Bond Valuation and Risk

Core Concept: Bonds represent a loan made by an investor to a borrower (typically a corporation or government). Understanding how to value bonds and assess their associated risks is crucial for fixed-income investing.

1. Present Value of a Bond

• Definition: The present value (PV) of a bond is the sum of the present values of all future cash flows the bond is expected to generate. These cash flows consist of:

  • Coupon Payments (C): Periodic interest payments made by the issuer.
  • Face Value (F): The principal amount repaid to the bondholder at maturity.

• Formula:

  P = Σ [C / (1 + r)^t] + [F / (1 + r)^n]

  • Where:
    • P = Present value (Price of the bond)
    • C = Coupon payment per period
    • r = Required rate of return (discount rate) per period
    • F = Face value (principal repaid at maturity)
    • n = Number of periods to maturity
    • t = Time period (1, 2, 3, ..., n)
    • Σ = Summation from t=1 to n

• Explanation: The formula discounts each future cash flow back to its present value using the required rate of return (r). The sum of these present values is the bond's price.

• Example:

  • Face value (F): ₹1,000
  • Annual coupon rate: 8% (Coupon payment C = ₹80 per year)
  • Maturity: 5 years (n = 5)
  • Required rate of return (r): 10%
  • Using the formula, the bond's price (P) is approximately ₹924.18.

• Relationship Between Price and Required Rate of Return:

  • There's an inverse relationship. If the required rate of return increases, the bond's price decreases, and vice-versa.

• Bond Pricing Terminology:

  • Discount Bond: When a bond's price is less than its face value (P < F). This occurs when the required rate of return is higher than the coupon rate.
  • Premium Bond: When a bond's price is greater than its face value (P > F). This occurs when the required rate of return is lower than the coupon rate.
  • Par Value Bond: When a bond's price is equal to its face value (P = F). This occurs when the required rate of return is equal to the coupon rate.

2. Yield to Maturity (YTM) - The Bond's Expected Return

• Definition: Yield to Maturity (YTM) is the total return an investor can expect to receive if they hold the bond until maturity. It's the discount rate that equates the present value of the bond's future cash flows to its current market price.

• Approximate Formula:

  YTM ≈ [C + (F - P) / n] / [(F + P) / 2]

  • Where:
    • C = Coupon payment
    • P = Current market price of the bond
    • F = Face value
    • n = Years to maturity

• Example:

  • Face value (F): ₹1,000
  • Current price (P): ₹950
  • Coupon rate: 8% (C = ₹80 per year)
  • Years to maturity (n): 5
  • YTM ≈ [80 + (1000 - 950) / 5] / [(1000 + 950) / 2] ≈ 8.86%

• Relationship between YTM, Coupon Rate, and Bond Price:

  • YTM > Coupon Rate: The bond is trading at a discount.
  • YTM < Coupon Rate: The bond is trading at a premium.
  • YTM = Coupon Rate: The bond is trading at par.

3. Yield to Call (YTC) & Yield to Put (YTP)

• Callable Bonds: These bonds give the issuer the right to redeem the bond before its maturity date, typically at a specified call price.

  • Yield to Call (YTC): The expected return if the bond is held until the call date.

    • Approximate Formula:

      YTC ≈ [C + (Call Price - P) / n] / [(Call Price + P) / 2]

      • Where:
        • Call Price = Price at which the issuer buys back the bond early
        • P = Current Market Price
        • n = Years to Call

    • Importance: YTC is relevant when a bond is trading at a premium and is likely to be called.

• Putable Bonds: These bonds give the investor the right to sell the bond back to the issuer at a predetermined put price on a specified put date.

  • Yield to Put (YTP): The expected return if the bond is held until the put date and then put back to the issuer.

    • Approximate Formula:

      YTP ≈ [C + (Put Price - P) / n] / [(Put Price + P) / 2]

      • Where:
        • Put Price = Price at which the investor can sell the bond back
        • P = Current Market Price
        • n = Years to Put

    • Importance: Useful for evaluating putable bonds, especially when interest rates are rising.

4. Risks in Bonds

• (a) Systematic Risk: Risks that affect all bonds in the market and cannot be diversified away.
  • Inflation Risk: The risk that inflation will erode the purchasing power of the bond's future cash flows.
  • Interest Rate Risk: The risk that changes in interest rates will negatively impact bond prices.
  • Economic Risk: Economic recessions or slowdowns can lead to lower corporate profits and increased default risk.
• (b) Price Risk (Market Risk): The risk that bond prices will decline due to changes in market interest rates.
  • Bond prices and interest rates have an inverse relationship.
• (c) Interest Rate Risk: The risk that changes in interest rates will have a greater impact on long-term bonds than on short-term bonds.
  • Duration: A measure of a bond's sensitivity to interest rate changes. Higher duration means greater sensitivity.
• (d) Default Risk (Credit Risk): The risk that the issuer will be unable to make interest or principal payments.
  • Credit Ratings: Credit rating agencies (e.g., Moody's, S&P, Fitch) assess the creditworthiness of bond issuers. Higher ratings indicate lower default risk.
  • Government bonds typically have low default risk, while corporate bonds (especially "junk bonds") have higher default risk.

Key Takeaways

• Bond value is derived from the present value of future cash flows (coupon payments and face value).
• YTM represents the expected return if held to maturity. YTC and YTP are relevant for callable and putable bonds, respectively.
• Bonds are subject to various risks, including systematic risk, price risk, interest rate risk, and default risk. Understanding these risks is critical for bond investors.