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Understanding Bond Characteristics and Pricing Relationships

Explore bond face values, coupon rates, and pricing based on yields to maturity. Learn about bond ratings and how duration affects bond prices.

malcolm-durham
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Understanding Bond Characteristics and Pricing Relationships

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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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