What is yield to maturity really measuring?

Yield to maturity is the number the market means when it says "the 10-year is at 4.2%". It is also the most over-trusted number in fixed income. Let's define it exactly, then be honest about what it assumes.

One definition, no hand-waving

YTM is the single discount rate that makes the present value of all the bond's remaining cash flows equal its current market price.

That's it. It is the bond's internal rate of return — the one rate that, applied to every coupon and to the final principal, reproduces today's price. You don't "read" it off the bond; you solve for it.

A worked example

Take a bond with €1,000 face, a 5% annual coupon (€50 a year), 5 years left, trading at €900. You are looking for the rate y that satisfies:

900 = 50 ÷ (1+y) + 50 ÷ (1+y)² + 50 ÷ (1+y)³ + 50 ÷ (1+y)⁴ + 1,050 ÷ (1+y)⁵

There is no clean algebraic solution — a solver (or a patient trial-and-error) finds y ≈ 7.47%. Sanity-check it with the classic approximation:

YTM ≈ [ coupon + (face − price) ÷ years ] ÷ [ (face + price) ÷ 2 ]

= [50 + (1,000 − 900) ÷ 5] ÷ [(1,000 + 900) ÷ 2] = 70 ÷ 950 = 7.37%

Within a tenth of a percent of the true 7.47% — good enough to catch a typo, never good enough to quote. Notice how far it sits above the 5.56% current yield of the last lesson: the €100 pull to par is doing a lot of work.

Price and yield are the same information

Because YTM is solved from the price, price and yield are two languages for one fact. Quoting in yield is simply more comparable: "€103.47" tells you nothing across bonds with different coupons and maturities; "4.2%" lets you line them up.

The solved rate can be below zero. Pay 105 for a bond that returns 100 plus 3 in coupons and the equation balances only at a negative yield: the contract returns less than it cost. This happened at scale. The 10-year German Bund yield, charted below, closed below zero on every session from 7 May 2019 to 28 January 2022, with a low of −0.86% on 9 March 2020 (checked 29 September 2026). The holders were banks that needed collateral, insurers matching liabilities under rules that count only government bonds, index funds, and central banks; some expected to sell at a still higher price. A negative close in that series is a price, and the pull to par runs downward.

The three conditions hiding inside the number

A YTM of 7.47% is a conditional promise. You earn it only if:

1. You hold to maturity (sell early and your return depends on the price you get).
2. Every payment arrives in full and on time (no default, no restructuring).
3. Every coupon is reinvested at that same 7.47% until maturity.

The first two are obvious. The third is invisible, unavoidable, and the subject of the next lesson — it is baked into the arithmetic whether you like it or not.

Conventions that trip people up

• Most US Treasuries and corporates pay semiannually, so their quoted yield is a bond-equivalent yield compounded twice a year. Our annual examples keep the maths readable; the logic is identical.
• The price you solve from should be the dirty price (including accrued interest), even though bonds are usually quoted clean.
• Day-count conventions (30/360, actual/actual) change the decimals, never the idea.

In the data

Benchmark government bonds are quoted as yields, not prices. The table is a week of the US 10-year: every close is a yield to maturity in per cent, so 5.165 means 5.165%, not $5.17.

Read it as the market's solved-for rate on that day's price, not as a price, and the direction flips: a rising line is falling bond prices. Nothing like a dividend or a corporate action ever adjusts it, because there is nothing to adjust in a yield.

Try it now

1. The chart below looks like a price series and is not. Every value on it is a yield to maturity in per cent, so 4.7 means 4.7% and not $4.70. Drop a Level at today's reading, then find the level three years back — two solved-for rates, not two coupons, and the difference between them is a repricing of every bond in the market.

2. Take a bond trading at a discount and run the approximation formula on paper. Does it land above the current yield, as the ordering from the last lesson demands?
3. Recite the three conditions. Then underline the third one — you'll spend the next lesson pulling it apart.