Bond Yield Calculator
Calculate yield to maturity (YTM), current yield, Macaulay & modified duration, and convexity for any coupon bond — includes total return and price sensitivity analysis.
Bond Yield Calculator (YTM)
Bond Details
Calculation Results
Yield to Maturity (YTM)
5.6617%
Annualized total return if held to maturity
Current Yield
5.26%
Bond Status
Discount
Coupon Details
Annual Coupon
$50.00
Per Period
$25.00
Total Periods
20
Total Coupon Income
$500.00
Total Return (if held to maturity)
Capital Gain/Loss
+$50.00
Total Return
$550.00 (57.89%)
Risk Metrics
Macaulay Duration
7.93 yrs
Modified Duration
7.71
Convexity
72.41
Price Sensitivity
+1%: 28.50% / −1%: +43.91%
Complete Guide to Bond Yield & Duration
What Is Bond Yield?
Bond yield is the return an investor earns from holding a bond. The two most common measures are current yield and yield to maturity (YTM). Current yield simply divides the annual coupon payment by the market price, while YTM accounts for coupon payments, price difference from par, and the time value of money.
YTM is considered the most comprehensive yield metric because it represents the internal rate of return of all future cash flows — coupon payments and the face value repayment at maturity — discounted back to match the current market price. It assumes coupons are reinvested at the same YTM rate.
Understanding bond yield helps investors compare fixed-income securities with different coupon rates, maturities, and prices on a level playing field. Use our IRR Calculator for similar internal-rate-of-return analysis on other investment cash flows.
Bond Yield Formulas
Current Yield:
Current Yield = (Annual Coupon / Market Price) x 100
Yield to Maturity (YTM):
Price = Sum(t=1..N) [ C / (1+r)^t ] + F / (1+r)^N
Where: C = periodic coupon, F = face value, N = total periods, r = YTM per period (solved iteratively)
Macaulay Duration:
D = Sum(t=1..N) [ (t/freq) x PV(CF_t) ] / Bond Price
Where: PV(CF_t) = present value of cash flow at period t, freq = coupons per year
Modified Duration & Convexity:
Modified Duration = Macaulay Duration / (1 + r)
Convexity = Sum[ t(t+1) x PV(CF_t) ] / (Price x (1+r)^2 x freq^2)
Price change estimate: dP/P = -ModDur x dr + 0.5 x Convexity x dr^2
Benefits of Bond Yield Analysis
Compare Across Bonds
YTM normalizes bonds with different coupons, prices, and maturities into a single comparable return metric.
Measure Interest Rate Risk
Duration and convexity quantify how much a bond's price will move when interest rates change.
Project Total Return
See total coupon income plus capital gain or loss if held to maturity, helping plan cash flows. Pair it with our Inflation Calculator for real-return estimates.
Portfolio Immunization
Match portfolio duration to your investment horizon to minimize reinvestment and price risk simultaneously.
Tips for Bond Investors
Tip 1: A bond trading at a discount (price < face) always has YTM > current yield > coupon rate. A premium bond reverses the order. This relationship is a quick sanity check.
Tip 2: Duration increases with maturity but decreases with higher coupon rates. Zero-coupon bonds have duration equal to maturity — the maximum sensitivity. Use our Compound Interest Calculator to model reinvestment growth of coupon payments.
Tip 3: Convexity is always positive for standard coupon bonds, meaning price gains from falling rates are larger than losses from rising rates by the same amount. Higher convexity is generally desirable.
Common Mistakes
Confusing Current Yield with YTM
Current yield ignores capital gains/losses at maturity and time value. For discount bonds, current yield understates the true return; for premium bonds, it overstates it.
Ignoring Reinvestment Risk
YTM assumes every coupon is reinvested at the same rate. In falling-rate environments, actual returns will be lower than YTM because coupons get reinvested at lower rates.
Using Duration Alone for Large Rate Moves
Duration provides a linear approximation. For rate changes beyond +/- 0.5%, the convexity adjustment matters significantly. Always use both metrics together for accuracy.
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OpenFrequently Asked Questions
What is yield to maturity (YTM)?
YTM is the total return a bondholder earns if they hold the bond until maturity, assuming all coupon payments are reinvested at the YTM rate. It accounts for the bond's purchase price, face value, coupon rate, and time to maturity. YTM is the most common 'true' yield measure when comparing bonds.
What's the difference between coupon rate, current yield, and YTM?
Coupon Rate = annual coupon ÷ face value (fixed). Current Yield = annual coupon ÷ current bond price (changes with price). YTM = total annualized return holding to maturity (most accurate). Example: 5% coupon bond bought at $950 with $1,000 face → 5.26% current yield, ~5.7% YTM. The differences matter when buying secondhand bonds.
What is bond duration?
Macaulay Duration = weighted-average time to receive all cash flows (coupons + face value), in years. Modified Duration = approximation of price sensitivity to interest rates: a 5-year modified duration means the bond loses ~5% if rates rise 1%. Duration is the key risk measure for bond investors — longer duration = more interest-rate risk.
How are bond prices and interest rates related?
Inversely. When rates rise, existing bonds become less attractive (because new bonds offer higher coupons), so their prices fall. When rates fall, existing bonds with higher fixed coupons become more valuable, so prices rise. The magnitude of price change is governed by duration — longer-duration bonds swing more.
What is convexity and why does it matter?
Convexity is the second-derivative correction to duration — it captures the curvature in the price/yield relationship. For large rate moves, duration alone underestimates price changes; convexity adds a correction term. Higher convexity is generally desirable (you gain more on rate falls than you lose on equal rate rises).
Are bonds safer than stocks?
On average, yes — but with caveats. Government bonds (US Treasuries, German Bunds) are very safe in nominal terms. Corporate bonds carry credit risk. ALL bonds carry interest-rate risk (price drops when rates rise). High-yield/junk bonds can lose 30%+ in a recession. The 60/40 stock/bond split historically reduces volatility compared to 100% stocks.