Current yield, yield to maturity and the yield curve
Current yield is the annual coupon divided by the price: quick, but it ignores the gain or loss to par. Yield to maturity is the single discount rate that equates the price with all remaining cash flows. Plotting an issuer's yields by maturity gives its yield curve; its gap over the government curve is the credit spread.
Before this: The features of a bond, Returns of Financial Assets
On the exam
- Describe the features of a fixed-income security
Describe yield measures and yield curves as bond features. Expect: compute a current yield; state when the realized return equals the yield to maturity; read a credit spread off two curves. Full YTM mechanics come in later modules.
How deeply to learn each part
- Know the idea
- Understand it in general. It frames other topics, but you will not calculate with it.
- Use it
- Understand it well enough to solve a question with it. Recognize when it applies.
- Memorize
- Learn it by heart. The exam will not give it to you.
You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.
You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.
What is current yield?
Current yield is a quick return measure: the annual coupon divided by the bond’s price. It is the bond’s version of a dividend yield.
The current yield uses the price, not par. That is what separates it from the coupon rate.
A bond pays an annual coupon of 5.25 per 100 of par and trades at 96.50. Its current yield is closest to:
5.25 ÷ 96.50 = 5.44%
Current yield5.44%
- 5.25÷96.5=a decimal
- multiplyby100forpercent
- 5.25ENTER96.5÷a decimal
- multiplyby100forpercent
ENTER enter (on the HP, puts the number on the stack)
What is yield to maturity?
Yield to maturity (YTM) is the bond’s internal rate of return: the single rate r that makes the present value of all remaining cash flows equal to today’s price. It is usually quoted as an annual rate.
You cannot rearrange this for r, so you solve it on the calculator.
A bond’s price and yield move in opposite directions. The investor’s realized return equals the YTM at purchase only under three conditions, the same ones as for any IRR.
- No default Memorize all coupons and par paid in full, on time
- Held to maturity Memorize sold early, the return depends on the sale price
- Coupons reinvested at the YTM Memorize not at the coupon rate
- Current yield Memorize annual coupon ÷ price; ignores the move to par
- Yield to maturity Memorize IRR of all cash flows at today's price; quoted annually
Exam tip Realized return = YTM needs three yeses: paid in full, held to maturity, reinvested at the YTM.
What does a yield curve show?
A yield curve plots the YTM of an issuer’s bonds against their maturities, using bonds with otherwise similar features. When longer bonds yield more, the curve slopes upward.
Compare an issuer’s curve with the government’s curve for the same maturities. Government bonds in developed markets carry little or no credit risk , which is the risk of loss if the issuer fails to pay interest or principal in full and on time. The gap at one maturity is the credit spread.
A corporate bond yields 5.35%. A government bond of the same maturity yields 4.10%. The credit spread is closest to:
(5.35% − 4.10%) × 100 = 125 bps
Credit spread (basis points)125
- 5.35−4.1=×100=percentage points to basis points
- 5.35ENTER4.1−100×percentage points to basis points
ENTER enter (on the HP, puts the number on the stack)
Try this 0 of 3
- Find the maturity with the widest spread
- Cut the issuer to a rating where the 10-year spread is above 3%
- Invert the government curve, then read the 5-year spread
Tap a maturity on the chart (or a button) to read the spread there. Then change the issuer's rating and the slope.
- Issuer (BBB)
- Government
Government yields 3.60%, 3.75%, 3.90%, 4.10%, 4.30%, 4.50% and BBB issuer yields 4.50%, 4.75%, 5.00%, 5.35%, 5.65%, 5.95% at 1, 2, 3, 5, 7 and 10 years. At 5 years the credit spread is 125 bps.
| Maturity | Government | Issuer | Spread |
|---|---|---|---|
| 1 year | 3.60% | 4.50% | 90 bps |
| 2 years | 3.75% | 4.75% | 100 bps |
| 3 years | 3.90% | 5.00% | 110 bps |
| 5 years | 4.10% | 5.35% | 125 bps |
| 7 years | 4.30% | 5.65% | 135 bps |
| 10 years | 4.50% | 5.95% | 145 bps |
At 5 years the BBB issuer yields 5.35% against 4.10% for the government: a credit spread of 125 bps.
