Yield to Maturity (YTM)
Yield to Maturity (YTM)
Yield to maturity is the internal rate of return (IRR) of all the bond's cash flows—the coupons and the principal repayment—if you buy the bond at the current price and hold it to maturity. It is the single most important number in bond markets and the standard way to compare bonds.
Key takeaways
- YTM is the discount rate that makes the present value of all future cash flows equal to the bond's current price
- YTM accounts for coupons, the purchase price, and the par value you receive at maturity
- A bond trading at par has a YTM equal to its coupon rate
- A bond trading at a discount has a YTM higher than its coupon rate
- A bond trading at a premium has a YTM lower than its coupon rate
- YTM is quoted on a semi-annual basis for U.S. bonds
What YTM measures
YTM is the average annual return you earn if you:
- Buy the bond at its current market price today
- Collect all coupon payments for the rest of the bond's life
- Receive the par value at maturity
- Hold the bond through maturity (do not sell before)
It is a complete return metric because it incorporates three elements: the income (coupons), the capital gain or loss (the difference between price and par), and the time value of money.
The mathematics behind YTM
YTM is computed by solving for the discount rate in the bond pricing formula:
Price = (C / (1 + y)) + (C / (1 + y)^2) + ... + (C / (1 + y)^n) + (Par / (1 + y)^n)
Where:
- Price = the current market price of the bond
- C = the semi-annual coupon payment (annual coupon ÷ 2 in the U.S. market)
- y = the semi-annual YTM (the semi-annual yield divided by 2)
- n = the number of semi-annual periods to maturity
- Par = the face value of the bond
You solve for y (the semi-annual yield), then multiply by 2 to get the annual YTM. Most bonds are quoted this way.
In practice, you do not solve this by hand. Yield calculation is built into every financial calculator, spreadsheet, and brokerage platform. You input the price, coupon, par, and days to maturity, and the system returns the YTM.
A concrete example
Suppose you can buy a corporate bond with:
- Par: $1,000
- Coupon: 4% ($40 annual, or $20 semi-annual)
- Years to maturity: 5
- Current price: $950
To find YTM, you solve for the discount rate that makes:
Present value of all coupons + Present value of par = $950
If you test a discount rate of 4.5% (semi-annual 2.25%):
PV of coupons: $20 / (1.0225) + $20 / (1.0225)^2 + ... + $20 / (1.0225)^10 = approximately $184 PV of par: $1,000 / (1.0225)^10 = approximately $795
Total PV: approximately $979
That is too high. Try 4.6%:
You will eventually find that a YTM of about 4.66% (or 2.33% semi-annually) equates the present value of the cash flows to $950.
The YTM for this bond is 4.66%. This means that if you buy at $950, hold to maturity, and reinvest all coupons at 4.66%, you earn an average annual return of 4.66%.
The inverse relationship between price and YTM
When a bond's price falls, its YTM rises. When the price rises, the YTM falls. This is because YTM is the yield (return) on the purchase price. A lower price means you are buying the same cash flows for less, so the return is higher.
Using our example bond, suppose the price falls to $900:
The YTM would rise to approximately 5.2%. The coupons and par are the same; only the price (the denominator in the return calculation) fell, so the return rose.
If the price rises to $1,000 (par):
The YTM equals the coupon rate, 4%.
This inverse relationship is the engine of bond markets. When interest rates rise, bond prices fall and yields rise. When rates fall, prices rise and yields fall. The market reprices every bond to a yield consistent with current interest rates and the bond's credit quality.
YTM vs current yield
Current yield is annual coupon ÷ current price. YTM is the internal rate of return including the capital gain or loss at maturity.
For our example:
- Current yield: $40 / $950 = 4.21%
- YTM: 4.66%
YTM is higher because the bond trades at a discount. You will receive a $50 capital gain at maturity ($1,000 minus $950), and YTM factors that in. Current yield ignores it.
If the bond were trading at a premium (say, $1,050):
- Current yield: $40 / $1,050 = 3.81%
- YTM: 3.20% (approximately)
YTM is lower because you will suffer a $50 capital loss at maturity.
YTM is the complete return measure; current yield is the income-only measure.
YTM and price: the relationship for different maturities
YTM is particularly sensitive to maturity. A small change in YTM causes a small change in price for a short-maturity bond but a large change for a long-maturity bond.
For example:
- A 2-year bond with a 4% coupon trading at a 5% YTM has a price of approximately $980 (a $20 discount)
- A 20-year bond with a 4% coupon trading at a 5% YTM has a price of approximately $850 (a $150 discount)
The longer the maturity, the bigger the discount needed to achieve a given YTM. This is the essence of duration: long-dated bonds are more price-sensitive.
YTM assumptions and limitations
YTM assumes:
- You hold to maturity — If you sell before maturity, your actual return may be higher or lower than the YTM, depending on what price you sell at.
- The issuer does not default — YTM assumes the issuer pays all coupons and par on time. If the issuer defaults, the actual return is lower.
- Coupons are reinvested at the YTM — YTM calculation assumes you reinvest every coupon at the same YTM. In reality, rates change, so you may reinvest at higher or lower rates.
