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Yield to Maturity (YTM): Definition and Calculation
Yield to maturity is the single discount rate that equates a bond's future cash flows to its current price, assuming the buyer holds the bond until maturity and reinvests every coupon at the same rate.
Key Takeaways
- YTM is the internal rate of return on a bond's promised cash flows given its current market price.
- A bond bought at a discount has a YTM above its coupon rate; a bond at a premium has a YTM below.
- YTM assumes all coupons are reinvested at the same rate, an assumption rarely met in practice.
- For callable bonds, yield to call or yield to worst is more appropriate than yield to maturity.
Key Takeaways
- YTM is the internal rate of return on a bond's promised cash flows given its current market price.
- A bond bought at a discount has a YTM above its coupon rate; a bond at a premium has a YTM below.
- YTM assumes all coupons are reinvested at the same rate, an assumption rarely met in practice.
- For callable bonds, yield to call or yield to worst is more appropriate than yield to maturity.
What It Is
YTM is the most comprehensive yield measure for a fixed-rate bond. It blends the coupon income, the price paid today, and the return of principal at maturity into one annualized percentage. When a bond is quoted in the secondary market, the yield shown next to the price is almost always YTM.
Formally, YTM is the internal rate of return on the bond's promised cash flows. It is the rate that, when used to discount each coupon and the face value, produces exactly the market price.
The Intuition
The coupon rate tells you what the issuer will pay. The current yield tells you the coupon relative to today's price. Neither captures the capital gain or loss that accrues as a bond's price converges to par by maturity. YTM fixes that gap.
If you buy a bond at a discount, you pocket both the coupons and the pull to par. YTM folds those together. If you buy at a premium, YTM reflects the fact that you will receive only face value at maturity, so part of your coupon income is really a return of the premium you paid.
Three caveats keep YTM honest: it assumes you hold to maturity, it assumes every coupon is reinvested at the YTM rate, and it assumes the issuer does not default or call the bond.
How It Works
For a bond with N coupon periods per year and T years to maturity, YTM is the rate y that solves:
Price = sum[ C / (1 + y/N)^t ] + FV / (1 + y/N)^(N*T)
Where:
C = periodic coupon payment (annual coupon / N)
FV = face value repaid at maturity
y = yield to maturity, quoted as an annual rate
N = number of coupon periods per year (usually 2 for US bonds)
t = period index, from 1 to N*T
There is no closed-form solution. Practitioners use iterative methods: bisection, Newton-Raphson, or the built-in solver in a spreadsheet or bond calculator. Excel's YIELD() function does the same thing with clean date handling and day-count conventions.
A rule of thumb for a rough estimate:
YTM approx = [ C + (FV - Price) / T ] / [ (FV + Price) / 2 ]
This gives you a ballpark. It underweights the time value of money compared to the exact calculation, but it is close enough to sanity-check a quoted yield.
Worked Example
Consider a 10-year US corporate bond with a 5 percent annual coupon paid semi-annually and a $1,000 face value. It trades today at $950.
- Coupon payment per period: $25 (10 periods per year would be wrong; for semi-annual it is $1,000 * 5 percent / 2 = $25)
- Number of periods: 20
- Price today: $950
- Face value at maturity: $1,000
The exact YTM is the rate y such that:
950 = sum[t=1..20] 25 / (1 + y/2)^t + 1000 / (1 + y/2)^20
Solving numerically gives y approximately 5.68 percent annualized.
Reading that result:
- Coupon rate is 5.00 percent
- Current yield is $50 / $950 = 5.26 percent
- YTM is 5.68 percent
The extra 42 basis points over current yield is the pull from $950 to $1,000 over ten years, spread across the cash-flow timeline. That is the piece current yield misses.
Common Mistakes
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Assuming the reinvestment rate is realistic. YTM locks in that every coupon received over ten or thirty years gets reinvested at the same YTM. In practice, rates fluctuate. If reinvestment rates fall below YTM, realized return will be lower. This reinvestment risk is why long-coupon bonds held to maturity rarely hit their quoted YTM exactly.
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Using YTM for callable bonds as if they will not be called. If a bond is callable and trading above par, the issuer will likely call it at the first opportunity. YTM assumes you hold to maturity, which may never happen. Use yield to call or yield to worst for callable issues.
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Comparing YTMs across different credit qualities. A 7 percent YTM on junk debt is not comparable to a 4 percent YTM on Treasuries. Part of the yield is compensation for default risk. Compare like-for-like, or decompose the yield into the risk-free rate plus the credit spread.
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Ignoring day-count conventions. Treasuries use actual/actual, corporate bonds typically use 30/360, and money-market instruments have their own conventions. A YTM calculated with the wrong convention can be off by several basis points, which matters for institutional pricing.
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Confusing quoted YTM with realized return. YTM is a promise under a set of assumptions. Realized return depends on reinvestment rates, whether you actually hold to maturity, and whether the issuer pays every coupon. They are rarely identical.
Frequently Asked Questions
Why is there no closed-form formula for yield to maturity? YTM appears as the variable in a polynomial equation once all the discounted cash flows are summed, and polynomials of degree higher than four have no general algebraic solution. Calculators and spreadsheets solve the equation iteratively, narrowing in on the rate that makes the present value equal the price.
How does YTM differ from the yield shown on a bond fund's fact sheet? Bond funds report yield to maturity (or SEC 30-day yield for mutual funds) as an average across all holdings weighted by market value. Individual bonds in the fund have their own YTMs that differ by maturity, credit quality, and coupon. The fund figure is a snapshot and changes daily as prices move and holdings change.
Can yield to maturity be negative? Yes. When investors pay more than the sum of all future cash flows, as happened with German bunds and Swiss government bonds after 2015, YTM is negative. The buyer accepts a guaranteed nominal loss in exchange for safety, liquidity, or regulatory necessity.
Does YTM account for taxes? No. Standard YTM is a pre-tax measure. After-tax yield depends on the investor's tax bracket, the bond's coupon structure, whether a discount must be amortized, and whether interest is exempt from state or federal tax. For munis, always compare tax-equivalent yield to determine if the lower coupon outperforms on an after-tax basis.
What happens to YTM if I sell before maturity? YTM is only realized if you hold to maturity. If you sell early, your actual return depends on the price at the time of sale, which reflects the market yield then prevailing. Selling after rates have risen means selling at a loss, producing a realized return below the original YTM.
Sources
- CFA Institute. "Yield and Yield Spread Measures for Fixed-Rate Bonds." https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/yield-and-yield-spread-measures-for-fixed-rate-bonds
- CFA Institute. "Fixed-Income Bond Valuation: Prices and Yields." https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/fixed-income-bond-valuation-prices-and-yields
- FINRA. "Understanding Bond Yield and Return." https://www.finra.org/investors/insights/bond-yield-return
- SEC Investor.gov. "Bonds FAQs." https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds-or-fixed-income-products/bonds
Disclaimer
This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.
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