Show working
Credit spread = issuer yield − government yield at the same maturity = 5.35% − 4.10% = 1.25% = 125 bps.
1 percentage point = 100 basis points (bps), so multiply the difference in percent by 100.
Compare yields at the same maturity only: subtracting a 5-year government yield from a 10-year issuer yield mixes credit risk with the slope of the curve.
- 5.35−4.1=×100=125 bps
- 5.35ENTER4.1−100×125 bps
ENTER enter (on the HP, puts the number on the stack)
Go deeper Why YTM inherits the IRR's assumptions
YTM is an IRR, so it carries the IRR’s hidden assumption that every cash flow is reinvested at that same rate. If coupons earn less than the YTM, the realized return falls short of it. If the bond is sold before maturity, the sale price replaces par and the return depends on where yields have moved. Only for a bond bought at par is the YTM equal to the coupon rate.
Go deeper Downward-sloping curves
When longer bonds yield less than shorter ones, the curve is inverted. It can signal that investors expect interest rates to fall. The shape of a curve and what drives it come back in the later modules on yield spreads and term structure.
Go deeper Semiannual bonds and the quoted YTM
Most corporate bonds pay twice a year, so the calculator works in half-years: N is the number of half-years, PMT is half the annual coupon, and the I/Y it returns is the half-year rate. The quoted annual YTM is that rate times two. This convention is covered fully in the valuation modules.
Memorize this
MemorizeYield measures
| Measure | Formula | Counts the move to par? |
|---|---|---|
| Current yield | coupon ÷ price | No |
| Coupon rate | coupon ÷ par | No |
| Yield to maturity | IRR at current price | Yes |
Memory hook Price down, yield up. Discount bond: YTM > CY > coupon rate. Premium bond: coupon rate > CY > YTM.
Know it cold Realized return = YTM only with no default, held to maturity and coupons reinvested at the YTM.
MemorizeCredit spread
Memory hook Spread = issuer minus government, same maturity. 1 point = 100 bps.
Know it cold The spread is the pay for credit risk.
- No default Memorize all coupons and par paid in full, on time
- Held to maturity Memorize sold early, the return depends on the sale price
- Coupons reinvested at the YTM Memorize not at the coupon rate
- Current yield Memorize annual coupon ÷ price; ignores the move to par
- Yield to maturity Memorize IRR of all cash flows at today's price; quoted annually
Quick example
A 7% annual coupon bond trades at 108.50 per 100 par. 7 ÷ 108.50 = 6.45%.
- 7÷108.5= 0.0645
- 7ENTER108.5÷ 0.0645
ENTER enter (on the HP, puts the number on the stack)
Quick example
5 years, 4% annual coupon, price 96.00 per 100 par. Solve for r: 4.92%.
- 2NDCLR TVM with P/Y set to 1
- 5N96+|-PV4PMT100FV
- CPTI/Y 4.92
2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · +|- change sign · PV present value · PMT payment · FV future value · CPT compute · I/Y interest rate per year (per period when P/Y is 1)
- fCLEAR FIN
- 5n96CHSPV4PMT100FV
- i 4.92
f gold shift key · CLEAR FIN clear the financial registers · n number of periods · CHS change sign · PV present value · PMT payment · FV future value · i interest rate per period
Quick example
Issuer 10-year yield 5.80%, government 10-year yield 3.95%. 5.80 − 3.95 = 1.85 points = 185 bps.
- 5.8−3.95=×100= 185
- 5.8ENTER3.95−100× 185
ENTER enter (on the HP, puts the number on the stack)
How it is asked
-
Current yield
7% annual coupon, price 108.50. Current yield?
7 ÷ 108.50 = 6.45%. Traps: 7.00% (the coupon rate) and 7.60% (multiplied by price).
