Key Takeaways
- A 10-year Treasury with a 4.5% coupon purchased at $950 yields approximately 5.07% to maturity, not 4.5%. The gap is 57 basis points on every dollar deployed.
- Investors who compare only coupon rates across bond positions routinely misprice duration risk by $8,000 to $15,000 per $250,000 invested.
- Yield to maturity accounts for purchase price, coupon payments, and the time value of each cash flow. It is the only apples-to-apples comparison across fixed income positions.
- Tool: Run your exact bond numbers with the CalcMoney Investment Calculator →
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What Yield to Maturity Actually Measures
Yield to maturity (YTM) is the annualized internal rate of return on a bond if you hold it until it matures and reinvest every coupon at the same rate. It ties together three variables: the price you paid, the coupon payments you receive, and the par value returned at maturity.
The coupon rate tells you only what percentage of face value the issuer pays annually. It says nothing about what you actually earn when you buy the bond in the secondary market at a price other than $1,000. Since most individual investors buy Treasuries after issuance, the coupon rate is rarely the relevant number.
YTM is the rate that makes the present value of all future cash flows equal to the bond's current price. That relationship is fixed. Every other yield metric is a simplification of it.
The Full YTM Formula
The exact formula for yield to maturity requires solving for the discount rate r in:
Price = C / (1 + r)^1 + C / (1 + r)^2 + ... + C / (1 + r)^n + F / (1 + r)^n
Where:
- C = annual coupon payment in dollars
- F = face value (par), typically $1,000 for Treasuries
- n = number of years to maturity
- r = yield to maturity (what you are solving for)
Because r appears in every denominator, there is no algebraic shortcut. You solve it iteratively, either by trial and error or by using a financial calculator or software. The approximation formula below gives you a working estimate without iteration.
The Approximation Formula
Approximate YTM = (C + (F - P) / n) / ((F + P) / 2)
Where:
- C = annual coupon payment
- F = face value
- P = current price
- n = years to maturity
This formula overstates or understates YTM by 10 to 25 basis points in most real-world cases. It is useful for quick screening. For any decision involving more than $50,000, use the full iterative calculation or the CalcMoney calculator below.
Worked Example 1: Treasury Bought at a Discount
Suppose you buy a 10-year Treasury note with the following characteristics:
- Face value: $1,000
- Annual coupon rate: 4.5% (coupon payment = $45 per year)
- Current market price: $950
- Years to maturity: 10
Step 1: Apply the approximation formula.
Numerator: $45 + ($1,000 - $950) / 10 = $45 + $5 = $50
Denominator: ($1,000 + $950) / 2 = $975
Approximate YTM = $50 / $975 = 5.128%
Step 2: Interpret the result.
You are earning a 4.5% coupon on a $1,000 face bond, but you paid only $950. The $50 discount amortizes over 10 years, adding roughly 50 basis points to your effective annual return. The investor who sees "4.5% Treasury" and stops there is leaving 57 to 62 basis points of analysis undone.
On a $250,000 position, 60 basis points equals $1,500 per year. Over 10 years, that misjudgment compounds to roughly $16,800 in unrealized analytical error.
Step 3: Verify with present value logic.
At a 5.07% discount rate (the iterative solution), the present value of 10 annual $45 coupon payments plus the $1,000 par repayment equals approximately $950. The math closes. The approximation at 5.128% is within 6 basis points of the true answer.
Worked Example 2: Treasury Bought at a Premium
Now consider a 7-year Treasury note trading above par because interest rates have fallen since issuance:
- Face value: $1,000
- Annual coupon rate: 5.0% (coupon payment = $50 per year)
- Current market price: $1,065
- Years to maturity: 7
Step 1: Apply the approximation formula.
Numerator: $50 + ($1,000 - $1,065) / 7 = $50 + (-$9.29) = $40.71
Denominator: ($1,000 + $1,065) / 2 = $1,032.50
Approximate YTM = $40.71 / $1,032.50 = 3.943%
Step 2: Interpret the result.
The bond carries a 5.0% coupon, but you are buying it at a premium. You will receive $1,000 at maturity despite paying $1,065 today. That $65 loss on principal amortizes over 7 years, subtracting approximately 107 basis points from the stated coupon rate.
