1. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 10 Bond Prices and Yields

2. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 2 Bond Characteristics Face or par value Coupon rate –Zero coupon bond Compounding and payments –Accrued Interest Indenture

3. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 Provisions of Bonds Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds

4. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 Factors Used by Rating Companies Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt

6. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 Protection Against Default Sinking funds Subordination of future debt Dividend restrictions Collateral

7. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 Bond Pricing P B =Price of the bond C t = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity

8. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 C t = 40 (SA) P= 1000 T= 20 periods r= 3% (SA) P B = $1,148.77 Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 t=1 + 20= P B 40 1 ) ( 1+.03) t 1000 1 ( 1+.03 ) 20

9. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 Prices and Coupon Rates Price Yield

11. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 Yield Curves Yields Maturity Upward Sloping Downward Sloping

14. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 Theories of Term Structure Expectations Liquidity Preference –Upward bias over expectations Market Segmentation –Preferred Habitat

15. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Chapter 11 Managing Fixed- Income Investments

16. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 Duration: Calculation

21. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 21 Duration Calculation

22. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 22 Duration/Price Relationship Price change is proportional to duration and not to maturity  P/P = -D x [  (1+y) / (1+y) D * = modified duration D * = D / (1+y)  P/P = - D * x  y

23. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 24 Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity

25. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 25 Correction for Convexity Modify the pricing equation: Convexity is Equal to: Where: CF t is the cashflow (interest and/or principal) at time t.

26. Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 26 Active Bond Management: Swapping Strategies Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap