Lesson Objective: To master the mechanics of bond pricing, including the calculation of present value, yield to maturity (YTM), current yield, and the critical relationship between bond prices and interest rates.

In-Depth Notes:

1. The Fundamental Principle of Bond Pricing:
The price of a bond is the present value of its future cash flows (coupon payments and principal repayment) discounted at the required rate of return (the yield) . This principle applies to all bonds, regardless of coupon structure, maturity, or credit quality.

2. The Discounted Cash Flow (DCF) Model for Bonds:
The general formula for the price of a bond is:

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Bond Price = Σ [Coupon / (1 + YTM)^t] + [Face Value / (1 + YTM)^n]

Where:

  • Coupon is the periodic interest payment.

  • YTM is the yield to maturity (the required rate of return).

  • t is the time period (1 to n, where n is the number of periods to maturity).

  • Face Value is the principal amount to be repaid at maturity.

3. Key Yield Measures:

  • Yield to Maturity (YTM): The most comprehensive measure of a bond’s return. YTM is the internal rate of return (IRR) of the bond’s cash flows, assuming the bond is held to maturity and all coupon payments are reinvested at the YTM rate. YTM is the discount rate that equates the present value of the bond’s cash flows to its current market price.

  • Current Yield: The annual coupon divided by the current market price. Current yield is a simple measure of income return but does not consider capital gains or losses at maturity.

  • Coupon Rate: The annual interest rate stated on the bond, expressed as a percentage of the face value.

  • Yield to Call (YTC): For callable bonds, YTC is the yield assuming the bond is called at the earliest call date.

  • Yield to Worst (YTW): The lower of YTM and YTC. This is a conservative measure of a bond’s potential return.

4. The Relationship Between Bond Prices and Yields:

  • Inverse Relationship: Bond prices and yields move inversely . When market interest rates rise, the required rate of return (YTM) increases, reducing the present value of the bond’s cash flows and lowering its price. Conversely, when interest rates fall, bond prices rise.

  • Premium, Par, and Discount Bonds:

    • Premium Bond: A bond trading above its face value (price > par). This occurs when the coupon rate exceeds the current market yield. Investors are willing to pay a premium for a higher coupon.

    • Par Bond: A bond trading at its face value (price = par). This occurs when the coupon rate equals the market yield.

    • Discount Bond: A bond trading below its face value (price < par). This occurs when the coupon rate is below the current market yield.

5. Accrued Interest and Clean vs. Dirty Price:

  • Accrued Interest: When a bond is bought between coupon payment dates, the buyer must compensate the seller for the interest that has accrued since the last coupon payment. Accrued interest is calculated as: Accrued Interest = (Coupon / 2) x (Days Since Last Coupon / Days in Coupon Period).

  • Clean Price vs. Dirty Price:

    • Clean Price: The quoted price of a bond, which excludes accrued interest. The clean price is the price that is typically quoted in the financial press and on trading platforms.

    • Dirty Price: The actual price paid for the bond, which includes accrued interest. The dirty price is the clean price plus accrued interest.

6. Day Count Conventions:
Different markets use different conventions to calculate interest accruals:

  • 30/360 (US Corporate and Municipal Bonds): Assumes each month has 30 days and the year has 360 days. This is a standard convention for US corporate and municipal bonds.

  • Actual/Actual (US Treasuries): Uses the actual number of days elapsed and the actual number of days in the year (365 or 366). This is the standard for US Treasury bonds and is also used for many European government bonds.

  • Actual/365 (Eurobonds and UK Gilts): Uses the actual number of days elapsed divided by 365 (or 366 for leap years). This is the standard for Eurobonds and UK Gilts.

7. Bond Pricing in Practice:
In practice, bond pricing involves using specialized financial calculators or spreadsheet functions (e.g., Excel’s PRICE, YIELD, and DURATION functions). The pricing model must consider the specific features of the bond (coupon, maturity, frequency of coupon payments, day count convention, and any embedded options).

 
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