What does yield to maturity quietly assume about your coupons?

Here is the part nobody puts in the headline. YTM is the single discount rate that makes the promised cash flows equal today's price — an internal rate of return, and computing it assumes nothing about your behaviour. What it does assume is buried in the word "return": you only end up with YTM as a compound rate on your money if every coupon is reinvested at the YTM itself until maturity. No investor controls that. Let's see how much it matters.

Where the money actually comes from

Buy a €1,000 bond with a 5% annual coupon, 5 years, at par — YTM 5%. If the quoted yield is real, €1,000 should grow to €1,000 × 1.05⁵ = €1,276.28 by maturity. Break that down:

• Principal returned: €1,000
• Coupons received: 5 × €50 = €250
• Interest earned on the coupons: €1,276.28 − €1,000 − €250 = €26.28

That last €26.28 — "interest on interest" — is about 9.5% of the total return, and it only exists if each coupon is put back to work at 5%.

Now stretch the maturity to 30 years. €1,000 × 1.05³⁰ = €4,321.94. Coupons total €1,500; interest on interest is €1,821.94 — more than half the total return. On a long coupon bond, the majority of the promised yield is a rate you have to go out and earn again, thirty separate times.

What happens when the world doesn't cooperate

Same 5-year 5% par bond, but suppose coupons can only be reinvested at 3%:

• Future value of the coupons: €50 × [(1.03⁵ − 1) ÷ 0.03] = €265.46
• Plus €1,000 principal = €1,265.46
• Realised compound yield: (1,265.46 ÷ 1,000)^(1/5) − 1 = 4.82%

Reinvest at 7% instead and you finish with €1,287.54 — a realised yield of 5.18%.

So a bond honestly quoted at "5%" delivers something else, and which way depends on where rates go while you hold it: reinvest above 5% and you beat it, below and you fall short. The quoted number is not the middle of a range — it is the figure you would hit only if reinvestment cooperated exactly. What you actually end up with has a name: the realised compound yield.

The two bonds where the assumption disappears

• A zero-coupon bond pays nothing until maturity, so there are no coupons to reinvest. Held to maturity, its YTM is its realised return, exactly. That is one reason zeros are the cleanest instrument in the toolkit — and Unit 2 gives you a second.
• A bond you hold for a very short time has barely any coupons to reinvest, so the assumption has little room to bite.

The tension worth remembering

Falling rates are bad for reinvestment and good for price. Rising rates are good for reinvestment and bad for price. The two risks point in opposite directions, and that opposition is what duration (Unit 2) and liability matching (Unit 3) are both built on.

In the data

What reinvested cash actually earned is published. The New York Fed compounds the overnight rate, SOFR, day after day into a running index; the two tables are that index a year apart.

The index level itself means nothing; the ratio of two readings is what cash rolled overnight earned in between. Set that beside a yield quoted at the start and you have realised against assumed reinvestment. The two agree only by coincidence.

Try it now

1. Take a €50 annual coupon over 5 years and compute its future value at 2%, 5% and 8% reinvestment. Watch the total swing by tens of euros on a €1,000 bond.
2. The newest Treasury curve is below: compare a short yield with the 30-year. Which leans more heavily on reinvestment, and why is the long one the more conditional promise?

3. Now the realised side, over one pinned year. The table below is what a one-year Treasury paid on 25 September 2025. Divide the later index reading in the section above by the earlier one and subtract 1: that is what cash rolled overnight actually earned over the year. Set it beside the one-year rate. One of the two is what cash was assumed to earn and the other is what it earned; say which, and which was higher.

4. Say it plainly: "YTM is what I get if the future reinvests my coupons at exactly today's yield — which it will not."