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Comprehensive Guide to Bond Pricing and Yields Analysis

Understand bond pricing methods, yield provisions, and types of bonds. Calculate prices, yields, and durations for various bond scenarios. Learn about premium, discount, and convertible bonds, and how to calculate pricing errors.

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Comprehensive Guide to Bond Pricing and Yields Analysis

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  1. Chapter 14 Bond Prices and Yields

  2. Provisions of Bonds • Secured or unsecured • Call provision • Convertible provision • Put provision (putable bonds) • Floating rate bonds • Sinking funds

  3. Bond Pricing PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity

  4. Price of 8%, 10-yr. with yield at 6% Coupon = 4%*1,000 = 40 (Semiannual) Discount Rate = 3% (Semiannual Maturity = 10 years or 20 periods Par Value = 1,000

  5. Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship • When yields get very high the value of the bond will be very low • When yields approach zero, the value of the bond approaches the sum of the cash flows

  6. Prices and Coupon Rates Price Yield

  7. Alternative Measures of Yield • Current Yield • Yield to Call • Call price replaces par • Call date replaces maturity • Holding Period Yield • Considers actual reinvestment of coupons • Considers any change in price if the bond is held less than its maturity

  8. Premium and Discount Bonds • Premium Bond • Coupon rate exceeds yield to maturity • Bond price will decline to par over its maturity • Discount Bond • Yield to maturity exceeds coupon rate • Bond price will increase to par over its maturity

  9. Types of Bonds • High Yield vs Investment grades • Example • AAA 5% with .2% historical default • B, 9% with 4% historical default rate • 40% recovery rate on defaults • Return = (1 – default rate) * interest rate – default rate * (1-recovery rate) • Return for A, .998 * .05 - .002*.6 = 4.87%. • Return for B, .96 * .09 - .04 * .6 = 6.24%

  10. Duration • A measure of the effective maturity of a bond • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment • Duration is shorter than maturity for all bonds except zero coupon bonds • Duration is equal to maturity for zero coupon bonds

  11. Duration: Calculation

  12. Duration Calculation

  13. Uses of Duration • Summary measure of length or effective maturity for a portfolio • Immunization of interest rate risk (passive management) • Net worth immunization • Target date immunization • Measure of price sensitivity for changes in interest rate

  14. Duration/Price Relationship Price change is proportional to duration and not to maturity DP/P = -D x [D(1+y) / (1+y) D* = modified duration D* = D / (1+y) DP/P = - D* x Dy

  15. Pricing Error from Convexity Price Pricing Error from Convexity Duration Yield

  16. Correction for Convexity Modify the pricing equation: Convexity is Equal to: Where: CFt is the cashflow (interest and/or principal) at time t.

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