-
YTM versus coupon and current yield
4% coupon, 5 years, price 96. Which yield is highest?
Discount bond, so YTM 4.92% > current yield 4.17% > coupon 4.00%.
-
When does return equal YTM?
Held to maturity, paid in full. Coupons reinvested at what rate?
At the YTM, not the coupon rate.
-
Read a spread
Issuer 10-year 5.80% vs government 3.95% (5-year is 3.60%).
5.80 − 3.95 = 185 bps. Same maturity only; 220 bps is the trap.
Exam traps
- Dividing the coupon by par instead of price: that is the coupon rate, not the current yield.
- Multiplying the coupon by the price instead of dividing.
- Saying the realized return equals the YTM if the bond is sold before maturity.
- Reading a spread from two different maturities.
- Assuming current yield equals YTM. For a bond at a discount or premium the YTM also counts the move to par.
Checkpoint
4 exam-style questions. About 90 seconds each.
1A bond with a 6% annual coupon trades at 104.20 per 100 par. Its current yield is closest to:
2A 4-year bond paying a 3% annual coupon is priced at 95.00 per 100 par. Its yield to maturity is closest to:
3An investor buys a bond and holds it to maturity; the issuer pays everything on time. The investor's realized return will equal the yield to maturity at purchase only if the coupons are reinvested at:
4A corporate 7-year bond yields 6.15%. A government 7-year bond yields 4.40% and a government 5-year bond yields 4.10%. The corporate bond's credit spread is closest to:
Key takeaways
- Current yield = annual coupon ÷ price; it ignores the move to par.
- YTM = the IRR of the bond's cash flows at its current price.
- Realized return = YTM only with no default, held to maturity and coupons reinvested at the YTM.
- Credit spread = issuer yield − government yield at the same maturity.
Quick example
A 7% annual coupon bond trades at 108.50 per 100 par. 7 ÷ 108.50 = 6.45%.
- 7÷108.5= 0.0645
- 7ENTER108.5÷ 0.0645
ENTER enter (on the HP, puts the number on the stack)
Quick example
5 years, 4% annual coupon, price 96.00 per 100 par. Solve for r: 4.92%.
- 2NDCLR TVM with P/Y set to 1
- 5N96+|-PV4PMT100FV
- CPTI/Y 4.92
2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · +|- change sign · PV present value · PMT payment · FV future value · CPT compute · I/Y interest rate per year (per period when P/Y is 1)
- fCLEAR FIN
- 5n96CHSPV4PMT100FV
- i 4.92
f gold shift key · CLEAR FIN clear the financial registers · n number of periods · CHS change sign · PV present value · PMT payment · FV future value · i interest rate per period
Quick example
Issuer 10-year yield 5.80%, government 10-year yield 3.95%. 5.80 − 3.95 = 1.85 points = 185 bps.
- 5.8−3.95=×100= 185
- 5.8ENTER3.95−100× 185
ENTER enter (on the HP, puts the number on the stack)
All Fixed Income formulas, every lesson
Practice exam-style questions on Fixed-Income Instrument Features
Questions about this lesson?
Where this comes back
- Bond indentures and covenants Fixed-Income Instrument Features
- Bond Valuation: Prices and Yields Fixed Income
- Yield and Yield Spread Measures for Fixed-Rate Bonds Fixed Income
Questions candidates ask
What is the difference between current yield and yield to maturity?
Current yield only divides the annual coupon by the price. Yield to maturity also counts the gain or loss as the price moves to par, and the timing of every payment. For a bond at a discount, YTM is higher than current yield.
When does a bond's return equal its yield to maturity?
When the issuer pays every coupon and the par amount in full and on time, the investor holds to maturity, and every coupon is reinvested at the yield to maturity. Break any one and the realized return differs.
What does an issuer's yield curve show?
The yields to maturity of its bonds with similar features, plotted against maturity. The gap between that curve and the government curve at the same maturity is the credit spread, the pay for taking its credit risk.
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