An investor comparing this bond to a newly issued 4.0% Treasury at par is effectively choosing between 3.94% YTM and 4.00% YTM. The premium bond loses that comparison by 6 basis points, even though its coupon rate is 100 basis points higher.
On a $500,000 position held for 7 years, that 6-basis-point difference accumulates to roughly $2,100. Small in percentage terms. Concrete in dollar terms.
Semi-Annual Compounding: The Adjustment Treasury Investors Must Make
US Treasuries pay coupons semi-annually, not annually. The formulas above assume annual payments. For precise YTM on actual Treasury securities, adjust as follows:
Use n as the number of semi-annual periods (years x 2), C as the semi-annual coupon payment (annual coupon / 2), and solve for the semi-annual rate r. Then annualize: Annual YTM = (1 + r)^2 - 1.
Example using Worked Example 1 adjusted for semi-annual payments:
- Semi-annual coupon: $22.50
- Periods: 20
- Price: $950
- Face: $1,000
Solving iteratively for r gives approximately 2.532% per period.
Annual YTM = (1 + 0.02532)^2 - 1 = 5.128%
In this case, the annual and semi-annual methods converge closely. At higher coupon rates or longer maturities, the gap widens and the semi-annual method becomes more material.
Why YTM Still Has Limits
YTM assumes you reinvest every coupon payment at the same yield. In practice, that reinvestment rate changes with market conditions. If rates fall after you purchase, your actual realized return will sit below the YTM calculated at purchase. If rates rise, realized return exceeds it.
This gap between calculated YTM and realized yield is called reinvestment risk. For short-duration Treasuries (under 3 years), the effect is minor. For 20-year or 30-year Treasuries, the reinvestment assumption is responsible for a substantial share of the projected total return. Never treat long-bond YTM as a guaranteed outcome.
Yield to Maturity vs. Current Yield
Current yield = Annual Coupon / Current Price.
For the discount bond in Example 1: $45 / $950 = 4.74%.
That 4.74% sits between the coupon rate (4.50%) and the YTM (5.07%). It accounts for price but ignores the time value of future cash flows and the par repayment. Use current yield only for rough income estimates on positions you expect to sell before maturity.
How to Use YTM in an Actual Portfolio Decision
Three practical applications:
Comparing two Treasuries of different maturities. A 5-year at 4.80% YTM and a 10-year at 5.10% YTM are not equivalent. The additional 30 basis points on the 10-year requires accepting 5 more years of duration risk and interest rate sensitivity. On a $300,000 allocation, that 30-basis-point spread generates $900 per year of additional income but exposes the position to a potential mark-to-market loss of roughly $14,000 to $18,000 if rates rise 100 basis points.
Laddering a Treasury portfolio. When constructing a ladder across 2, 4, 6, 8, and 10-year maturities, YTM at each rung tells you the blended effective return on the entire ladder. Average the YTMs weighted by the dollar amount at each rung.
Deciding between Treasuries and a CD. A 12-month CD at 5.10% APY vs. a 1-year Treasury bill at 4.95% YTM favors the CD by 15 basis points before tax treatment. Treasuries are exempt from state and local income tax. If your combined state and local marginal rate is 6%, the tax-adjusted Treasury yield = 4.95% / (1 - 0.06) = 5.27%. The Treasury wins by 17 basis points on an after-tax basis.
Run Your Numbers Before You Commit Capital
The approximation formula is a starting point. The exact YTM, adjusted for semi-annual compounding, requires an iterative solver. Manual trial-and-error across 10 to 15 iterations costs time and introduces arithmetic risk.
The CalcMoney Investment Calculator handles the full iteration. Enter your purchase price, coupon rate, face value, and maturity date. The calculator returns exact YTM, current yield, and total dollar return at maturity. It also lets you model reinvestment rate sensitivity, which is the variable most fixed income investors never stress-test.
If you are allocating more than $100,000 to Treasuries, the difference between approximate and exact YTM is worth 5 to 15 minutes of analysis. Run the numbers with precision before the order settles.
Results are estimates for informational purposes only. Consult a licensed financial professional before making financial decisions.
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