What is a Bond?
A bond is a fixed-income debt instrument that represents a loan made by an investor to a borrower, typically a corporation or government. Bonds are used by companies, municipalities, states, and governments to finance projects and operations. When you purchase a bond, you are essentially lending money to the issuer in exchange for periodic interest payments and the return of the bond's face value when it matures.
Bonds are considered safer investments than stocks because bondholders have a higher claim on the issuer's assets in the event of bankruptcy. However, they typically offer lower returns compared to equities over the long term.
Key Bond Components
- Face Value (Par Value): The amount the bondholder will receive when the bond matures. Corporate bonds typically have a face value of $1,000.
- Coupon Rate: The annual interest rate paid by the bond issuer, expressed as a percentage of face value.
- Coupon Payment: The actual dollar amount of interest paid each period (coupon rate × face value ÷ payment frequency).
- Maturity Date: The date when the bond expires and the issuer must repay the face value to the bondholder.
- Yield to Maturity (YTM): The total return anticipated if the bond is held until maturity, accounting for all coupon payments and the difference between market price and face value.
- Market Price: The current trading price of the bond, which may be above (premium) or below (discount) face value.
Bond Pricing Formula
The price of a bond is the present value of all future cash flows, discounted at the yield to maturity:
P = C × [1 - (1 + r)^(-n)] / r + F / (1 + r)^n
Where:
P = Bond Price
C = Coupon payment per period
r = Yield per period (YTM / frequency)
n = Total number of periods
F = Face value
Understanding Clean Price vs Dirty Price
When bonds trade between coupon payment dates, there are two prices to consider:
- Clean Price: The quoted market price that does not include accrued interest. This is what you'll see in bond quotes and financial publications.
- Dirty Price (Invoice Price): The actual price the buyer pays, which includes accrued interest. Dirty Price = Clean Price + Accrued Interest.
- Accrued Interest: The interest that has accumulated since the last coupon payment date. The buyer pays this to the seller because the buyer will receive the full next coupon payment.
AI = C × (Days Since Last Coupon / Days in Coupon Period)
Where C = Coupon payment per period
Day-Count Conventions
Day-count conventions determine how the number of days is calculated for accrued interest:
- 30/360: Assumes 30 days per month and 360 days per year. Common for corporate and municipal bonds.
- Actual/360: Uses actual days in the period divided by 360. Common for money market instruments.
- Actual/365: Uses actual days divided by 365. Common in the UK and some other markets.
- Actual/Actual: Uses actual days in both the numerator and denominator. Standard for U.S. Treasury bonds.
Types of Bonds
Government Bonds
Issued by national governments. U.S. Treasury bonds are considered virtually risk-free. Include T-Bills, T-Notes, and T-Bonds with various maturities.
Corporate Bonds
Issued by companies to raise capital. Higher yields than government bonds but with greater credit risk. Rated by agencies like Moody's and S&P.
Municipal Bonds
Issued by state and local governments. Interest is often exempt from federal taxes and sometimes state taxes for residents.
Zero-Coupon Bonds
Pay no periodic interest. Sold at a deep discount to face value. The return is the difference between purchase price and face value at maturity.
Convertible Bonds
Can be converted into a predetermined number of company shares. Offer lower interest rates in exchange for conversion potential.
Callable Bonds
Can be redeemed by the issuer before maturity. Usually offer higher yields to compensate for call risk.
Bond Price and Yield Relationship
Bond prices and yields move in opposite directions. When interest rates rise, existing bond prices fall, and vice versa. This inverse relationship exists because:
- When rates rise, new bonds offer higher coupons, making existing lower-coupon bonds less attractive.
- To compete, existing bonds must sell at a discount, which increases their effective yield.
- Longer-maturity bonds are more sensitive to interest rate changes (higher duration).
Bond Trading Terminology
At Par: Bond trades at face value when coupon rate equals market yield.
At Premium: Bond trades above face value when coupon rate exceeds market yield.
At Discount: Bond trades below face value when coupon rate is less than market yield.
Current Yield vs Yield to Maturity
Current Yield is simply the annual coupon payment divided by the current market price. It doesn't account for capital gains or losses if held to maturity.
Yield to Maturity (YTM) is a more comprehensive measure that considers:
- All coupon payments until maturity
- The capital gain or loss when the bond matures at face value
- The time value of money through discounting
CY = Annual Coupon / Current Price × 100%
Example: A bond with $50 annual coupon trading at $950
CY = $50 / $950 × 100% = 5.26%
Bond Investment Risks
- Interest Rate Risk: The risk that rising rates will decrease bond values.
- Credit Risk (Default Risk): The risk that the issuer cannot make interest or principal payments.
- Inflation Risk: The risk that inflation erodes the purchasing power of future payments.
- Liquidity Risk: The risk of being unable to sell the bond quickly at fair value.
- Call Risk: The risk that callable bonds may be redeemed early, typically when rates fall.
- Reinvestment Risk: The risk that coupon payments must be reinvested at lower rates.
Bond Duration and Convexity
Duration measures a bond's price sensitivity to interest rate changes. It represents the weighted average time until cash flows are received. Higher duration means greater price volatility.
Convexity measures the curvature in the relationship between bond prices and yields. It provides a more accurate estimate of price changes for larger yield movements.
Duration Rule of Thumb
A bond with duration of 5 years will change approximately 5% in price for each 1% change in interest rates. If rates rise 1%, the bond price falls roughly 5%. If rates fall 1%, the price rises roughly 5%.