04 Bonds

Companies raise capital through equity and Debt (bank loans + bonds)

1. Key features of bonds

Par value (principal of a bond)

Coupon interest rate :

= nominal rate (yield)
= Stated interest rate (generally fixed) paid by the issuer each year.
Coupon interest rate * Par value = Dollar Payment of interest

• Yield to maturity: rate of return earned on a bond held until maturity.

Maturity

• The tenor (= term to maturity) time remaining until the bond's maturity date.
• Money market securities fixed-income securities with maturity <= one year.
• Capital market securities are fixed-income securities with maturity > one year.

2. Bond Pricing and listings

What is the discount rate (rd)?

The market discount rate is used in the time-value-of money calculation to obtain the present value.
rd =/=the coupon interest rate (i)

Bond values over time

At maturity, the value of any bond must equal its par value.
if rd is constant:

• The value of a premium bond would decrease over time, until it reached the par value.
• A value of a par bond stays at.
• The value of a discount bond would increase over time until it reaches the par value.
  
• If i = rd then, PVB = Par Value ► Par bond
• If i > rd then, PVB > Par Value ► Premium bond
• If i < rd then, PVB < Par Value ► Discount bond
  Points = % Discount/Premium (1 point = 1% of face value).

3. The Yield to Maturity (YTM)

• When Yield (YTM) goes up, the Price of the bond goes down.
• When Yield (YTM) goes down, the Price of the bond goes up.

Pricing Bonds with Spot Rates

4. Current Yield, Capital Gains Yield and Total Return

YTM = Current Yield + Capital Gains Yield.

5. Semiannual Bonds

6. Bond Pricing between two coupon payment dates

Clean price, Full price and Accrued interest

You must account for accrued interest

• Clean Price: Bond price excluding accrued interest (just the market value).
• Dirty (Full) Price: Clean price + accrued interest (what you actually pay).
  ==> dirty price = clean price + Accrued interest
  
  Secondary market: Prices fluctuate with interest rates (↑ rates = ↓ prices)
  
• Bond prices rise daily between coupons (accrued interest piling up).
• On payment day: Price drops (like a sawtooth).
• You always pay the dirty price—no free lunches!
  

Primary Market (Where Bonds Are Born)

Issuer (e.g., a company) sells bonds directly to investors.
Coupon rate = Investors’ required return (r).
Exception: If demand is super high/low, bonds may sell above/below par.

Secondary Market (Where Bonds Trade Between Investors)

• Pricing: Bonds rarely trade at par because interest rates change constantly.

  • Premium: Price > Par → Yield < Coupon Rate (investors pay extra for higher coupons).
  • Discount: Price < Par → Yield > Coupon Rate (investors get a deal for lower coupons).

• Interest Rate Rule:

  • ↑ Rates → ↓ Bond Prices (existing bonds with lower coupons lose value).
  • ↓ Rates → ↑ Bond Prices (existing bonds with higher coupons gain value).

Bond Pricing between two coupon dates

Full Price calculation

1. Calculate the (clean price) bond’s price right after the last coupon payment.
   • Discount all future cash flows (coupons + face value) to the last coupon date.
2. Measure the time between: Last coupon date (when the seller got their last payment) and Settlement date
3. Add Accrued Interest: Capitalize = Grow the clean price by the daily interest
   • 

Actual/Actual Day Count

1. • Count ALL actual days between dates (even weird months like February in leap years).
2. First day = COUNTED | Last day = NOT COUNTED

7. Zero-coupon Bonds

• zero coupon bonds
• original issue discount (OID) Bonds.

Why Buy Them?

1. Predictable Profit: Know exactly what you'll get at maturity.
2. Less Reinvestment Risk: No coupons to reinvest (good when rates are falling).
3. Cheaper Entry: Pay way less than face value upfront

⚠️ Watch Out!

• Tax Trickery: In the U.S., you pay taxes on "imputed interest" yearly (even though you get no cash until maturity!).
• Sensitive to Rate Changes: Prices swing wildly if interest rates move (longer maturities = bigger swings).
  *For every 1% rate increase, a bond’s price drops by roughly its duration., A 1% rate rise → 30-year zero drops ~30% (!), but a 5-year zero drops only *~5

8. Callable Bonds

1. Call Provision
   • Contractual clause permitting early redemption.
   • Specifies call schedule and call premium structure.
2. Call Price
   

• Call Premium

  • Initial Premium: Often equals one year’s coupon payment
    

• Investors must evaluate both YTC and YTM to assess worst-case returns.
  

Cause of calling a bond

• A decline in market interest rates (rd).
  ==> good for the company but bad for the bondholders

🤯 Why This Sucks for You

Translation: Heads they win, tails you lose.

💰 The Only Consolation

• Callable bonds pay higher coupons upfront to compensate for this risk.

But is it worth it?
✅ Yes if you think rates will stay flat/rise slightly.
❌ No if you expect big rate drops (your bond will vanish).

🛡️ How to Protect Yourself

1. Demand call protection (e.g., "Can't call for 5 years").
2. Compare yields:
   • Yield-to-Worst (YTW) = Lower of YTM or YTC.
3. Prefer non-callables if you want stability.