Bond Yield Formulas
Calculate current yield and approximate yield to maturity for bonds.
Essential formulas for fixed-income investors.
The Formulas
Bond yield measures the return an investor earns from holding a bond. There are two main yield calculations that every fixed-income investor should know: current yield and yield to maturity.
Current yield is the simplest measure. It divides the annual coupon payment by the bond's current market price. This tells you what percentage return you earn from coupon payments alone, without considering capital gains or losses at maturity. It is useful for a quick comparison but does not capture the full picture.
Yield to maturity is a more complete measure. It accounts for the coupon payments, the difference between the purchase price and face value, and the time remaining until the bond matures. The exact YTM requires solving a complex equation iteratively, but the approximation formula shown above gives a reasonably accurate estimate that is widely used in practice.
When a bond trades below its face value (at a discount), the YTM will be higher than the current yield because the investor also profits from the price rising to face value at maturity. When a bond trades above face value (at a premium), the YTM will be lower than the current yield because the investor loses money as the price falls to face value.
Understanding bond yields is essential for comparing bonds with different coupon rates, maturities, and prices. Institutional investors, portfolio managers, and individual investors all rely on these calculations to make informed fixed-income decisions.
Variables
| Symbol | Meaning |
|---|---|
| C | Annual coupon payment (in dollars or currency) |
| F | Face value (par value) of the bond, typically $1,000 |
| P | Current market price of the bond |
| n | Number of years remaining until maturity |
| YTM | Yield to maturity (approximate annual return) |
Example 1
Problem
A bond with a face value of $1,000 pays a 6% annual coupon and currently trades at $950. What is the current yield?
Annual coupon = $1,000 × 0.06 = $60
Current Yield = $60 / $950 × 100
Current Yield = 6.32%. The bond yields more than its coupon rate because it trades at a discount.
Example 2
Problem
The same bond ($1,000 face, 6% coupon, $950 price) matures in 10 years. What is the approximate YTM?
C = $60, F = $1,000, P = $950, n = 10
YTM ≈ [60 + (1000 − 950) / 10] / [(1000 + 950) / 2]
YTM ≈ [60 + 5] / [975] = 65 / 975
YTM ≈ 6.67%. This is higher than the 6.32% current yield because it includes the capital gain from buying at $950 and receiving $1,000 at maturity.
When to Use It
Bond yield formulas are essential for anyone investing in or analyzing fixed-income securities.
- Comparing bonds with different coupon rates and prices to find the best value
- Evaluating whether a bond is priced at a premium, discount, or par
- Building a fixed-income portfolio with target yield requirements
- Assessing interest rate risk — bonds with lower YTM relative to market rates may lose value