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💰 What is Yield to Maturity (YTM)?

Yield to Maturity (YTM) is the total return you can expect from a bond if you hold it until it matures. It accounts for the bond's current market price, coupon payments, face value, and time to maturity. YTM is expressed as an annual percentage rate.

Key Point: YTM is the most important measure for comparing bonds because it standardizes returns across different bonds with varying coupon rates, prices, and maturities. It tells you: "If I buy this bond today and hold to maturity, what annual return will I earn?"

Understanding Bonds Basics

Key Bond Terms:

Term Definition Example
Face Value (Par) Amount paid at maturity $1,000
Coupon Rate Annual interest rate on face value 5% ($50/year)
Market Price Current trading price $950 (below par)
Maturity Date When principal is repaid 5 years from now
YTM Total annual return to maturity 6.2%

Simple YTM Example

NZ Government Bond:

Face value: $1,000
Coupon rate: 4% (pays $40/year)
Current market price: $950
Years to maturity: 5
Simplified YTM calculation:
Annual coupon: $40
Capital gain over 5 years: $1,000 - $950 = $50
Annual capital gain: $50 / 5 = $10
Total annual return: $40 + $10 = $50
Average investment: ($950 + $1,000) / 2 = $975
YTM ≈ $50 / $975
YTM ≈ 5.13% per year

Interpretation: If you buy this bond for $950 and hold to maturity, you'll earn approximately 5.13% annually through coupon payments plus the gain from price appreciation to par value.

Why Bond Prices Change

Inverse Relationship with Interest Rates:

Interest rates RISE → Bond prices FALL → YTM rises
Interest rates FALL → Bond prices RISE → YTM falls

Example:

You own a bond paying 4% coupon. New bonds now pay 6%. Your bond becomes less attractive, so its price falls to compensate buyers with higher YTM.

Scenario Market Price YTM Term
Interest rates rise $900 (discount) 6.5% Trading below par
Interest rates unchanged $1,000 (par) 4.0% Trading at par
Interest rates fall $1,050 (premium) 2.8% Trading above par

YTM vs Other Yield Measures

Measure Formula What It Shows
Current Yield Annual Coupon / Market Price Simple income return only
Coupon Rate Annual Coupon / Face Value Original fixed rate
YTM Complex (includes capital gains) Total return if held to maturity

Example Comparison:

Bond: $1,000 face, 5% coupon, trading at $950
Coupon Rate = 5% (fixed forever)
Current Yield = $50 / $950 = 5.26%
YTM = 5.8% (includes $50 capital gain over time)

YTM is most comprehensive because it includes both income and capital appreciation.

Uses of YTM

1. Comparing Bonds:

Compare bonds with different coupons, prices, and maturities on equal footing.

2. Portfolio Decisions:

Choose bonds that meet your required return threshold.

3. Interest Rate Forecasting:

YTM reflects market expectations about future interest rates.

4. Benchmarking:

Government bond YTM is the risk-free rate used in CAPM and other models.

Typical YTM Ranges (2024)

Bond Type Typical YTM Risk Level
NZ Government 10-year 4.0-4.5% Very low
AAA Corporate 4.5-5.5% Low
BBB Corporate 5.5-7.0% Moderate
High Yield (Junk) 8.0-12.0% High
Emerging Market 7.0-10.0% High
💡 YTM Assumptions

YTM assumes you:
1. Hold the bond to maturity (no selling early)
2. Reinvest all coupon payments at the same YTM rate
3. Issuer doesn't default
If any assumption fails, actual return may differ from YTM.

Duration and Interest Rate Risk

Duration measures how sensitive a bond's price is to interest rate changes.

Rule of Thumb: 1% interest rate change causes price change of Duration%
Example: Bond with 5-year duration
Interest rates rise 1% → Bond price falls ~5%
Interest rates fall 1% → Bond price rises ~5%

Longer Maturity = Higher Duration = More Price Volatility

Maturity Typical Duration Price Sensitivity
2 years 1.9 years Low
5 years 4.5 years Moderate
10 years 8.2 years High
30 years 18 years Very high
⚠️ YTM Limitations

Ignores reinvestment risk: Assumes you can reinvest coupons at YTM rate (unlikely)
Assumes held to maturity: If you sell early, actual return may differ
Doesn't reflect default risk: High YTM may signal high default risk
Point-in-time measure: YTM changes daily with market prices

🔢 Calculating Yield to Maturity

The YTM Formula

Exact YTM requires solving for the discount rate that equates present value of cash flows to current price:

Price = C/(1+YTM)¹ + C/(1+YTM)² + ... + (C+FV)/(1+YTM)ⁿ
Where:
C = Annual coupon payment
FV = Face value
n = Years to maturity
YTM = Yield to maturity (solve for this)

This requires trial and error or a financial calculator. For approximation, use the simplified formula.

