Yield to Maturity (YTM): Definition, Formula & How to Calculate It
Why YTM Matters
The coupon rate only tells you how much interest a bond pays relative to its face value. The current yield only tells you the income relative to today’s price. Neither captures the full picture.
YTM does. It accounts for three things simultaneously: the coupon payments you receive, the price you paid for the bond (premium or discount to par), and the time remaining until maturity. It’s the internal rate of return (IRR) of the bond — the discount rate that makes the present value of all future cash flows equal to the bond’s current market price.
If you’re comparing a 5-year corporate bond trading at $1,050 with a 10-year Treasury trading at $970, coupon rates alone are useless. YTM gives you the true comparable return.
The YTM Formula
The exact YTM formula requires solving for the discount rate in the bond pricing equation. There’s no clean algebraic solution — it requires iteration (trial and error, or a financial calculator).
Where:
| Variable | Meaning |
|---|---|
| Price | Current market price of the bond |
| C | Coupon payment per period (annual coupon ÷ number of payments per year) |
| r | YTM per period (this is what you’re solving for) |
| n | Total number of coupon periods remaining |
| FV | Face value (typically $1,000) |
You solve for r — the rate that makes the right side equal the left side. Multiply by the number of periods per year (usually 2 for semiannual bonds) to get the annualized YTM.
Approximation Formula
Since the exact calculation requires iteration, there’s a widely used approximation that gets you close:
Where C = annual coupon, FV = face value, Price = current price, and n = years to maturity.
Example Calculation
A corporate bond has the following characteristics:
| Input | Value |
|---|---|
| Face Value | $1,000 |
| Coupon Rate | 5% ($50/year) |
| Current Price | $950 |
| Years to Maturity | 8 |
Step 2: Capital gain over 8 years = $1,000 − $950 = $50 → $6.25 per year
Step 3: Average price = ($1,000 + $950) / 2 = $975
Step 4: YTM ≈ ($50 + $6.25) / $975 = 5.77%
Notice the YTM (5.77%) is higher than both the coupon rate (5.0%) and the current yield ($50 ÷ $950 = 5.26%). That’s because YTM captures the capital gain you’ll earn when the bond matures at $1,000 — something current yield ignores entirely.
YTM vs. Coupon Rate vs. Current Yield
These three metrics are constantly confused. Here’s the definitive comparison:
| Metric | What It Captures | Accounts for Price? | Accounts for Time? |
|---|---|---|---|
| Coupon Rate | Annual interest relative to face value | No | No |
| Current Yield | Annual interest relative to market price | Partially (income only) | No |
| Yield to Maturity | Total annualized return to maturity | Yes (income + capital gain/loss) | Yes |
The pattern depends on whether the bond is at a premium or discount:
| Bond Trades At | Relationship |
|---|---|
| Discount (price < par) | Coupon Rate < Current Yield < YTM |
| Par (price = par) | Coupon Rate = Current Yield = YTM |
| Premium (price > par) | Coupon Rate > Current Yield > YTM |
YTM and Interest Rate Risk
YTM moves inversely with bond prices — just like all yield measures. When market interest rates rise, bond prices fall, and YTM increases. When rates fall, prices rise, and YTM decreases.
The sensitivity of a bond’s price to changes in YTM is measured by duration. A bond with higher duration will see larger price swings for a given change in YTM. For even more precision, convexity captures the curvature of that price-yield relationship.
Assumptions and Limitations
Other limitations to keep in mind:
Default risk isn’t priced in. YTM assumes the issuer makes every payment on time and in full. For investment-grade bonds, this is reasonable. For high-yield bonds, the actual return could be significantly lower if the issuer defaults.
Call features distort it. If a bond is callable, the issuer may redeem it before maturity. In that case, the relevant metric is yield to call (YTC), not YTM. For callable bonds, analysts typically quote the “yield to worst” — the lower of YTM and YTC.
Taxes are ignored. YTM is a pre-tax measure. Your after-tax return depends on your bracket and whether the bond is a municipal bond (often tax-exempt) or a taxable corporate bond.
How to Calculate YTM in Practice
Almost nobody solves the YTM equation by hand. Here are the practical methods:
Financial calculator: Enter N (periods), PV (current price as negative), PMT (coupon payment), FV (face value), and compute I/Y. This is the standard method on the CFA exam and in banking.
Excel: Use the RATE function or the YIELD function. For example: =YIELD(settlement, maturity, coupon_rate, price, redemption, frequency).
Bond screeners: Any brokerage platform or financial data provider (Bloomberg, FINRA’s TRACE) will display the YTM alongside the bond’s price and coupon.
For a broader look at bond pricing mechanics, see our guide on Bond Pricing Explained. For the role of YTM in the broader rate environment, see Yield Curve.
Key Takeaways
- YTM is the total annualized return you’d earn holding a bond to maturity, making it the most comprehensive bond return metric.
- It accounts for coupon payments, the difference between purchase price and face value, and the time to maturity.
- For discount bonds: Coupon Rate < Current Yield < YTM. For premium bonds: the reverse.
- YTM assumes reinvestment of coupons at the same rate — an assumption that rarely holds perfectly in practice.
- For callable bonds, yield to worst (the lower of YTM and yield to call) is the more relevant measure.
Frequently Asked Questions
What is a good yield to maturity?
There’s no universal “good” YTM — it depends on the rate environment and the bond’s risk. A YTM of 5% might be excellent for a Treasury bond in a low-rate environment but mediocre for a junk bond. Compare YTM against similar bonds with the same maturity and credit rating to judge whether it’s attractive.
Can YTM be negative?
Yes. If a bond’s price is high enough above par, the capital loss at maturity can exceed the total coupon income, resulting in a negative YTM. This happened widely with European government bonds during the negative interest rate era (2014–2022). Investors accepted a guaranteed small loss, essentially paying for the safety of government debt.
What is the difference between YTM and current yield?
Current yield only considers the annual coupon relative to the current price — it ignores any capital gain or loss at maturity. YTM accounts for both the income and the price movement, making it a far more complete measure. Current yield is a quick snapshot; YTM is the full picture.
Does YTM change after I buy a bond?
Your personal YTM is locked in at purchase (assuming you hold to maturity and reinvest at that rate). However, the YTM quoted in the market changes constantly as the bond’s price fluctuates. When people say “yields are rising,” they mean the YTM on newly traded bonds is increasing because prices are falling.
How is YTM used in the yield curve?
The yield curve plots YTM on the vertical axis against maturity on the horizontal axis, typically for Treasury securities. It shows how much investors demand for lending money over different time horizons. When the curve inverts — short-term YTMs exceed long-term YTMs — it’s historically been a reliable recession signal.