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Bond yield to maturity
YTM from face value, coupon rate, price, and years to maturity — with current yield and total return comparison.
Discount bond — trading $50 below par
Exact YTM (Newton-Raphson)
Annualized return if held to maturity
Current yield
Annual coupon ÷ current price
Approximate YTM
(C + (F−P)/n) ÷ ((F+P)/2)
Show the work
- Annual coupon payment$50.00
- Approximate YTM formula($50 + ($1,000−$950)/10) / (($1,000+$950)/2)
- Approx YTM result5.64%
- Exact YTM (iterated)5.67%
- Total simple return5.79%
Bond yield to maturity — what it means and how to use it
When you buy a bond, three different yield figures describe your return in different ways. Understanding the distinction between coupon rate, current yield, and yield to maturity is essential for comparing bond investments accurately.
Coupon rate vs. current yield vs. YTM
The coupon rate is set at issuance and determines how much cash the bond pays annually relative to its face value. A $1,000 bond with a 5% coupon pays $50/year regardless of what you paid for it.
Current yield adjusts for price: if that bond now trades at $950, the current yield is $50 / $950 = 5.26%. This tells you your running income yield but ignores the $50 gain you'll realize when the bond matures at $1,000.
Yield to maturity incorporates everything — all coupon payments plus the difference between your purchase price and face value, spread over the remaining years. It's the internal rate of return of the bond's entire cash flow stream. Because it assumes coupons are reinvested at the same rate, YTM is a theoretical construct, but it remains the standard comparison metric across the bond market.
Why bond prices and yields move inversely
A bond's coupon is fixed at issuance. When the Federal Reserve raises the federal funds rate, newly issued bonds must offer higher coupons to attract buyers. Existing bonds with lower coupons become less attractive, so their prices fall until the YTM on the old bond equals the yield available on the new bond. This is why the bond market experiences capital losses when rates rise — not because anything has gone wrong with the issuer, but because math requires prices to adjust.
The magnitude of this price sensitivity is measured by duration — a bond with a 10-year duration will lose approximately 10% of its value for every 1% rise in interest rates. Shorter-duration bonds are less rate-sensitive; longer-duration bonds are more sensitive. This is why long-term Treasury bonds lost 40–50% of their value in 2022 when the Fed raised rates aggressively.
Callable bonds and yield-to-call
Many corporate and municipal bonds are callable, meaning the issuer can redeem them before maturity (usually at par or a slight premium) after a call protection period. If rates fall significantly after issuance, the issuer will call the bond and refinance at a lower rate — leaving you with reinvestment risk.
For callable bonds, calculate both YTM (assuming held to maturity) and yield-to-call (YTC) — the same calculation but using the call date and call price instead of maturity date and face value. Investors should buy callable bonds at the lower of YTM or YTC, known as yield-to-worst (YTW).
How to read a bond quote
Bond prices are quoted as a percentage of face value. A price of 98.50 means $985 for a $1,000 face value bond (a discount to par). A price of 102.25 means $1,022.50 (a premium). Treasury bonds trade in fractions of 1/32nd — a quote of 99-16 means 99 + 16/32 = 99.5% of par. Corporate bonds typically trade in decimal format.
Tax treatment of bonds
Corporate bond interest is taxed as ordinary income federally and at the state level. Treasury bond interest is exempt from state and local tax (a meaningful benefit in high-tax states like California and New York) but fully subject to federal tax. Municipal bond interest is generally exempt from federal income tax and, if you hold bonds issued by your state or municipality, often exempt from state tax too.
To compare a municipal yield to a taxable yield, compute the tax-equivalent yield: muni yield ÷ (1 − marginal federal rate). A 4% muni yield for someone in the 37% bracket is equivalent to a 6.35% taxable yield.
Duration as a rate sensitivity measure
Modified duration tells you approximately how much a bond's price changes for a 1% move in interest rates. A bond with modified duration of 7 will rise ~7% in price if rates fall 1%, and fall ~7% if rates rise 1%. Matching your bond portfolio's duration to your investment horizon is the core of liability-driven investing — the approach used by pension funds and insurance companies to hedge their obligations.
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