Approximation Formula

YTM ≈ [C + (FV - P) / n] / [(FV + P) / 2]
Where:
C = Annual coupon payment
FV = Face value
P = Current market price
n = Years to maturity

Example 1: Bond Trading at Discount

Contact Energy Bond:

Face value: $1,000
Coupon rate: 5.5% (pays $55/year)
Current price: $920
Years to maturity: 7

Calculation:

Annual coupon (C) = $55
Capital gain = $1,000 - $920 = $80
Annual capital gain = $80 / 7 = $11.43
Total annual return = $55 + $11.43 = $66.43
Average price = ($920 + $1,000) / 2 = $960
YTM ≈ $66.43 / $960
YTM ≈ 6.92%

Interpretation: Bond trades below face value because its 5.5% coupon is below current market rates. YTM of 6.92% compensates buyer through both coupons and capital appreciation.

Example 2: Bond Trading at Premium

Fletcher Building Bond:

Face value: $1,000
Coupon rate: 7.0% (pays $70/year)
Current price: $1,080
Years to maturity: 4

Calculation:

Annual coupon (C) = $70
Capital loss = $1,000 - $1,080 = -$80
Annual capital loss = -$80 / 4 = -$20
Net annual return = $70 - $20 = $50
Average price = ($1,080 + $1,000) / 2 = $1,040
YTM ≈ $50 / $1,040
YTM ≈ 4.81%

Interpretation: Bond trades above face value because 7% coupon exceeds current market rates. YTM of 4.81% is lower than coupon because buyer pays premium and will receive capital loss at maturity.

Example 3: Zero-Coupon Bond

NZ Treasury Bill (no coupons, just discount):

Face value: $10,000
Current price: $8,500
Years to maturity: 3

YTM Calculation:

FV / (1 + YTM)ⁿ = Price
$10,000 / (1 + YTM)³ = $8,500
(1 + YTM)³ = $10,000 / $8,500
(1 + YTM)³ = 1.1765
1 + YTM = 1.1765^(1/3)
1 + YTM = 1.0557
YTM = 5.57%

All return comes from buying at discount and receiving face value at maturity.

Example 4: Comparing Two Bonds

Which bond offers better return?

Bond A:

$1,000 face, 6% coupon, $1,020 price, 5 years
YTM = [60 + (1,000-1,020)/5] / [(1,000+1,020)/2]
YTM = [60 - 4] / 1,010
YTM = 5.54%

Bond B:

$1,000 face, 5% coupon, $950 price, 5 years
YTM = [50 + (1,000-950)/5] / [(1,000+950)/2]
YTM = [50 + 10] / 975
YTM = 6.15%
Decision: Bond B offers higher YTM (6.15% vs 5.54%) despite lower coupon. The discount price more than compensates for lower coupon payments. Choose Bond B for better return.

Impact of Time to Maturity

Same bond, different maturities:

Years to Maturity Price YTM
1 year $980 7.14%
5 years $920 6.92%
10 years $880 6.84%
20 years $850 6.78%

Longer maturity bonds trade at bigger discounts because buyers lock in rates for longer periods.

Yield Curve

Plot YTM against maturity to see yield curve:

Normal curve: Longer maturity = Higher YTM
Flat curve: Similar YTM across maturities
Inverted curve: Shorter maturity = Higher YTM (recession signal)

NZ Government Bond Yield Curve Example:

Maturity YTM Spread vs 1-year
1 year 3.5% -
2 years 3.8% +0.3%
5 years 4.2% +0.7%
10 years 4.5% +1.0%

Normal upward-sloping curve compensates investors for locking in money longer.

🌍 Real-World YTM Examples

1
NZ Government Bond Investment

Retiree choosing between bonds for income

Option A: Short-Term Government Bond

NZ Treasury 2-year bond
Face value: $10,000
Coupon: 3.5% ($350/year)
Price: $9,920
YTM = [350 + (10,000-9,920)/2] / [(10,000+9,920)/2]
YTM = [350 + 40] / 9,960
YTM = 3.92%

Option B: Long-Term Government Bond

NZ Treasury 10-year bond
Face value: $10,000
Coupon: 4.5% ($450/year)
Price: $10,200
YTM = [450 + (10,000-10,200)/10] / [(10,000+10,200)/2]
YTM = [450 - 20] / 10,100
YTM = 4.26%

Analysis:

