Understanding your yield result
| Price vs. face value | YTM vs. coupon rate | What it means |
|---|---|---|
| Price below face value (discount) | YTM > coupon rate | The bond's total return includes both coupon income and a capital gain as it accretes toward face value at maturity |
| Price at face value (par) | YTM = coupon rate | The coupon rate alone reflects the bond's total annualized return |
| Price above face value (premium) | YTM < coupon rate | The bond's total return is reduced by a capital loss as its price amortizes down to face value at maturity |
- This calculator solves for YTM using bisection on the semiannual discount rate, the standard numerical method since no algebraic formula exists for YTM given only price, coupon, face value and maturity.
- YTM assumes every coupon payment is reinvested at the same YTM rate for the remaining life of the bond — an assumption that may not hold if market rates change, which is a well-known limitation of the YTM measure.
- Current yield is easier to calculate but incomplete: it ignores the capital gain or loss that occurs between the purchase price and the face value repaid at maturity.
What is yield to maturity?
Yield to maturity is the single discount rate that makes the present value of a bond's remaining coupon payments and face value repayment equal to its current market price. It represents the total annualized return an investor would earn by holding the bond to maturity and reinvesting each coupon at that same rate, and it is the standard yield measure used to compare bonds with different prices, coupons and maturities.
Current yield is a simpler measure: the bond's annual coupon payment divided by its current market price. Unlike YTM, current yield ignores any capital gain or loss that occurs if the bond is bought at a discount or premium and later repaid at face value, so it does not capture the full return from holding the bond to maturity.
Because bond price and yield move inversely, this calculator solves for YTM by iteratively testing discount rates until the resulting bond price matches the entered market price — the same relationship used in the standalone bond price calculator, applied in reverse.
How to use this bond yield calculator
- Enter the current market price of the bond.
- Enter the face value (par value) the bond repays at maturity.
- Enter the annual coupon rate — the fixed percentage of face value paid out each year.
- Enter the years remaining until maturity.
- Read the yield to maturity, the current yield, and the nominal coupon rate for comparison.
- Example: a $1,000 face-value bond with a 5% coupon and 10 years to maturity, priced at $950, has a yield to maturity of approximately 5.662% and a current yield of 5.263%.
The formula behind yield to maturity
There is no closed-form algebraic solution for YTM from a bond price, so it is found numerically: the calculator searches for the semiannual discount rate that, when used in the standard bond-pricing formula, reproduces the entered market price, then annualizes that rate. Current yield, by contrast, has a simple direct formula using only the coupon payment and price.
Common mistakes
- Treating current yield and yield to maturity as interchangeable — current yield ignores the capital gain or loss embedded in a bond bought at a discount or premium, while YTM accounts for it.
- Forgetting that YTM assumes coupons are reinvested at the same YTM rate, which may not be achievable in a changing interest-rate environment.
- Comparing YTM figures across bonds with very different credit quality without accounting for the additional yield (credit spread) that compensates for default risk.
- Assuming a bond's coupon rate is its current return — the coupon rate is fixed at issuance and only equals current yield or YTM when the bond trades exactly at par.
- Overlooking that this calculator, like most standard YTM formulas, does not incorporate call provisions; a callable bond's actual realized yield can differ from YTM if it is called before maturity.
الأسئلة الشائعة
What is the difference between yield to maturity and current yield?
Current yield is simply the annual coupon payment divided by the bond's current price, ignoring any gain or loss from the price converging to face value at maturity. Yield to maturity is more complete: it is the single discount rate that equates all future coupon payments and the face value repayment to the bond's current price, capturing both income and price convergence.
Why is yield to maturity higher than the coupon rate for a bond trading at a discount?
A bond trading below face value will, if held to maturity, repay its full face value — a gain above the purchase price — in addition to paying its fixed coupons. That built-in capital gain adds to the coupon income, producing a yield to maturity higher than the coupon rate alone.
How is yield to maturity actually calculated?
There is no direct algebraic formula for YTM given only a bond's price, coupon, face value and maturity, so it is found through iterative numerical methods such as bisection: testing successive discount rates in the standard bond pricing formula until the resulting price matches the bond's actual market price.
Does yield to maturity assume the bond is held until it matures?
Yes. YTM represents the annualized return an investor earns only if the bond is held to maturity and every coupon payment received along the way is reinvested at that same YTM rate. Selling the bond earlier, or reinvesting coupons at different rates, would produce a different realized return.
What does it mean if yield to maturity is lower than the coupon rate?
This occurs when a bond is trading at a premium — above its face value. The bond will lose that premium as its price converges down to face value at maturity, a built-in capital loss that partly offsets the coupon income, producing a yield to maturity below the coupon rate.
المراجع
- U.S. Securities and Exchange Commission (SEC), Investor.gov. Bonds — understanding yield to maturity and current yield. investor.gov.
- Financial Industry Regulatory Authority (FINRA). Bond yields explained — current yield vs. yield to maturity. finra.org.
- CFA Institute. CFA Program Curriculum — Fixed Income: Yield Measures and the Yield Curve.
- TreasuryDirect (U.S. Department of the Treasury). How Treasury bond and note yields are calculated. treasurydirect.gov.