1 Bodie Kane Marcus Essentials of Investments Fourth
1 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 10 Bond Prices and Yields Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
2 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Bond Characteristics • Face or par value • Coupon rate – Zero coupon bond • Compounding and payments – Accrued Interest • Indenture Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
3 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Provisions of Bonds • • • Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
4 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Default Risk and Ratings • Rating companies – Moody’s Investor Service – Standard & Poor’s – Duff and Phelps – Fitch • Rating Categories – Investment grade – Speculative grade Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
5 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Factors Used by Rating Companies • • • Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
6 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Protection Against Default • • Sinking funds Subordination of future debt Dividend restrictions Collateral Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
7 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
8 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Solving for Price: 10 -yr, 8% Coupon Bond, Face = $1, 000 20 P B = 40 S t =1 1 1 + 1000 (1+. 03) t (1+. 03) 20 PB = $1, 148. 77 Ct P T r Irwin / Mc. Graw-Hill = 40 (SA) = 1000 = 20 periods = 3% (SA) © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
9 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Bond 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
10 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Prices and Coupon Rates Price Yield Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
11 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
12 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
13 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Yield Curves Yields Upward Sloping Downward Sloping Maturity Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
14 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Theories of Term Structure • Expectations • Liquidity Preference – Upward bias over expectations • Market Segmentation – Preferred Habitat Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
15 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Chapter 11 Managing Fixed. Income Investments Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
16 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
17 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
18 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
19 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
20 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Duration: Calculation Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
21 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Duration Calculation Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
22 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
23 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
24 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Pricing Error from Convexity Price Pricing Error from Convexity Duration Yield Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
25 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Correction for Convexity Modify the pricing equation: Convexity is Equal to: Where: CFt is the cashflow (interest and/or principal) at time t. Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
26 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Active Bond Management: Swapping Strategies • • • Substitution swap Intermarket swap Rate anticipation swap Pure yield pickup Tax swap Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.
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