Chapters

Chapters

Lesson 01 / 05

In this lesson

Price and scheduled payments
Reinvestment and terminal wealth
Calls and realised outcomes
Yield and the goal

What yield to maturity tells you

Read a yield as the rate connecting a price to specified payments, then examine what changes the wealth you actually accumulate.

One purchase price; payments at two dates.

You do not need to calculate a yield yourself to maintain a simple portfolio. Build on the basic bond claim to interpret a quote.

Invented non-callable bond: €1,000 face value, annual €50 coupons, two years remaining. Buy just after a coupon. No accrued interest, fees or taxes; annual discount-rate convention.

TodayYou → seller€980 paid
Year 1Issuer → you€50 coupon
Year 2 · maturityIssuer → you€1,000 principal
+ €50 coupon€1,050 total

Equal one-year intervals; box sizes do not represent euros. Future payments are promised, not guaranteed.

Yield to maturity (YTM) connects the price to all scheduled amounts and dates: about 6.09% annually here. Coupon rate uses face value; current yield divides the coupon by price but omits the principal difference. None of these figures guarantees payment.

Calculate the rate and check quote conventions

Coupon rate: €50 ÷ €1,000 = 5%. Current yield: €50 ÷ €980 ≈ 5.10%. Including repayment and timing: €980 = €50 ÷ (1 + y) + €1,050 ÷ (1 + y)², giving y≈6.09%. The second payment is discounted twice because it arrives later.

Check payment frequencies, settlement dates and day-count conventions in the bond’s terms. FINRA’s US bond guide describes accrued interest being added to the contract price between coupon dates. Check whether a displayed quote includes it and reconcile the quote with the actual cash paid; quotation conventions need not be identical across markets.

The coupon needs its own reinvestment rate.

Scheduled-flow YTM remains about 6.09% in both cases below. Ending wealth also depends on what the first coupon earns after receipt.

Year 1: €50 received → one year available before maturity

Keep at 0%€50 → €50+ final €1,050 = €1,100

Reinvest at the original YTM€50 → €53.05+ final €1,050 = €1,103.05

Both branches receive and retain every payment, with no costs or tax. The extra €3.05 requires reinvestment at the unrounded YTM for that year; the bond does not promise it.

Compare terminal wealth after two years, retaining both coupons.

At 0% reinvestment, annual compound growth of ending wealth is √(1,100 ÷ 980) − 1 ≈ 5.95%. Reinvesting at the unrounded YTM gives €980 × (1 + y)² ≈ €1,103.05.

Spending a coupon changes what remains invested; retaining every payment no longer describes that spending plan.

“Yield to worst” sets no floor on wealth.

Yield to call uses a specified call date and amount; yield to worst selects the lowest among the redemption scenarios included in the quote. Check permitted dates, amounts and which scenarios were included. A call is the issuer’s contractual option, not a forecast.

Default, an early sale at a poor price, costs or currency losses can produce less. An early sale replaces maturity receipts with uncertain proceeds; purchase YTM does not establish return over a shorter spending horizon. The SEC distinguishes contractual payments from the risk they never arrive.

Keep the payment assumptions with the quote.

Record price, date, currency, payments, redemption options and cost/tax scope. A high foreign-currency yield does not reliably fund spending in another currency.

Coupon rate, YTM and fund distribution yield are different measures. Even equal YTMs can carry different credit, duration and access risks; match the claim and payment timing to the goal.

Check your understanding

Try each question, then check your answer.

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Interpreting a yield quote

What does yield to maturity calculate for an ordinary non-callable fixed-rate bond at a given price?

The discount rate connecting that price to the scheduled coupons and principal.
The annual coupon divided by face value, regardless of price.
The annual coupon divided by the current purchase price.

Show the explanation

Correct answer: The discount rate connecting that price to the scheduled coupons and principal.

YTM discounts all scheduled coupons and principal to the purchase price. Coupon rate uses face value; current yield divides one year’s coupon by purchase price. Neither incorporates the complete payment schedule. YTM guarantees neither payment nor later reinvestment rates.

Return to the explanation

Lower reinvestment rates

You buy a bond at a quoted YTM. Its scheduled payments arrive, but coupons can only be reinvested at lower rates. What follows?

The original purchase amount compounds at the quoted YTM because the issuer paid the full schedule.
The original YTM still describes its scheduled cash-flow calculation; the accumulated terminal wealth can differ.
The coupon rate should instead be used to compound the whole purchase into terminal wealth.

Show the explanation

Correct answer: The original YTM still describes its scheduled cash-flow calculation; the accumulated terminal wealth can differ.

Discounting the bond's payments and accumulating reinvested coupons answer related but different questions. The quoted YTM does not make that rate available on later cash receipts. Lower reinvestment rates can change the ending wealth without changing the bond's fixed payment terms.