Bond Yield Calculator

The inverse relationship between bond prices and yields is the most fundamental concept in fixed income investing. A bond's coupon is fixed in dollar terms at issuance: a $1,000 bond paying $50 per year (a 5% coupon) pays exactly $50 every year regardless of market conditions. But if market rates rise to 6%, new bonds pay $60 per year and your bond becomes less attractive. The market price of your bond must fall until that $50 annual payment represents a 6% yield on the new (lower) price.

The reverse holds when rates fall: a bond paying 6% becomes more valuable when new bonds only pay 4%. Its price rises until buyers effectively earn 4%. This mechanic is why long-term bond funds fell 20–30% in 2022 when the Federal Reserve rapidly raised rates — older bonds with lower coupons had to be repriced downward to compete with new higher-rate issuances.

Current yield is the simplest measure: annual coupon ÷ current market price. A $1,000 bond paying $50/year purchased at $950 has a current yield of 5.26%. This is useful for income-focused investors comparing how much cash a bond generates relative to its cost, but it ignores what happens at maturity.

Yield to maturity (YTM) is more complete. It accounts for coupon payments, the current price, and the gain or loss when the bond matures at face value. If you buy the $950 bond above, you receive $50/year in coupons plus a $50 capital gain at maturity. YTM captures both components and produces a yield higher than the current yield. Conversely, paying $1,050 for the same bond yields below the coupon — you lose the $50 premium at maturity.

YTM is the standard metric used by bond screeners, broker platforms, and financial advisors. It normalizes every bond to a single comparable annual return figure, regardless of coupon, price, or remaining maturity. For US bonds it's quoted as a Bond-Equivalent Yield (BEY) — 2 × the semi-annual periodic rate — which is why semi-annual compounding matters: it changes the YTM number by 5–10 bps versus an annual-compounding calculation.

Duration measures how sensitive a bond's price is to yield changes. Macaulay duration is the weighted average time (in years) until you receive all bond cash flows. Modified duration is Macaulay ÷ (1 + r/freq) and gives the closest linear approximation: a 7-year modified duration means a 1% rate rise costs ~7% of price.

This is why long-term bonds are riskier than short-term bonds when rates might rise. A 30-year Treasury might have modified duration of 18–20 years, so a 1% rate increase produces an ~18–20% price decline. A 2-year Treasury note has duration closer to 1.9 years — the same rate move only costs ~1.9%. Zero-coupon bonds have the highest duration possible (equal to maturity) because all cash flow comes at the end.

Convexity captures what duration misses: the curve in the price-yield relationship. Positive convexity is a free option — bonds gain more when rates fall than they lose when rates rise by the same amount. The full second-order approximation is: ΔP/P ≈ −Mod × Δy + ½ × Conv × Δy². For small rate moves duration is enough; for large moves convexity matters and is consistently in the bondholder's favor.

Many corporate and municipal bonds are callable: the issuer can redeem the bond before maturity, usually at par or at a small premium. This is bad for bondholders, because the issuer will call exactly when it hurts you most — when rates have fallen and your bond is now valuable. Once called, you receive the call price and must reinvest the proceeds at lower current rates (reinvestment risk).

For callable bonds, Yield to Maturity is optimistic — it assumes the bond runs to its stated end date. Yield to Call (YTC) computes the yield assuming the bond is called at the earliest call date. Yield to Worst (YTW) is the minimum of YTM and YTC across all call dates and is the conservative number bond screeners report. A premium callable trading above the call price will often show a sharply lower YTW than YTM — a signal the call is highly likely and your true expected return is closer to YTW.

The reinvestment-rate input lets you stress-test the YTM assumption. Textbook YTM assumes coupons reinvest at the YTM rate; in practice you reinvest at whatever rates prevail when each coupon is paid. If you expect reinvestment rates to be lower than today's YTM (a typical concern when rates are high), your realized holding-period return will be below the quoted YTM.