Factor 2-Year Bond 10-Year Bond
YTM 3.92% 4.26%
Annual income $350 $450
Price risk Low (2-year duration) High (8+ year duration)
Reinvestment risk High (reinvest in 2 years) Low (locked 10 years)
Decision: For stable income, choose 10-year bond (higher YTM, higher income). For flexibility and less price volatility, choose 2-year bond. Retiree chose 10-year for reliable $450/year income stream.
2
Corporate Bond vs Government Bond

Investor comparing safety vs return

NZ Government Bond:

$10,000 face, 4% coupon, $10,000 price, 5 years
YTM = 4.0% (at par)
Credit rating: AAA (virtually risk-free)

Fonterra Corporate Bond:

$10,000 face, 5.5% coupon, $9,800 price, 5 years
YTM = [550 + (10,000-9,800)/5] / [(10,000+9,800)/2]
YTM = [550 + 40] / 9,900
YTM = 5.96%
Credit rating: BBB+ (investment grade)

Comparison:

Fonterra YTM: 5.96%
Government YTM: 4.00%
Credit spread: 1.96%
This compensates for default risk

Risk-Return Trade-off:

Investment Annual Income 5-Year Total Risk
Government $400 $2,000 None
Fonterra $596 $2,980 Moderate
Extra return $196 $980 -

Decision factors: Is extra $980 over 5 years worth the corporate default risk? For conservative investors, government bond safer. For return-focused investors, Fonterra offers 50% more yield.

3
Interest Rate Change Impact

Investor holds bond when rates rise

Original Purchase (1 year ago):

Bought at par: $10,000
Coupon: 4.5%
Maturity: 10 years (now 9 years left)
YTM at purchase: 4.5%

Today (Market Rates Rose):

New similar bonds: 6% YTM
Your bond's price fell to: $8,750
Current YTM on your bond: ~6%

Investor's Options:

Option 1: Sell Now

Sale price: $8,750
Received coupons (1 year): $450
Total: $9,200
Loss: -$800 (-8%)

Option 2: Hold to Maturity

Continue receiving $450/year for 9 years = $4,050
Receive face value at maturity: $10,000
Total: $14,050
Original investment: $10,000
Profit: $4,050 over 10 years (4.05% annualized)
💡 Key Lesson

Rising interest rates cause bond prices to fall, creating paper losses. But if you hold to maturity, you still receive all promised coupons plus face value. Only realize loss if you sell. This is why bonds are considered "safe" for buy-and-hold investors despite price volatility.

4
Building a Bond Ladder

Retiree creates steady income stream

Strategy: Buy bonds maturing in different years

Bond Maturity Face Value Price Coupon YTM
A 1 year $20,000 $19,800 3.5% 4.5%
B 2 years $20,000 $19,600 4.0% 5.0%
C 3 years $20,000 $19,400 4.5% 5.5%
D 4 years $20,000 $19,200 5.0% 6.0%
E 5 years $20,000 $19,000 5.5% 6.5%

Total Investment:

$97,000 (5 bonds)

Annual Income:

Year 1: $700 + $800 + $900 + $1,000 + $1,100 + $20,000 (Bond A matures)
Year 2: $800 + $900 + $1,000 + $1,100 + $20,000 (Bond B matures)
Reinvest matured bonds in new 5-year bonds
Benefits of Bond Ladder: Steady income, reduced reinvestment risk (only 1/5 of portfolio matures yearly), liquidity (bond matures annually), average YTM of 5.5%. Provides stability and predictability for retirement income.

🎯 Test Your Knowledge

Complete this quiz on Yield to Maturity

1. What does YTM represent?
The coupon rate of the bond
Total annual return if held to maturity
Current dividend yield
The bond's credit rating
2. When interest rates rise, bond prices:
Fall (inverse relationship)
Rise
Stay the same
Become more volatile
3. A bond trading below face value is trading at:
Premium
Discount
Par
Maturity
4. Bond: $1,000 face, 5% coupon, $950 price, 5 years. Approximate YTM is:
5.0%
5.3%
6.2%
7.0%
5. YTM is higher than coupon rate when a bond trades at:
Premium (above face value)
Discount (below face value)
Par (equal to face value)
Maturity
6. Which bond type typically has the highest YTM?
Government bonds
AAA corporate bonds
Investment grade bonds
High-yield (junk) bonds
7. Duration measures:
Time until bond matures
Bond price sensitivity to interest rate changes
Credit quality of bond
Coupon payment frequency
8. YTM assumes you:
Sell the bond before maturity
Hold to maturity and reinvest coupons at YTM rate
Only receive coupon payments
Default will occur
9. A normal yield curve shows:
Short-term bonds have higher YTM
Long-term bonds have higher YTM
All maturities have same YTM
No relationship between maturity and YTM
10. If you hold a bond to maturity, you will receive:
Only coupon payments
Only face value
All coupon payments plus face value
Current market price

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