Chapter 14 Bond Prices and Yields

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Provisions of Bonds Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Prices and Coupon Rates Price Yield

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 * *.6 = 4.87%. Return for B,.96 * *.6 = 6.24%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration: Calculation

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Duration Calculation

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Pricing Error from Convexity Price Yield Duration Pricing Error from Convexity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Correction for Convexity Modify the pricing equation: Convexity is Equal to: Where: CF t is the cashflow (interest and/or principal) at time t.