The third assumption is subtle but important. YTM is a single number that blends the coupon income, the capital gain/loss, and reinvestment. It assumes a specific reinvestment rate (the YTM itself). If you actually reinvest at lower rates, your realized return will be lower than the stated YTM.
For a short-maturity bond, reinvestment risk is minimal (you reinvest for only a short time). For a long-maturity bond, reinvestment risk is large (you reinvest many times at unknown future rates).
Callable bonds: YTM is not the whole story
For a callable bond, the issuer has the right to call (early redemption) if rates fall. This caps your upside. If you buy a callable bond with a high YTM and rates fall, the issuer will call it, you lose the high coupons, and you are forced to reinvest at lower rates.
For callable bonds, analysts quote yield to call (YTC) as well as YTM. The YTC assumes the bond is called at the earliest call date. The YTC is usually lower than the YTM because the call scenario is worse for you (fewer years of high coupons).
A bond's quoted yield should be yield to worst (YTW), which is the lower of YTM and YTC. This is the yield you can count on in the least favorable scenario.
YTM and credit risk
YTM includes credit risk. A high-risk bond (say, a junk bond from a shaky company) will have a high YTM. A low-risk bond (a Treasury or AAA corporate) will have a low YTM. The difference is the credit spread—the extra yield you demand to compensate for credit risk.
If a Treasury bond yields 3% and a corporate bond from the same maturity yields 4%, the credit spread is 1% (100 basis points). This 1% is compensation for the credit risk you are taking on.
YTM does not predict whether the issuer will default. A high YTM is not a guarantee of return; it is a market price reflecting the risk. Some high-yield bonds default and you lose money despite the high YTM. Some default-free bonds (like Treasuries) have low YTM but zero default risk.
Historical YTM context
In 2019, 10-year Treasury yields were around 1.5–2%. Investors could buy a 10-year U.S. government bond and expect a 1.5–2% return. In 2023, 10-year Treasury yields rose to 4–5%, reflecting higher short-term rates and inflation expectations. The same maturity offered a YTM of 4–5%.
This difference is enormous for investors. A 3% yield difference (from 2% to 5%) compounds over 10 years. An investor who bought Treasuries in 2019 accepted a low 2% YTM; an investor who bought in 2023 earned 5% YTM on the same maturity. The 2023 investor is better off (higher income) assuming rates do not fall further.
YTM across bond types
Treasury securities, corporate bonds, municipal bonds, and international bonds all use YTM as the standard yield measure. The YTM varies based on maturity and credit risk, but the calculation is the same.
- Short Treasuries (1–3 year maturity): 5–5.5% YTM in 2023
- Long Treasuries (20–30 year maturity): 4–4.5% YTM in 2023
- Investment-grade corporates (10-year maturity): 5–6% YTM in 2023
- High-yield corporates (10-year maturity): 8–10% YTM in 2023
The upward slope (higher yield for longer maturities) is typical when the economy is healthy and inflation is under control. An inverted curve (lower yield for longer maturities) is a warning sign.
Calculating YTM in a spreadsheet
In Excel or Google Sheets, YTM is calculated using the YIELD function:
=YIELD(settlement, maturity, rate, pr, redemption, frequency, [basis])
Where:
- settlement = today's date
- maturity = the bond's maturity date
- rate = the coupon rate (as a decimal, e.g., 0.04 for 4%)
- pr = the bond's price as a percentage of par (e.g., 95 for $950 on a $1,000 par bond)
- redemption = the par value (typically 100 for percentage, or 1000 for dollars)
- frequency = coupon frequency (1 for annual, 2 for semi-annual, 4 for quarterly)
This function returns the YTM, making it easy to build a spreadsheet of bonds and their yields.
YTM and bond funds
A bond fund's YTM is the weighted average YTM of all the bonds it holds. If a fund holds 100 bonds with an average YTM of 3.5%, the fund's stated YTM is 3.5%. This is the average return you would expect if the fund holds all bonds to maturity and reinvests coupons at the current YTM.
In practice, bond funds do not hold to maturity; they trade actively. But the stated YTM gives you a benchmark for expected returns.
YTM and spot rates
YTM is the yield to maturity of a single bond. Spot rates are the yields of zero-coupon bonds (or the implied zero-coupon yields) for each maturity. The spot curve and the YTM curve are related but different. YTM bundles coupons and maturity into one number; spot rates break them apart.
For most investors, YTM is the practical measure. Spot rates are more relevant for advanced analysis (e.g., pricing derivatives or decomposing bond returns).
Conclusion: YTM is the bond market's universal language
YTM is how bond professionals compare bonds. A Treasury yielding 4%, a corporate bond yielding 5%, and a municipal bond yielding 3% are all quoted in YTM. You compare them and decide which offers the best value for your risk tolerance. YTM is not a perfect measure—it has limitations (reinvestment assumptions, default risk, callability)—but it is the standard, and understanding it is essential for bond investing.
Process
Related concepts
Next
YTM assumes you hold the bond to maturity, but for callable bonds the issuer has the right to redeem early. Yield to call is the return if the bond is called, and we need to understand when this becomes your limiting return.