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Chapter 14

Chapter 14. Bond Prices and Yields. Provisions of Bonds. Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds. Bond Pricing. P B = Price of the bond C t = interest or coupon payments

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Chapter 14

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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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