later years will not support it.
Rising prices and falling reinvestment rates are the same event. Judge a bond holding by the income it will produce for the rest of its life, not by the value it shows today.
A common shape in individual portfolios is a bond allocation held for decades, every coupon drawn and spent, and a nominal capital value at the end almost exactly equal to the sum originally invested. Nothing was lost; the contract was honoured every year. But the holder frequently describes the outcome as having earned the coupon rate over that period, and they did not - they earned the coupon rate on money that never compounded, and the capital that came back at the end buys considerably less than the capital that went in. The mistake is not the spending. It is the accounting afterwards.
Money you draw stops compounding the day you draw it. If income is the purpose of the holding, measure the outcome against what you actually needed to spend, not against the yield on the certificate.
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