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Chapter 10

Chapter 10. Bond Prices and Yields. Bond Characteristics. Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest Indenture. Provisions of Bonds. Secured or unsecured Call provision Convertible provision Put provision (putable bonds)

malcolm-durham
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Chapter 10

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  1. Chapter10 Bond Prices and Yields

  2. Bond Characteristics • Face or par value • Coupon rate • Zero coupon bond • Compounding and payments • Accrued Interest • Indenture

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

  4. Default Risk and Ratings • Rating companies • Moody’s Investor Service • Standard & Poor’s • Duff and Phelps • Fitch • Rating Categories • Investment grade • Speculative grade

  5. Factors Used by Rating Companies • Coverage ratios • Leverage ratios • Liquidity ratios • Profitability ratios • Cash flow to debt

  6. Protection Against Default • Sinking funds • Subordination of future debt • Dividend restrictions • Collateral

  7. 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

  8. 20 S 1 1 = + P 40 1000 B t 20 (1+.03) (1+.03) t =1 Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 PB = $1,148.77 Ct = 40 (SA) P = 1000 T = 20 periods r = 3% (SA)

  9. 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

  10. Prices and Coupon Rates Price Yield

  11. Approximate Yield to Maturity YTM = (Avg. Income) / (Avg. Price) Avg. Income = Int. +(Par-Price) / Yrs to maturity Avg. Price = (Price + Par) / 2 Using the earlier example Avg. Income = 80 + (1000-1149)/10 = 65.10 Avg. Price = (1000 + 1149)/2 = 1074.50 Approx. YTM = 65.10/1074.50 = .0606 or 6.06% Actual YTM = 6.00%

  12. Term Structure of Interest Rates • Relationship between yields to maturity and maturity • Yield curve - a graph of the yields on bonds relative to the number of years to maturity • Usually Treasury Bonds • Have to be similar risk or other factors would be influencing yields

  13. Yield Curves Yields Upward Sloping Downward Sloping Maturity

  14. Theories of Term Structure • Expectations • Liquidity Preference • Upward bias over expectations • Market Segmentation • Preferred Habitat

  15. Chapter11 Managing Fixed-Income Investments

  16. Managing Fixed Income Securities: Basic Strategies • Active strategy • Trade on interest rate predictions • Trade on market inefficiencies • Passive strategy • Control risk • Balance risk and return

  17. Bond Pricing Relationships • Inverse relationship between price and yield • An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield • Long-term bonds tend to be more price sensitive than short-term bonds

  18. Bond Pricing Relationships (cont.) • As maturity increases, price sensitivity increases at a decreasing rate • Price sensitivity is inversely related to a bond’s coupon rate • Price sensitivity is inversely related to the yield to maturity at which the bond is selling

  19. 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

  20. Duration: Calculation

  21. Duration Calculation

  22. 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

  23. 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

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

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

  26. Active Bond Management: Swapping Strategies • Substitution swap • Intermarket swap • Rate anticipation swap • Pure yield pickup • Tax swap

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